Rock Properties Model (RPM3.1) Rev 00, ICN 01

MDL-NBS-GS-000004

January, 2000

 
1. PURPOSE 
The purpose of this Analysis and Model Report (AMR) is to document Rock Properties Model 
(RPM) 3.1 with regard to input data, model methods, assumptions, uncertainties and limitations 
of model results, and qualification status of the model. The report also documents the differences 
between the current and previous versions and validation of the model. 
The rock properties models are intended principally for use as input to numerical physicalprocess 
modeling, such as of ground-water flow and/or radionuclide transport. The constraints, 
caveats, and limitations associated with this model are discussed in the appropriate text sections 
that follow. 
This work was conducted in accordance with the following planning documents: WA-0344, 
3-D Rock Properties Modeling for FY 1998 (SNL 1997), WA-0358, 3-D Rock Properties 
Modeling for FY 1999 (SNL 1999), and RPM3.1, (CRWMS M&O 1999c). These work plans 
describe the scope, objectives, tasks, methodology, and implementing procedures for model 
construction. The constraints, caveats, and limitations associated with this model are discussed in 
the appropriate text sections that follow. 
The work scope for this activity consists of the following: 
1. Conversion of the input data (laboratory measured porosity data, x-ray diffraction 
mineralogy, petrophysical calculations of bound water, and petrophysical calculations of 
porosity) for each borehole into stratigraphic coordinates 
2. Re-sampling and merging of data sets 
3. Development of geostatistical simulations of porosity 
4. Generation of derivative property models via linear coregionalization with porosity 
5. Post-processing of the simulated models to impart desired secondary geologic attributes 
and to create summary and uncertainty models 
6. Conversion of the models into real-world coordinates. 
The conversion to real world coordinates is performed as part of the integration of the RPM into 
the Integrated Site Model (ISM) 3.1; this activity is not part of the current analysis. The ISM 
provides a consistent volumetric portrayal of the rock layers, rock properties, and mineralogy of 
the Yucca Mountain site and consists of three components: 
 Geologic Framework Model 
 RPM, which is the subject of this AMR 
 Mineralogic Model. 
The interrelationship of the three components of the ISM and their interface with downstream 
uses are illustrated in Figure 1. Figure 2 shows the geographic boundaries of the RPM and other 
component models of the ISM. 

Figure 1. Interrelationships Between Component Models, Integrated Site Model, and Downstream Uses 
Title: Rock Properties Model (RPM3.1) 
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Hydrologic Flow and 
Radionuclide Transport Models 
Through Saturated Zone (SZ) 
Rock Properties Model 
(RPM) 
Total System 
Performance Assessment 
Geologic Framework Model 
(GFM) 
Mineralogic Model 
(MM) 
Repository Design 
Hydrologic Flow and 
Radionuclide Transport Models 
Through Unsaturated Zone (UZ) 
INTEGRATED SITE MODEL

Figure 2. Index map showing the location of the Geologic Framework Model, the Rock Properties 
Model (this report), and the Mineralogic Model. 
Contour Interval 200 Feet 
Boundary of Rock Properties Model 
Boundary of Geologic Framework 
Model and Mineralogic Model 
Exploratory 
Studies Facility 
Cross-Block 
Drift 
Yucca Crest 
Tonsil Ridge 
Drill Hole 
NEVADA 
TEST 
SITE 
STATE 
OF 
NEVADA 
YUCCA 
MOUNTAIN 
SITE 
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2. QUALITY ASSURANCE 
The modeling effort was evaluated in accordance with QAP-2-0, Conduct of Activities, and 
was determined to be quality affecting and subject to the requirements of the Quality Assurance 
Requirements and Description (DOE 1998). This evaluation is documented in Activity 
Evaluation of M&O Site Investigations (Q) (CRWMS M&O 1999a, 1999b). Accordingly, all 
efforts to construct the rock properties models have been conducted in accordance with approved 
quality assurance procedures. All work was performed in accordance with the Quality Assurance 
Requirements and Description under the auspices of the Civilian Radioactive Waste 
Management System Management and Operating contractors quality assurance program. 
Modeling work was performed in accordance with QAP-SIII-3, Scientific Notebooks. Prior to 
the effective date of QAP-SIII-3, AP-3.10Q, and AP-SIII.2Q, modeling work was performed in 
accordance with Sandia National Laboratories QAIP 20-2, Scientific Notebooks. The 
procedures that currently pertain to the rock properties modeling effort are listed in CRWMS 
M&O (1999c). This Analysis and Model Report was developed in accordance with AP-3.10Q, 
Analyses and Models. 

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3. COMPUTER SOFTWARE AND MODEL USAGE 
3.1 SOFTWARE TRACKED BY CONFIGURATION MANAGEMENT 
The Rock Properties Model was constructed principally using geostatistical algorithms that are 
part of the public-domain GSLIB geostatistical subroutine library (Deutsch and Journel 1992, 
1998). The major modeling codes subject to configuration management are listed below in 
Table 1, together with a brief description of their functionality. These computer software 
packages were obtained from configuration management and are judged appropriate for use in 
this type of modeling activity. The software was used within the range of calibration (to the 
extent that this statement applies to these codes). All codes listed in Table 1 run on Intel-type 
personal computers under the Microsoft Windows NT Version 4.0 operating system, except 
EARTHVISION, which is a Unix-based software product operating on a Silicon Graphics Octane 
workstation under IRIX Version 6.4 operating system. 
A number of additional software routines have been developed as part of the rock properties 
modeling process. These routines are listed in Table 2 and they are documented for quality 
assurance purposes in the scientific notebooks associated with this activity (Table 11); the use of 
scientific notebooks is explained in Section 6.3.2. Exceptions to this practice are included as 
attachments to this report (noted in tables that follow). With the exception of STRATC4 (which is a 
macro-type software routine), all software routines listed in Table 2 run as Microsoft Fortran 
Table 1. Software Tracked by Configuration Management 
Code Name Version 
STN 
Number 
Brief Description 
GSLIB V1.4 
SGSIM 
1.4 
10110- 
1.4MSGSI 
MV1.40-00 
Generates conditional or unconditional gaussian simulations of a 
continuous variable; optional normal-score forward and back 
transformation (from the software library, GSLIB) 
GSLIB V2.0 
IK3D 
2.0 
10122- 
2.0MIK3D 
V2.0-00 
Conducts indicator kriging of continuous or discrete variables using 
either hard or soft data or both (from the software library, GSLIB) 
GSLIB V1.4 
NSCORE 
1.201 
10109- 
1.4MNSC 
OREV1.20 
1-01 
Transforms a distribution of values to standard-normal form while 
preserving quantile relationships (from the software library, GSLIB) 
EARTHVISION 4.0 
30035 
V4.0 
3-D earth science modeling package; used only to produce 
visualizations (report figures; e.g., Figure 38) of the Integrated Site 
Model 3.0/Rock Properties Model 3.0 for this report 
MATCHUP 12/5/98 
10196- 
12598-00 
Software routine that creates a single file of depth-matched values 
from two columnar input files 
MATCH 12/5/98 
10195- 
12598-00 
Modification of software routine MATCHUP for one GSLIB format file

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PowerStation Version 4.0 and have been compiled and executed on Intel-type personal 
computers under the Microsoft Windows NT Version 4.0 operating system. 
Table 2. Software Routines 
Routine 
Name 
Version/ 
Date1 Reference Brief Description 
Acquired Software 
TRANS 1.3 Attachment III 
Transforms an input distribution to match the histogram of a target 
distribution (both in GSLIB format) while preserving the quantile 
relationships (from the software library, GSLIB) 
BICALIB 2.0 
Rautman and 
McKenna 1998, 
p. 1143 
Calibrates soft data (GSLIB format) for use as prior cdf values from 
matched hard-soft data pairs (from the software library, GSLIB) 
BACKTR 1.2 
Rautman and 
McKenna 1998, 
p. 1127 
Transforms a standard-normal distribution (GSLIB format) to match a 
reference histogram (from the software library, GSLIB; inverse of 
program NSCORE [Table 1]) 
Developed Software 
BUD 6/25/98 
Rautman and 
McKenna 1998, 
p. 1013 
Reads a log-analysis standard .las file and extracts specified well log 
traces 
TWOFOOT 6/25/98 
Rautman and 
McKenna 1998, 
p. 1020 
Reads an ascii file of well log data and resamples it on a 
user-specified spacing, averaging values over two-foot intervals 
COREGPC 5/22/99 
Rautman 1999 
p. 307 
Post-processes a porosity simulation (GSLIB format) in standardnormal 
format and an unconditional simulation with the same spatial 
correlation structure, and generates a coregionalized simulation of a 
secondary property given a correlation coefficient between the two 
variables 
ETYPE 6/30/98 
Rautman and 
McKenna 1998, 
p. 1134 
Reads a set of simulation output (GSLIB format) files and creates 
summary E-type model; optional uncertainty output as standard 
deviation of simulations 
ZEOLITE5 9/10/98 
Rautman and 
McKenna 1998, 
p. 1266 
Post-processes a set of simulated Ks values (GSLIB format) together 
with an indicator model of zeolite alteration that is used as a 
template to insert random gaussian Ks values at altered grid notes; 
appropriate only for altered units 
VITROPHY 
RE 
9/10/98 
Rautman and 
McKenna 1998, 
p. 1274 
Post-processes a set of simulated Ks values (GSLIB format) together 
with the corresponding porosity simulation and substitutes uniform 
random Ks values at grid nodes where the simulated porosity value is 
less than 0.05; appropriate only for TSw model unit. 
COORDS 12/17/98 
Rautman and 
McKenna 1998, 
p. 1287 
Adds Nevada state plane (x,y,z) coordinates to a GSLIB-format output 
file given a grid specification and a corresponding structure contour 
file of top elevations and thicknesses 
STRATC4 4 Attachment II 
Computes unit-specific stratigraphic coordinates using Equation 2 
from Section 6.4.3.2 using a SIGMA PLOT transform (macro). 
Notes: 1. Formal version numbers were not used for software routines under SNL QAIP 19-1; instead, the Date is shown 
that the documentation associated with the routine was entered into the referenced scientific notebook.

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3.2 EXEMPT SOFTWARE 
Various nonqualified software products were also used during the course of this modeling 
activity to assist in organizing, managing, manipulating, comparing, and displaying data and 
information and computing standard statistical measures. This includes commercial off-the-shelf 
software and other industry-standard software. These software packages are used to perform 
support activities and are not used as the controlled source of information for the analysis, as 
defined in AP-SI.1Q. They are therefore not required to be qualified under these procedures. 
EXCEL95 and/or EXCEL97 were used to compile and organize rock properties measurements by 
drill hole and depth, and later by modeling unit prior to writing the final ASCII text files used as 
input to the modeling algorithms. Standard cell-based arithmetic operations of Excel were used 
on a temporary basis to check for and identify duplicate sample data (by depth), but the results of 
these calculations did not change any measurement values, and the columns involved were 
deleted prior to writing the final ASCII text input files. Standard cell-based arithmetic operations 
were also used to construct two new variables in selected data files related to hydrous-phase 
mineral alteration. One variable represents the total hydrous mineral phase content, and was 
constructed simply as the sum of the four relevant mineral fractions described in Section 6.4.3.1. 
The other variable is an indicator variable constructed using the logic of Equation 1, also 
described in Section 6.4.3.1. These computations are immediately verifiable by visual 
inspection. Cell-based arithmetic was also used to adjust the core bound-water contents for parity 
with the petrophysically based bound-water contents, as described in Section 6.4.7.1. This 
computation also is immediately verifiable by visual inspection. 
SIGMA PLOT, versions 2.0 and 5.0, was used to compile and organize rock properties 
measurements and to generate graphic displays of drill hole data for sanity checking that the 
selection and organization of the drill hole data was conducted properly. SIGMA PLOT arithmetic 
spreadsheet operations were also used to create the bound-water content variable described in 
Sections 6.4.3.1 and 6.4.7.1 as the simple difference between two original variables. This 
calculation is immediately verifiable by visual inspection. SIGMA PLOT was also used to generate 
various statistical measures, including histograms, cumulative distribution functions, crossplots, 
and linear regressions of selected data sets. 
EVS, version 3.75, was used to generate selected graphic visualizations (report figures, including 
block diagrams and cross-sectional views: e.g., Figures 38 [top half] and 39) of the completed 
rock properties models in stratigraphic coordinates only. The geostatistical and other modeling 
capabilities of EVS were not used for this analysis. 
VARIO, versions 1.16 and 1.20, from the geostatistical package UNCERT, was used to compute 
standard three-dimensional experimental variograms using the input data files. Proper operation 
of this software was verified by visual inspection of the results and by a simple manual 
verification documented in Attachment IV. 
VARIOFIT, version 1.20, from the geostatistical package, UNCERT, was used to fit standard 
variogram models to the experimental variograms produced with VARIO. Proper operation of this

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software was verified by visual inspection of the results and by a simple manual verification 
documented in Attachment V. 
HISTPLT, version 1.2, from the geostatistical software library GSLIB (Deutsch and Journel 1992), 
was used to generate histograms and summary statistics for various data sets, including sanity 
checks of completed simulations and other models. Proper operation of this software was 
verified by visual inspection of the results and by comparison of results with similar values 
produced by other software (especially SIGMA PLOT, above). 
GAM3, version 1.2, from the geostatistical software library GSLIB (Deutsch and Journel 1992), was 
used to generate exhaustive three-dimensional variogram data for plotting as a sanity check of 
completed simulations and other models. Proper operation of this software was verified by visual 
inspection of the results.

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4. INPUTS 
4.1 DATA AND PARAMETERS 
There are seven different classes of data used as input to rock properties modeling. Four of these 
categories (Sections 4.1.1 through 4.1.4) involve actual measurements of rock material properties, 
either in the laboratory or by calculation from geophysical measurements obtained in the field. A 
fifth class of property (Section 4.1.5) is also derived from in-situ geophysical measurements; it is 
sufficiently different in nature and used for a different purpose, therefore it is discussed 
separately. The remaining two classes of input data (Sections 4.1.6 and 4.1.7) consist of the 
stratigraphic contacts bounding the four rock properties modeling units. The sixth class consists 
of actually observed (measured) contacts. The seventh class involves interpreted or modeled 
contacts, used in cases where a given drill hole did not go deep enough to penetrate a unit 
completely. These seven types of data are described in the paragraphs that follow. Data tracking 
numbers (DTNs) associated with each type of data are provided in tables in the relevant section. 
The qualification (To Be Verified (TBV)) status of these data sources is provided in Attachment I, 
Document Information Reference System (DIRS). 
4.1.1 Laboratory Core Porosity Data 
Laboratory measurements of porosity (measurement process described by Flint 1998, 
pp. 11 to 17) have been obtained for core samples taken from boreholes within both the potential 
repository block and immediately adjoining areas. DTNs associated with the laboratorymeasured 
core porosity values used in the Rock Properties Model are presented in Table 3. 
Flint (1998, pp. 11 to 17, Table 3) reports two porosity values for each sample: one obtained after 
drying the sample in a relative humidity (RH) oven at elevated humidity levels (60C and 
65 percent RH), and the other after drying in a 105C oven (oven-dried) and ambient, but very 
low RH. The distinction is important, as Flint (1998, pp. 17 and 32 to 33, Figure 12) has 
demonstrated that matrix saturated hydraulic conductivity is better correlated with the RH 
porosity values. Because part of the intent of this rock properties modeling exercise is to model 
spatial variability in the hydraulic conductivity of the site, the RH core porosity values were used 
exclusively as input to the geostatistical modeling of porosity. 
Table 3. Source of Input Laboratory Core Porosity 
Data 
Data Source Description Reference 
RH core porosity data DTN: MO9911INPUTRPM.000 
RH porosity, SD-6 DTN: GS980808312242.014 
RH porosity, WT-24 DTN: GS980708312242.010

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4.1.2 Calculated Petrophysical Porosity Data 
Borehole petrophysical logs have been converted to quantitative estimates of porosity by 
CRWMS M&O (1999d, pp. 5-1 to 5-2). These data provide substantial information regarding 
spatial heterogeneity across the entire site area (Figure 2), particularly for regions remote from 
the potential repository block for which no core samples exist. Use of data from these regions 
outside the immediate rock properties model boundaries is important in identifying long-range 
spatial correlation patterns that reduce uncertainty within the modeled area. The DTN associated 
with the calculated petrophysical porosity data is presented in Table 4. 
CRWMS M&O (1999d, p. 5-1) generated two different porosity values using petrophysics. 
These values are identified in his files as POREF, which corresponds approximately to the RH 
laboratory core measurements, and POROTOT, corresponding approximately to the 105C ovendried 
samples. Using the same logic that influenced the choice of the RH laboratory core 
measurements, POREF values have been used exclusively as input to porosity modeling for 
Integrated Site Model 3.0. The data files in Table 4 also include a calculated petrophysical value, 
VWC, representing the volumetric water content, derived from neutron logging (CRWMS M&O 
1999d, p. 5-2). Values of VWC have been substituted for POREF in certain geologic intervals and 
under certain circumstances that are described in Section 6. 
4.1.3 Laboratory Measured Secondary Property Data 
A second class of laboratory measurements performed on core samples consists of secondary 
material properties that generally are of greater interest in design or performance assessment 
modeling than simple porosity (completed models are referred to in Section 6 as derivative 
properties). Laboratory values of bulk density, matrix saturated hydraulic conductivity (Ks) 
(Flint 1998, pp. 11 to 17), thermal conductivity, and additional measurements of porosity 
(specifically those correlated with the secondary properties) were also measured for selected 
samples, in addition to the primary porosity data of Section 4.1.1. This measurement of 
multiple properties on the same physical specimen allows identification of statistically valid 
cross-variable correlations. Such correlations thus permit modeling the spatial variability of 
these secondary or derivative properties in regions where no actual measurements of these 
properties exist. DTNs associated with the secondary laboratory property data are presented in 
Table 5. 
4.1.4 X-Ray Diffraction Indicators of Mineral Alteration 
The identification and modeling of hydrous-phase mineral alteration (see Section 6.2.4) as it 
affects matrix Ks is complicated by a general scarcity of both mineralogic and hydraulic 
conductivity data across the entire Yucca Mountain site area. As described in more detail 
Table 4. Source of Input Petrophysical Porosity Data 
Data Source Description Reference 
POREF, VWC DTN: MO9910POROCALC.000

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(Section 6.2.4), the approach is to use both direct (x-ray diffraction analyses [XRD]) and indirect 
(petrophysical data) in combination to model this type of alteration. Quantitative XRD 
mineralogic data (as mineral fractions of several zeolite minerals and smectite clays) are used as 
input to the alteration modeling portion of the rock properties modeling effort. The mineralogic 
data are both converted to hard (certain) indicators of mineral alteration and used to calibrate 
petrophysical data (Section 4.1.5 below) as soft (uncertain) indicators. Generation of both types of 
indicators is described in Section 6.4.7. The DTN associated with the XRD mineralogic analyses 
is presented in Table 6. 
4.1.5 Petrophysical Indicators of Hydrous-Phase Mineral Alteration 
The use of both direct and indirect indicators to model hydrous-phase mineral alteration as it 
affects the magnitude and spatial distribution of matrix Ks was noted in Section 4.1.4 above. 
Petrophysically derived data, specifically the POROTOT and POREF calculated porosity values 
described in Section 4.1.2, are used to generate soft indicators of mineral alteration. The DTN 
associated with the petrophysical porosity data used to create the petrophysical indicators of 
hydrous-phase mineral alteration is presented in Table 7. The mechanics of generating and 
calibrating those indicators is presented in Section 6.4.7. 
4.1.6 Observed (Measured) Lithostratigraphic Contacts 
Rock properties modeling has been conducted within stratigraphic coordinates, which represent 
the relative vertical position of each measured property value within a model unit. This 
stratigraphic coordinate conversion requires depth values for both the upper and lower contact of 
each aggregate model unit in each borehole, as described in Section 6.3.2. Typically, the required 
depth values were physically observed, either in core, in geophysical logs, or in downhole video 
Table 5. Source of Input Secondary Property Data 
Data Source Description Reference 
Porosity, bulk density, Ks data DTN: MO9911INPUTRPM.000 
Porosity, thermal conductivity samples DTN: SNL01A050593001.007 
Thermal conductivity, NRG- holes DTN: SNL01A05059301.005 
Table 6. Source of Input X-ray Diffraction Mineralogy Data 
Data Source Description Reference 
Zeolite mineral contents DTN: LA9910DB831321.001 
Table 7. Source of Input Petrophysical Data Used for 
Identification of Mineral Alteration 
Data Source Description Reference 
POREF, POROTOT, VWC DTN: MO9910POROCALC.000

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records. DTNs associated with the observed lithostratigraphic contact data are presented in 
Table 8. 
4.1.7 Modeled Lithostratigraphic Contacts 
The vast majority of model-unit contacts required for the stratigraphic coordinate conversion are 
taken directly from a tabulation of observed contacts (Table 8). However, a small number of 
contacts were projected using Geologic Framework Model (GFM) 3.0 or GFM3.1 because the 
drill hole did not fully penetrate the model unit. This situation most frequently involves 
projecting the depth of the lower contact of a given modeling unit where the borehole bottomed 
within that unit. A few upper contacts had to be projected where the top of a particular model 
unit had been eroded at the borehole location. The stratigraphic coordinate conversion is also 
complicated for boreholes that intercept a fault. In this case, it has been necessary to use modeled 
isochore information to reconstruct the missing portion of the stratigraphic section and infer the 
unfaulted depths based on unit-thickness trends obtained using the GFM. These instances are 
documented in the scientific notebooks associated with this modeling activity. DTNs associated 
with the geologic framework models used to extract the projected lithostratigraphic contacts are 
presented in Table 9. Note that Rock Properties Model (RPM) 3.1 was created simply by 
inserting the new drill hole data for holes SD-6 and WT-24 into the data set from RPM3.0 
(created using projected contacts from GFM3.0) and regenerating the model. 
4.2 CRITERIA 
This Analysis and Model Report complies with the U.S. Department of Energy interim guidance 
(Dyer 1999). Subparts of the interim guidance that apply to this analysis or modeling activity are 
those pertaining to the characterization of the Yucca Mountain site (Subpart B, Section 15), the 
compilation of information regarding geology of the site in support of the License Application 
(Subpart B, Section 21(c)(1)(ii)), and the definition of geologic parameters and conceptual 
models used in performance assessment (Subpart E, Section 114(a)). 
Table 8. Source of Input Observed Lithostratigraphic 
Contacts 
Data Source Description Reference 
Contacts for Geologic 
Framework Model 3.0 
DTN: MO9811MWDGFM03.000 
Contacts for SD-6 DTN: SNF40060298001.001 
Contacts for WT-24 DTN: SNF40060198001.001 
Table 9. Source of Input Projected Lithostratigraphic Contacts 
and Isochore Information 
Data Source Description Reference 
Geologic Framework Model 3.0 DTN: MO9804MWDGFM03.000 
Geologic Framework Model 3.1 DTN: MO9901MWDGFM31.000

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4.3 CODES AND STANDARDS 
No codes or standards are applicable to the Rock Properties Model.

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5. ASSUMPTIONS 
The principal assumption involved in constructing the rock properties models involves the use of 
porosity-as-a-surrogate for modeling the spatial variability of other, secondary material 
properties that are typically of greater interest in performance modeling than porosity itself, but 
which are almost universally undersampled at Yucca Mountain. This concept of using abundant 
porosity data as a surrogate for other properties is not new. Rautman and McKenna (1997, p. 13) 
list a sampling of published references using the porosity-as-a-surrogate technique. For Rock 
Properties Model 3.0, porosity has been used to model the spatial distributions of bulk density, 
saturated hydraulic conductivity, and thermal conductivity. 
The concept of porosity as a surrogate is based on empirically observed correlations of porosity 
with undersampled secondary properties. A consequence of undersampling is that the spatial 
variability of the undersampled variable cannot be described confidently on a stand-alone basis, 
let alone such that the joint spatial continuity patterns of the two (or more) variables cannot be 
reproduced simultaneously. It is important to understand that modeling the spatial distribution of 
several material properties without considering the inter-variable correlations can lead to highly 
unrealistic input to physical-process modeling codes, which in turn can lead to highly 
unreasonable estimates of performance parameters. Simply sampling randomly from separate 
(univariate) probability density functions may easily produce such un-physical combinations as a 
low porosityhigh thermal conductivityhigh hydraulic conductivity tuff. The severity of 
neglecting cross-variable correlations in modeling spatially variable domains increases as 
physical-process modeling attempts to capture multiple coupled processes. 
Using porosity as a surrogate for various other materials in modeling Yucca Mountain is 
supported by consideration of the physics involved in the site-specific rock units being modeled. 
For example, for a given rock type, increasing the volume of pore space must decrease the bulk 
density of the rock mass. The part of the rock that isnt there is available to hold fluids, but it 
contributes nothing to the total mass contained within a unit volume: the definition of bulk 
density. Again for a given rock type, the conduction of heat energy through the material is 
directly related to the density (or, inversely to the pore space) of the material. All else being 
equal, a higher porositylower density tuff will conduct heat less readily, leading to a lower 
thermal conductivity value. Note here that it is the total amount of void space in a rock that 
affects thermal conductivity, not simply the amount of pore space that is conducting water within 
the unsaturated zone. This fact has important implications to modeling of whole-rock thermal 
conductivity in the presence of large-diameter (to 1 meter) lithophysal cavities. 
As another example, although hydraulic conductivity is not generally well correlated with 
porosity across many classes of soils and/or rock materials, the empirical observation at Yucca 
Mountain is that this correlation is quite strong within limited groupings of rock types. 
Specifically, both welded and nonwelded lithologies appear to be associated with a continuum of 
saturated hydraulic conductivity values (see Section 6.4.5.1). Evidently, unless affected by some 
additional physical process (such as zeolitic or other similar alteration), there is a strong 
relationship between the progressive, overall reduction in porosity and the progressive reduction 
in the average diameter of the passages between interconnected pores (which is what exerts 
principal control on the flow of water through the existing pore space) across this continuum of

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nonwelded to densely welded materials. Conversely, a genetic process that changes the diameter 
and/or geometry of the pore throats (e.g., zeolitization), while not commensurately filling in the 
total quantity of void space, can reduce the hydraulic conductivity of the rock by orders of 
magnitude while leaving the porosity essentially unchanged. In fact, both these cases are 
observed and modeled at Yucca Mountain.

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6. ANALYSIS/MODEL 
6.1INTR ODUCTION A ND ROCK PROPER TIES MODEL OVER VIEW 
Yucca Mountain is located in the southwestern Nevada volcanic field and consists of faulted and 
tilted blocks composed of layered sequences of ash-flow, ash-fall, and bedded tuffs of Miocene 
age (Sawyer et al. 1994, pp. 1304 to 1318). 
The Rock Properties Model (RPM) is a 3-D (three-dimensional), discretized numerical 
representation of spatial variability and heterogeneity of a number of fundamental bulk and 
hydrologic material properties for the majority of the rocks within the unsaturated zone (UZ) at 
Yucca Mountain. The model divides the model volume into four internally lithologically similar 
model units. In descending stratigraphic order these are (1) the Paintbrush nonwelded (PTn) 
model unit, (2) the Topopah Spring welded (TSw) model unit, (3) the Calico Hills nonwelded 
(CHn) model unit, and (4) the Prow Pass Tuff (Tcp). The Tiva Canyon Tuff was not modeled for 
two primary reasons, which are discussed in detail in Rautman and McKenna (1997, p. 10). First, 
such a model is not needed because the Tiva Canyon Tuff is highly fractured, so that matrix 
properties are subordinate to the role of fractures in hydrologic flow. Second, because most 
boreholes are located in ravines eroded into the Tiva, few boreholes penetrate a meaningful 
stratigraphic section of the Tiva Canyon Tuff and data are accordingly sparse. Table 10 presents 
a correlation of the RPM model units with other project stratigraphies. For all four model units, 
the modeled material properties are: 
 Matrix porosity 
 Whole-rock bulk density 
 Matrix saturated hydraulic conductivity. 
For the TSw model unit, additional material properties are: 
 Lithophysal porosity 
 Whole-rock thermal conductivity. 
Lithophysal porosity and the two whole-rock properties in the above list are intended to 
represent the effect of the large (up to 1 meter in diameter) lithophysal cavities that are a very 
prominent feature of certain intervals within the Topopah Spring Tuff and the potential repository 
horizon. The rock properties model is tied geometrically to the bounding surfaces of model units 
within Geologic Framework Model (GFM) 3.1. 
There are three fundamentally different types of models included within the RPM. First, a suite of 
50 simulated property models have been generated for each material property using Monte Carlostyle 
geostatistical conditional simulation techniques. These models reproduce both the measured 
data values and the full range of spatial heterogeneity and spatial continuity exhibited by those 
data. At locations other than those of the measured values, material properties are generated 
(simulated) randomly from the local conditional probability density functions, and the variability 
of these values is interpreted to represent the uncertainty associated with predictions 

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Table 10. Correlation Chart for Model Stratigraphy 
Note: 1. Shaded areas represent header lines for subdivided units. 
Source: DTN: MO9510RIB00002.004

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of material properties at these unsampled locations. The second type of model included in the 
RPM are summary expectation (E-type) models for each rock property. These E-type models 
are computed as the node-by-node mathematical expectation (average) across the 50 simulated 
realizations, and they represent the property values most likely to be encountered at each 
discretized location. The third type of model included in the RPM is also a summary-type model, 
and these are computed as the node-by-node standard deviations of the 50 individual simulated 
property models. This third type of model is intended to provide users with a first-pass estimate of 
geologic uncertainty throughout the potential repository site, where geologic uncertainty 
consists of that uncertainty that results from less-than-exhaustive site characterization. 
The two primary data sources used to model the spatial variability of rock properties at Yucca 
Mountain are laboratory-measured core samples and down-hole measured petrophysical property 
values. Porosity is the primary variable for which spatial variability and heterogeneity have been 
modeled directly from measured values. The other material properties are derivative properties 
that have been generated from the simulated porosity models using the geostatistical technique 
known as linear coregionalization. Additional information has been incorporated from x-ray 
diffraction (XRD) measurements of (principally) zeolite mineral content. This form of rock 
alteration is considered to be an important control on the variability of matrix saturated hydraulic 
conductivity. Correlation between XRD alteration mineralogy and down-hole petrophysical 
measurements has been used to extend modeling of this type of alteration into regions from which 
no mineralogical samples have been obtained. 
The rock properties models are intended principally for use as input to numerical physical-process 
modeling, such as of ground-water flow and/or radionuclide transport. In anticipation of such use 
on a site scale, the models are discretized uniformly in the horizontal plane on a 200-m by 200-m 
(656.2-ft by 656.2-ft) grid. Vertical discretization is unit-dependent at a nominal 2-m (7-ft) 
spacing in the PTn model unit and 5-m (16-ft) spacing elsewhere. The rock property models can 
be regenerated at virtually any desired level of discretization to meet the needs of downstream 
model users. 
6.2 CHANGES BETWEEN MODEL VERSIONS 
Four significant changes in modeling methodology and data from those used in RPM2 (Rautman 
and McKenna 1997; note that RPM2 is the first numbered rock properties model) have been 
implemented for the current version of the rock properties model (RPM3). These changes are 
described briefly in this section. Expanded discussions are presented as appropriate in the sections 
on Data and Parameters (Section 4.1) and Development of the Models (Section 6.4). 
6.2.1Cha nges in Model Un it Sub divisions and Modeled Region 
The first major change in the rock properties models of Integrated Site Model (ISM) 3.1 is that the 
combined Calico Hills-Prow Pass model unit of ISM2 (Rautman and McKenna 1997) has been 
subdivided into two new modeling units along the formation boundary at the top of the Prow Pass 
Tuff (Table 10). This revised subdivision scheme was adopted because the area of rock properties 
modeling for ISM3 is smaller than that for ISM2. The smaller model area is a consequence of 
increased focus on the immediate repository area by the YMP site-scale UZ hydrologic model.

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This decrease in the modeled volume resulted in an improved spatial distribution of boreholes 
within the remaining area and decreased the need to aggregate data in search of statistical mass, as 
that term was described by Rautman and McKenna (1997, pp. 10 to 11). 
6.2.2 Adjustment of Model Unit Contacts to Reflect Mineralogy 
A second change is the adjustment of contacts between the welded interior core of the Topopah 
Spring Tuff (model unit TSw) and the respectively overlying and underlying PTn and CHn 
nonwelded units. For RPM3, these contacts were moved outward one lithostratigraphic interval, 
with the result that the breaks are now between the Tptrv3Tptrv2 and the Tptpv2Tptpv1 
lithostratigraphic units (Table 10). The rationale for this contact adjustment is that the revised 
boundaries better separate rocks with the potential to have been altered to zeolite minerals from 
high-temperature-crystallized rocks that almost never undergo such alteration. The spatial 
distribution of one derivative property, matrix saturated hydraulic conductivity, is strongly 
affected by the presence or absence of zeolitic minerals; thus a more accurate representation of 
this particular transition is the objective. Note that such modeling of alteration at this time has 
been conducted only for the CHn and Tcp model units. 
6.2.3 Revised Petrophysical Data 
The third and most significant, but perhaps least obvious change between the rock properties 
models of ISM2 and 3, is that all of the petrophysically based porosity data have been recalculated 
by CRWMS M&O (1999d, pp. 5-1 to 5-2) following identification of a number of problems with 
the earlier data sets (see Rautman and McKenna 1997, pp. 138 to 139). Specifically, the original 
petrophysical porosity data for ISM2 involved two different calculational approaches (described 
by Nelson 1996, pp. 17 to 23 and CRWMS M&O 1996, pp. 26 to 29), with the result that some 
spatial variability appeared to represent only the source of the calculated values (see discussion in 
Rautman and McKenna 1997, pp. 26 to 29 and 49 to 51). A separate issue involved the absolute 
magnitude of some of the porosity values calculated by Nelson (1996; the data values themselves 
are contained in GS960708312132.002) within selected stratigraphic intervals, principally the 
densely welded vitric subzones (Tptrv1, Tptpv3) of the Topopah Spring Tuff. As a consequence, 
it was unclear if some portion of the inferred spatial heterogeneity was related simply to the 
mathematical calculations and not to physical geology. 
For RPM3, CRWMS M&O (1999d, pp. 4-1 to 4-25) re-examined all of the underlying 
petrophysical logs, and processed the necessary fundamental petrophysical traces through a 
common data-reduction algorithm to calculate porosity. Specifically, use of the balanced-water 
approach using resistivity logs (CRWMS M&O 1996, p. 28) to calculate water saturation and 
volumetric water content was abandoned. Instead, porosity was calculated directly from the 
downhole density logs (separately above and below the water table), with volumetric water 
content derived directly from calibrated neutron logs (CRWMS M&O 1999d, p. 4-13 to 4-25 and 
30 to 31). This recalculation and common processing history eliminate one (non-geologic) source 
of apparent variability. 
Recalculation of the petrophysical porosity data involved not only a common data-reduction 
algorithm, but also calibration of the input bulk density trace against a set of internal standards

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(CRWMS M&O 1999d, pp. 3-1 to 3-2 and 4-2 to 4-5). Bulk density is the principal petrophysical 
measurement used in the porosity calculation. The internal standards are provided by four 
distinctive lithostratigraphic units, at least one of which is present in virtually each of the site 
boreholes. These units are the crystal-rich densely welded vitric (Tptrv1) and nonlithophysal 
(Tptrn) lithostratigraphic units, and the crystal-poor middle nonlithophysal (Tptpmn) and densely 
welded vitric (Tptpv3) units. Based on evidence from recovered drill core that these four intervals 
are of relatively uniform material, a set of density-correction factors was developed for each 
borehole (CRWMS M&O 1999d, pp. 6 to 9, Table 3). The density logs throughout each borehole 
were then adjusted proportionately (by individual logging run if appropriate) so that the average 
value in these distinctive zones indicated the correct bulk density. 
6.2.4 Revised Approach to Identifying Hydrous-Phase Mineral Alteration 
The term hydrous-phase mineral alteration is used in this report to indicate changes in initial 
(volcanic) mineral compositions that collectively act to reduce the matrix hydraulic conductivity 
of laboratory specimens (and in-situ rocks) compared with equivalent unaltered rocks of 
approximately the same porosity (Rautman and McKenna 1997, pp. 35 to 40, Figures 25 and 26 
and Table 8; Flint 1998, pp. 31 to 33 and Figure 12). Such rocks typically exhibit mineralogical 
alteration either to zeolite minerals, principally but not exclusively clinoptilolite and mordenite, 
or to expandable-layer clay minerals (smectite or montmorillonite; Flint 1998, p. 33). Within 
the two rock properties modeling units of principal interest (CHn and Tcp), hydrous-phase 
mineral alteration translates fairly precisely to zeolitic alteration. However, this distinction is 
maintained with respect to petrophysically based indicators of reduced Ks to emphasize that this 
approach is unable to distinguish zeolites and montmorillonitic clays in the downhole 
environment. 
A fourth change in rock properties modeling procedure involves the approach used to identify the 
spatial distribution of hydrous-phase mineral alteration, which affects the coregionalization of 
hydraulic conductivity with porosity in the lower two (CHn, Tcp) of the four properties modeling 
units. For version 2 of the rock properties models, each grid node was identified as either likely or 
unlikely to exhibit such alteration based on a spatial continuity model identified through 
petrophysical measurements (see Rautman and McKenna 1997, pp. 43 to 44 and 57 to 59). For 
version 3, altered grid nodes were modeled as a weighted combination of both hard (XRD 
analyses; Section 4.1.4) and soft (petrophysical; Section 4.1.5) data. Generation and use of the 
combined alteration data set is described in see Section 6.4.7. 
6.3 PHILOSOPHICAL AND CONCEPTUAL MODELING FRAMEWORK 
This section is intended to provide a relatively high-level conceptual description of the 
geostatistical modeling approach, including a brief discussion of how stochastic material-property 
models such as these fit into the overall performance modeling of the Yucca Mountain site. The 
methodology has been described in some detail by Rautman and McKenna (1997, pp. 6 to 69). 
Additional information regarding geostatistical modeling techniques in general may be found by 
following the references cited in the Rautman and McKenna document.

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6.3.1Modelin g Phil osophy and Conceptual App roach 
Licensing of the Yucca Mountain site as a geologic disposal site for nuclear waste will require 
quantitative predictions of waste-isolation performance of both the rocks that form Yucca 
Mountain and the engineered barrier system for an extended period of time into the future. These 
predictions will require the use of numerical modeling techniques in an effort to capture critical 
aspects of highly complex physical processes; for example, the flow of ground-water and the 
transport of radionuclide contaminants under both unsaturated and saturated conditions. Modeling 
the performance of the site will be influenced both by present-day conditions and by future 
conditions that must account for perturbation of ambient conditions by the thermal pulse related 
to the presence of heat-generating radioactive materials and potential changes in climate. 
A fundamental principle involved in the numerical representation of real-world physical 
processes is that the relevant material properties of the modeled domain must be known at all 
positions within that domain. However, in contrast to this requirement for an exhaustive spatial 
description, the process of describing or characterizing a site invariably consists of collecting 
observations of properties or state variables at a limited number of locations, the exact positions 
of which are frequently determined by less-than-optimal external factors. This is particularly true 
for the 3-D characterization of a geologic site, such as Yucca Mountain. Because descriptive 
characterization is limited both by access (particularly to the subsurface) and by the availability of 
resources, that description is necessarily incomplete. Therefore, the exhaustive description of a 
geologic site for purposes of numerical modeling requires the prior assumption of some type of 
conceptual model for the site, which is then implemented to assign the necessary properties and 
other variables at every relevant point in space. 
Many types of conceptual models of varying complexity are available to guide an exhaustive 
representation of material properties at Yucca Mountain. The simplest possible conceptual model 
of rocks at Yucca Mountain is to assume that the material properties needed for numerical process 
modeling are homogeneous and uniform throughout the site. However, although such a model 
might possess some utility for rough, back-of-the-envelope calculations, even the most cursory 
inspection of Yucca Mountain indicates that such a representation is vastly oversimplified and of 
limited value in addressing regulatory-related issues. 
6.3.1.1 Capturing Heterogeneity 
A slightly refined, but still quite simplified, conceptual model for the site makes use of the fact 
that, at Yucca Mountain (as in many other geologic environments), the lithologic deposits were 
produced by relatively widespread but temporally variable geologic processes. In particular, the 
volcanic activity responsible for the formation of Yucca Mountain was episodic in nature, with 
thick, widespread ash deposits produced by near-instantaneous (geologically speaking) eruptions 
separated by thin inter-eruption deposits that probably represent much longer intervals of time. If 
the time represented by a progressively accumulating geologic deposit is considered to be 
frozen and preserved in the vertical dimension, then the resulting conceptual model is one of 
successive subhorizontal layers, that may be broken and tilted, or folded and otherwise moved 
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The GFM component of the ISM is such a layered representation of Yucca Mountain. However, 
without further refinement, a layered rock-properties model corresponding precisely to the GFM 
still relies upon the prior assumption that, within each originally subhorizontal layer, the material 
properties of interest are essentially uniform and homogeneous. Geologic studies of the 
volcanogenic rocks at Yucca Mountain and of similar deposits elsewhere in the world indicate that 
the geologic processes responsible for deposition of these materials vary both temporally and 
areally. For example, variations in cooling rates caused by local conditions affect the material 
properties in the resultant rocks. This spatial variation of process has produced spatial 
heterogeneity of material properties in all three dimensions. Yet despite the existence of vertical 
and lateral heterogeneity, the spatial distribution of material properties within geologic layers is 
not simply random. Knowledge of property values at one location imposes limits on the values 
of those properties likely to exist at nearby locations Therefore, an alternative conceptual model 
of filling-in a geologic framework with values randomly assigned from some inferred 
univariate distribution without regard for other nearby values (spatial correlation) is an 
unnecessary oversimplification (and potentially an unwarranted distortion) of the real world. 
6.3.1.2 Heterogeneity vs. Uncertainty 
In contrast to heterogeneity, which is an objective feature of the real world, uncertainty is a 
knowledge-based concept. Distinguishing properly between uncertainty (as a state of imperfect 
information resulting from less-than-complete observation) and spatial heterogeneity (as a state of 
being, unaffected by the availability or lack of information) becomes critically important in the 
application of predictive engineering methods to the geologic environment. Natural earth 
materials are heterogeneous to a far greater degree than most materials of conventional 
engineering interest. Heterogeneity in rock properties affects the actual operation of physical 
processes, even though there is only one, unique heterogeneous reality. The impact of that 
heterogeneity on the numerical approximation (modeling) of those physical processes is only 
compounded by geologic uncertainty. Incomplete information must be accounted for in predictive 
modeling, as must the effects of material properties that are different in different locations. A key 
attribute, therefore, of the rock properties modeling activities, has been the description and 
quantification of the effects of geologic uncertainty on the physical description of the Yucca 
Mountain site. 
6.3.1.3 Geostatistical Methods 
The current approach to modeling rock properties as part of the ISM attempts to strike a balance 
between the inherent simplification of a hollow-shell GFM and the near-infinite degree of 
complexity that is the real world. Selected major lithostratigraphic horizons are used as the 
constraining (framework) boundaries for a statistically based description of the measured rock 
material properties that have been sampled within those boundaries. Geostatistical methods have 
been used to create the exhaustive material property descriptions comprising the rock properties 
model. Geostatistical methods in general are one of a variety of methods for distributing isolated 
measurements of different attributes in space, and thus for modeling spatial heterogeneity. A 
fundamental principle underlying all geostatistical techniques is the quantification and use of 
some measure of spatial correlation, which may be defined informally as the degree to which 
samples close to one another resemble each other more than do samples far away from each

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other, where close and far are defined from the data values. Furthermore, unlike many other 
methods for predicting the material property attributes of a large volume from direct observation 
of a relatively minuscule fraction of that volume, geostatistical methods offer a quantitative and 
more-or-less rigorous approach to the issues of knowledge-based uncertainty discussed in 
Section 6.3.1.2. 
Within the purview of geostatistical methods are two broad classes of algorithms for predicting 
attributes at unsampled locations constrained by some limited set of actual measurements: 
estimation and simulation. Geostatistical estimation is focused on the prediction of the attribute 
values most likely to be encountered at a given spatial position, and may be thought of as 
modeling the expected value of a variable of interest. Geostatistical estimation is most frequently 
described using the term, kriging, and it is simply a weighted-average interpolation method using 
some neighborhood of near-by relevant data. A common thread connecting all estimation 
methodologies (including non-geostatistical ones) is that they are interpolation techniques 
directed toward producing a model in which the estimated values grade progressively and 
generally smoothly away from the data locations and away from one another. 
The other broad class of geostatistical methods comprises a variety of simulation algorithms. In 
contrast with estimation, geostatistical simulation places principal emphasis on reproducing the 
input data values and the overall statistical character (including the spatial correlation 
characteristics) exhibited by the data ensemble, the total collection of input values. Models 
produced by geostatistical simulation typically do not grade smoothly between measured data 
values, but rather are more highly variable at the same time that they represent the broad 
heterogeneity structure of the measurements. These techniques are conceptually equivalent to the 
Monte Carlo simulation process frequently employed in engineering analyses. In common with 
other Monte Carlo simulation approaches, the emphasis is less on the specific predicted values, 
which are in effect simply the products of a random number generator with certain desirable 
properties, and much more on evaluation of the space of uncertainty associated with some 
performance measure computed to represent the behavior of the modeled system. 
6.3.1.4 Evaluating the Consequences of Heterogeneity and Uncertainty 
A schematic diagram of the geostatistical process for combining statistical description with the 
Monte Carlo generation of multiple replicate models, which are then evaluated for performance 
consequences is presented in Figure 3 (see also Rautman and McKenna 1997, Figure 6). The logic 
is straightforward Monte Carlo, except that the need to capture both heterogeneity and spatial 
correlation jointly causes the geostatistical simulation process to consist of drawing entire intact 
property models (rather than single property values) from a conceptual distribution of alternative 
realities. 
As suggested by the upper row of panels in Figure 3, the individual measured values of a material 
property are combined with the overall statistical character of the complete data set (the data 
ensemble) and with the spatial correlation patterns exhibited by the data to produce replicate 
exhaustive models (center part of Figure 3) showing the distribution of that material property in 
space. Each replicate model reproduces the measured data at the data locations, and the overall 
variability of all the values in the model reproduces the histogram of the measurements.

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Figure 3. Conceptual representation of a Monte Carlo process incorporating geostatistical simulation 
techniques as the basis for assessing the impact of geologic uncertainty on a performance 
measure relevant to licensing of a geologic repository. A consequence analysis is any postsimulation 
mechanism for computing a measure of performance across the suite of replicate 
stochastic simulations (from Rautman and McKenna, 1997, Figure 6).

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Additionally, the spatial correlation structure of the model, evaluated as a whole, approximates 
the spatial correlation among the input measurements. Completing the Monte Carlo methodology, 
each of these individual realizations (property models) may then be processed through some 
relevant transfer function or consequence analysis (for example, a radionuclide-transport 
computer code), and the likelihood of various acceptable vs. unacceptable performance responses 
evaluated. This final step is represented in the lower portion of Figure 3. 
6.3.2 Methodology Overview 
Construction of the 3-D rock properties models has been guided by the philosophically separate 
but related concepts of heterogeneity and uncertainty described in the preceding section. The 
models attempt to make maximum use of deterministic genetic processes to constrain the 
modeling of measured property values away from the physical locations of those measurements. 
The effort to capture genetic processes as they relate to material properties has led to the 
separation of the geologic column of interest into several discrete geologic units, each of which is 
internally more homogeneous in some identifiable manner than subdivisions based on other 
criteria. 
An interpretation that the material properties of the rocks are controlled principally by the original 
genetic geologic processes and that much of the post-depositional alteration that has produced 
second-order variability in properties occurred before tectonic tilting and faulting suggests that 
the influence of such deformation should be discounted in the modeling process. A concept has 
been adopted of using a stratigraphic coordinate system during the modeling process, as distinct 
from a real-world coordinate system that describes the present-day location of points within the 
several geologic units. Both the measured data and the geostatistical models are described in 
stratigraphic coordinates throughout the modeling exercise. Models are back-transformed into 
real-world coordinates upon completion. 
Because measurements of most material properties of direct interest for use in performance 
calculations are quite limited in number and spatial distribution, the concept of porosity-as-asurrogate 
is adopted in order to use relatively abundant and widely distributed (in three 
dimensions) porosity data as a first approximation of the geologic heterogeneity of the site. The 
conceptual assumption (Section 5) is that the spatial variation and trends in many different 
properties should be roughly the same, as the entire ensemble of material properties is related to 
the geologic processes responsible for formation of these rocks. 
Sequential gaussian simulation techniques are used to generate the discretized, exhaustive, 
primary porosity models, conditioned to both laboratory core and downhole petrophysical 
measurements in an effort to integrate virtually all available data from the entire Yucca Mountain 
site. Conditional simulation methods produce models that effectively reproduce both the 
conditioning measurements and the overall (geo)statistical character of those measurements. A 
technique known as linear coregionalization is then used to produce similarly exhaustive models 
of selected derivative material properties. For certain material properties, additional 
postprocessing of these derivative models is required to induce desired geologic attributes in the 
final models. For example, an indicator-kriged model of hydrous-phase mineral alteration is used

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to constrain the derivative models of saturated hydraulic conductivity for two units where the 
presence of this type of alteration is known. 
The modeling process has been conducted using a scientific notebook procedure 
(SNL QAIP 20-2, Rev. 02). Details of the modeling process, including expansion of topics 
discussed only in abbreviated or illustrative form in this report, may be found in the scientific 
notebooks listed in Table 11. 
6.4 DEVELOPMENT OF THE MODELS 
6.4.1Model Domain 
The location of the 3-D rock properties model is shown in relationship to the general Yucca 
Mountain area and to the Exploratory Studies Facility (ESF) in Figure 2. The modeled region 
extends from west to east from the vicinity of Fatigue Wash to the middle of Midway Valley, and 
from north to south from central Yucca Wash to the middle portion of Dune Wash. The model 
domain for the rock properties model is closely tied to the location of the YMP UZ site-scale 
model numerical process-model grid. 
6.4.2 Separate Modeling of Distinctive, Aggregate Geologic Units 
Rock properties models have been created for four distinctly different aggregate geologic units: 
the upper Paintbrush nonwelded interval, the welded portion of the Topopah Spring Tuff, the 
Calico Hills nonwelded interval, and the Prow Pass Tuff. The relationship of these four aggregate 
modeling units to the detailed lithostratigraphic subdivision of Yucca Mountain and to other 
modeling units involved in the GFM and the mineralogical model of Yucca Mountain is shown in 
Table 10. 
Note that the aggregate geologic units selected for separate rock properties modeling efforts do 
not coincide in general with the breaks between genetic packages of rock, which at Yucca 
Mountain are typically collections of virtually coeval pyroclastic flow deposits associated with a 
major volcanic event such as a caldera-collapse sequence. However, as documented by Rautman 
and McKenna (1997, pp. 6 to 11, Figures 3 and 4), the available measurements of material 
properties indicate that the modeling units defined here are more homogeneous (consistent) 
internally than are the major genetic packages. 
Table 11. Scientific Notebooks for Rock Properties Models 
Scientific Notebooks Title Reference 
SNL-SCI-006 
Scientific Notebook, Geostatistical Modeling of Porosity and 
Derivative Properties (FY 1998) 
Rautman and 
McKenna 1998 
SNL-SCI-011 
Scientific Notebook, Geostatistical Modeling of Porosity and 
Derivative Properties (FY 1999) 
Rautman 1999

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6.4.3 Available Data and Preliminary Processing 
The data used in modeling the spatial variability of material properties in the rock properties 
model were obtained from a number of sources, as described in Section 4, including both 
laboratory measurements of core samples (Sections 4.1.1 and 4.1.3) and down-hole petrophysical 
measurements (Sections 4.1.2 and 4.1.5) of in-situ rocks. Only surface-based drill holes have been 
used in constructing the rock properties model, as the large areal extent of the model and the 
requirement that the vertical positions of all data be expressed in stratigraphic coordinates 
effectively precludes the use of samples from the underground workings of the ESF. The locations 
of the various drill holes used in modeling each separate geologic unit are shown in 
Figures 4 through 7. Note that although there is major consistency of the drill hole coverage from 
unit to unit, the suite of holes that contain data relevant to any particular model unit is unique. 
Data tracking numbers associated with all data values are tabulated in Section 4. 
6.4.3.1Data Compilation, Re sampling, an d G eneration of De rived Q uantities 
Compilation of porosity, secondary property data, and mineralogical analyses into initial working 
files, even though from a large number of sources, is relatively straightforward. Laboratory core 
data were used essentially as-is. Relevant petrophysical variables were extracted from much more 
massive source files, containing all extant downhole geophysical data, using software routine BUD 
(Table 2). Core and petrophysical porosity data were compiled on an individual drill hole basis in 
spreadsheets using the graphics package Sigma Plot (Section 3), prior to being combined on a byunit 
basis in Excel. 
Because the petrophysical data were recorded in the field on 0.5-ft depth spacings (some older 
holes were recorded on only 1-ft spacings), it was determined that direct use of all available 
petrophysical values would statistically overwhelm the available core porosity measurements 
(collected on a nominal 3-ft spacing) available for an equivalent length of drill hole. Therefore, to 
maintain approximate parity of statistical mass across the two different types of porosity data, the 
petrophysical values were resampled to a 3-ft depth spacing as well. In keeping with the practice 
of Rautman and McKenna (1997, pp. 29 to 30, Figure 14) in developing RPM2, the resampling 
algorithm also calculated a simple average of the adjoining measurements within plus and minus 
1 ft of the nominal 3-ft depth value. This averaging process is necessary to deal with missing 
values present in the original petrophysical data (generally related to unacceptable borehole 
conditions). Both resampling and computation of the desired two-foot average values was 
accomplished using software routine TWOFOOT (Table 2). 
Relevant mineralogical analyses (hydrous-mineral phase altered mineral fractions of smectite, 
clinoptilolite, mordenite, and chabazite) were extracted from the source data files (Section 4.1.4) 
using the data manipulation capabilities of Excel. A new variable, total hydrous-phase mineral 
content, was created as the sum of these individual mineral fractions. A hydrous-mineral phase 
alteration-indicator variable, I, was also constructed for the mineralogical data set by the logical 
statement: 
(Eq. 1) I 
1 Altered Minerals ( ) . 5-percent = . 
0 Otherwise . . . .
=

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Figure 4. Drill holes used in modeling the PTn model unit. Note: some holes may include only partial 
penetrations of the unit.
Nevada State Plane Easting, in feet 
550000 560000 570000 580000 
Nevada State Plane Northing, in feet 
740000 
750000 
760000 
770000 
780000 
790000 
UZ Site-Scale Model Boundary 
RPM3 
G-1 
G-2 
G-3 
G-4 
H-1 
H-3 
H-4 
H-5 
H-6 
NRG-4 
NRG-5 
NRG-6 
NRG-7 
ONC-1 
SD-7 
SD-9
SD-12 
UZ-1,14 
UZ-4,5 
UZ-6 
UZ-7a UZ-16 
WT-1 
WT-2 
WT-4 
WT-7
WT-10 
WT-11 
WT-12 
WT-13 
WT-14 
WT-15 
WT-16 
WT-17 
WT-18 
WT-24 
UZN11 
UZN31,32 
UZN33,34 
UZN37 
UZN53,54,55

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Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 50 of 150 
Figure 5. Drill holes used in modeling the TSw model unit. Note: some holes may include only partial 
penetrations of the unit. 
Nevada State Plane Easting, in feet 
550000 560000 570000 580000 
Nevada State Plane Northing, in feet 
740000 
750000 
760000 
770000 
780000 
790000 
UZ Site-Scale Model Boundary 
RPM3 
G-1 
G-2 
G-3 
G-4 
H -1 
H-3 
H -4 
H-5 
H -6 
NRG-4 
NRG-5 
NRG-6 
NRG-7 
ONC-1 
p#1 
SD-7 
SD-9 
SD-12core 
UZ-1 
UZ-4,5 
UZ-6 
UZ-7a 
UZ-14 
UZ-16 
WT-1 
WT-2 
WT-3 
WT-4 
WT-7 
WT-10 
WT-11 
WT-12 
WT-13 
WT-14 
WT-15 
WT-16 
WT-17 
W T-18 
WT-24 
UZN37 
UZN53,54,55 
UZN5 7,58 ,59 ,61

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 51 of 150 
Dr ill Holes in the CHn 
Nevada State P lane Easting, in feet 
550000 560000 570000 580000 
Nev ada State Plane Northing, in feet 
740000 
750000 
760000 
770000 
780000 
790000 
UZ Site-Scale Model Boundary 
RPM3 
G-1 
G-2 
G-3 
G-4 
H -1 
H-3 
H -4 
H-5 
H-6 
NRG-7 
ONC-1 
p#1 
S D -7 
S D -9core 
SD-12 
UZ-6
UZ-14 
UZ-16 
WT-1 
WT-2 
WT-3 
WT-4 
WT-7 
WT-12 
WT-14 
WT-15 
WT-16 
WT-17 
WT-18 
WT-24 
Figure 6. Drill holes used in modeling the CHn model unit. Note: some holes may include 
only partial penetrations of the unit.

Title: Rock Properties Model (RPM3.1) 
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Figure 7. Drill holes used in modeling the Tcp model unit. Note: some holes may include only partial 
penetrations of the unit. 
Nevada State Plane Easting, in feet 
550000 560000 570000 580000 
Nevada State Plane Northing, in feet 
740000 
750000 
760000 
770000 
780000 
790000 
UZ Site-Scale Model Boundary 
RPM3 
G-1
G-2 
G-3 
G-4 
H-1 
H-3 
H-4 
H-5 
H-6 
p#1 
SD-7 
SD-9 
SD-12 
UZ-6
UZ-14 
UZ-16 
WT-2 
WT-3 
WT-7 
WT-12 
WT-17 
WT-18

Title: Rock Properties Model (RPM3.1) 
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In preparation for calibrating the soft indicators of hydrous-phase mineral alteration 
(Section 6.2.4), additional variables were created for both the core and petrophysical data sets. 
These variables, referred to as bound-water, were calculated simply as the arithmetic difference 
between the OD and relative humidity (RH) porosity values (for core; Section 4.1.1) or between 
the POROTOT and POREF porosity values (for petrophysics; Section 4.1.5). Further manipulation 
and use of the bound-water variables is discussed below in Section 6.4.7.1. 
6.4.3.2 Stratigraphic Coordinate Conversion 
Each major lithologic interval selected for modeling has been modeled in a stratigraphic 
coordinate system that reflects the original, pre-faulting depositional continuity of these ash-flow 
and air-fall tuffaceous deposits (Figure 8). Stratigraphic coordinates use the same east-west and 
north-south coordinates (Nevada state plane coordinate system, defined in feet) as the drill hole 
from which the relevant data were obtained. However, the vertical coordinate of a sample is 
represented as the relative fractional position of that sample within the thickness of the entire unit 
at that horizontal location. The stratigraphic coordinate concept effectively removes the effect 
both of depositional thinning away from the source volcanic vent(s) and of post-depositional 
tilting and deformation, and it thus positions samples from equivalent portions of the overall unit 
at the same nominal internal position within a rectangular volume. 
As shown schematically in part (a) of Figure 8, regions of varying material properties are 
presumed to have been emplaced or otherwise formed by various alteration processes in an 
essentially stratiform manner. At Yucca Mountain, the volumetrically dominant rocks were 
formed by deposition by pyroclastic flows to form thick ash-flow sheets that thin laterally away 
from their source. Thus, there is a tendency for regions of somewhat similar material properties 
that were formed under somewhat similar pressure-temperature conditions to occupy roughly the 
same relative vertical position within a unit. Later faulting as part of Basin and Range tectonism 
disrupted the originally continuous volcanic rocks and tilted the rock units, with their contained 
material properties, toward the east, as indicated in part (b) of the figure. Modeling of those rock 
properties is illustrated in part (c) of Figure 8. The vertical locations of drill hole samples are 
specified within the stratigraphic coordinate system as a fractional distance where the base of the 
unit is assigned a distance of zero and the top of the unit is assigned a distance of one. 
Stratigraphic coordinates are thus dimensionless. 
As suggested by the mesh of intersecting dotted lines in the right-hand portion of Figure 8, a 
regular rectangular modeling grid is defined within each stratigraphic coordinate system. Because 
the various material property zones have been stretched or compressed vertically so that the 
overall stratigraphic thickness of the unit is constant, defining the modelling grid within this 
framework generally positions nodes with similar materials on a stratigraphically horizontal 
plane. This repositioning of similar materials in similar relative locations greatly simplifies the 
search for data in the neighborhood of an unsampled location, as shown conceptually by the 
search ellipse in part (c) of Figure 8. Although it is possible to rotate the principal direction of the 
search ellipse to match the overall tectonic dip of the unit (see part (b) of the figure), it is virtually 
impossible to modify the search strategy to account for vertical displacement of the material 
property zones by discrete faults.

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 54 of 150 
Figure 8. Conceptual illustration of the construction and use of stratigraphic coordinates. (a) Rock unit is 
formed by areally extensive volcanic (or sedimentary) processes. Zones of differing rock 
properties (shaded colors) are formed in a stratiform manner. (b) Tectonic deformation tilts and 
disrupts original stratiform continuity by faulting. (c) Modeling unit is returned to an 
approximation of original continuity in a rectangular coordinate system in which all vertical 
distances are measured as a fractional position measured from the top or bottom of the 
rock unit. 
(a) 
(b) 
(c) 
Original Depositional Continuity 
Conversion to Stratigraphic Coordinates 
Ash-Flow 
Deposition 
0
1 
Tectonic Tilting and Faulting 
356' 
932' 
Search Ellipse 
Structure- 
Contour 
Horizon 
Isochore 
Information 
7356' 
528' 
Drill Hole Search Ellipse 
Stratcoords.cdr

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 55 of 150 
At the end of a modeling exercise, the transformation process between parts (b) and (c) in 
Figure 8 is reversed by assigning each grid node a computed vertical position derived from 
knowledge of the structure contour model for the top of each unit and the spatially varying 
thickness of each unit (software routine COORDS, Table 2). These values are obtained from the 
independently developed 3-D GFM (e.g., GFM3). 
In practice, implementation of the stratigraphic-coordinate concept is slightly more complicated 
than the idealized example of Figure 8. First, sample locations are typically specified in terms of 
their depth within a specific drill hole (the drilling process measures all locations from the collar 
of the hole regardless of the physical elevation of the hole and its contained samples). Thus, the 
measured depths were converted to stratigraphic depths initially, and only to stratigraphic 
elevations at the time of modeling. Second, for reasons involving principally numerical precision 
within the computer programs that implement the actual rock properties modeling algorithm(s), 
the fractional stratigraphic positions indicated in Figure 8 are multiplied by unit-specific scaling 
constant to obtain values that approximate the nominal thickness of the different units in the real 
world. Additionally, unlike the two-dimensional example shown in Figure 8, actual modeling of 
rock properties was conducted in full 3-D space. 
Finally, the issue arises regarding how to treat samples from a drill hole that fails to penetrate the 
entire thickness of the geologic unit in question (represented by the drill hole on the left-hand side 
of Figure 8). Clearly it is inappropriate to assign a stratigraphic elevation of zero to a sample 
obtained from the very bottom of the hole itself, as the materials at this elevation in general are 
not representative of materials at the base of the unit here or elsewhere. Yet, without drilling 
deeper, the distance between the foot of the hole and the true base of the unit is unknown. Such 
situations have been reconciled by inferring the base of the unit in question from the GFM (e.g., 
GFM3) and adjusting the fractional position accordingly. The presumption is that the base of the 
unit projected using the framework model is a reasonable approximation of the unknown true 
position at that location. Similar reconstructions are required in the case where erosion has 
removed the top of a particular modeling unit at a drill hole location or if part of a unit is missing 
from a drill hole because of faulting. 
The equation for calculating stratigraphic depth (StratDepth) is: 
, (Eq. 2) 
where SampleDepth is the depth of the relevant sample measurement in a given drill hole, 
UnitTop and UnitBottom are the measured or projected depths to the top and bottom contacts of 
that model unit at the drill hole location used to determine the thickness of the unit, and 
NominalThickness is the appropriate unit-specific scaling constant from Table 12. Conversion of 
drill hole depths to stratigraphic depths was accomplished using the transform capabilities of 
Sigma Plot (STRATC4.XFM; Table 2; Attachment II). Stratigraphic elevation is calculated simply as 
NominalThicknessStratDepth, and was calculated using the mathematical capabilities of Excel 
prior to writing final ASCII text files of the data values. 
StratDepth 
SampleDepth UnitTop  
UnitBottom UnitTop  
--------------------------------------------------------------- NominalThickness  =

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 56 of 150 
6.4.4 Statistical and Spatial Description of Porosity 
Porosity is the primary material property used to generate the material properties models 
contained in RPM3. Even the models of derivative properties such as hydraulic conductivity are 
based ultimately on porosity. This section presents the statistical description (the ensemble 
characteristics; Sections 6.3.1.3 and 6.3.1.4) of the underlying porosity measurements that have 
been used to condition the stochastic models of each modeling unit. This presentation consists 
principally of histograms for the various model units and a summary of their descriptive statistics 
(Table 13). Experimental variograms calculated using the measured values and a fitted model for 
each unit are presented to represent the spatial continuity patterns expressed in the data. Finally, 
because of the unique geologic nature of the TSw model unit, two different types of porosity 
(matrix and lithophysal) are presented and justified. 
6.4.4.1P Tn Model Unit 
Porosity DataPorosity data obtained from the upper Paintbrush nonwelded model unit are 
portrayed in histogram format in Figure 9. A statistical summary of these data is given in 
Table 13. 
Spatial Continuity DataModeled variograms for porosity in the PTn model unit are presented 
in Figure 10. Parameters of the fitted variogram model are presented in Table 14. Details of the 
variogram modeling exercise for the PTn model unit may be found in the scientific notebook 
(Rautman and McKenna 1998, pp. 361 to 368). 
Table 12. Unit-Specific Scaling Constants for Nominal Model Unit Thickness 
Model Unit 
Nominal 
Thickness 
PTn 200 
TSw 1000 
CHn 400 
Tcp 400 
Table 13. Statistical Summary of Porosity Data Used in Modeling 
PTn 
TSw 
CHn Tcp 
Matrix Lithophysal 
Mean 0.342 0.122 0.146 0.254 0.229 
Std.Dev. 0.122 0.061 0.076 0.075 0.090 
Minimum 0.001 0.001 0.001 0.001 0.001 
Maximum 0.750 0.519 0.551 0.511 0.494 
N 2,300 11,052 11,796 2711 2603 
Note: All values are porosity as a fraction (equivalent to m3/m3), except number of 
values (N).

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Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 57 of 150 
6.4.4.2 TSw Model Unit 
Porosity DataPorosity values obtained from the Topopah Spring welded (TSw) model unit are 
presented graphically in histogram format in Figure 11; the corresponding statistical summary of 
these data is presented in Table 13. Examination of the raw porosity data indicates that there are 
two different porosity values of interest in modeling rock material properties: matrix and 
lithophysal. Lithophysal porosity, as that term is used in this report, is taken to mean the porosity 
of volumes of rock many tens of centimeters in diameter, such that the porosity effect of large 
(decimeter scale and larger) lithophysal cavities is included. In contrast, the term matrix porosity 
is used in this report to refer to the porosity approximately equivalent to that measured for 
Figure 10. Experimental and fitted model variograms of matrix porosity in the PTn model unit in the 
(a) stratigraphic vertical and (b) stratigraphic horizontal directions. 
Separation Distance, in feet 
0 50 100 150 200 
Normal-Score Variogram 
0.0 
0.5 
1.0 
1.5 
Data 
a priori Variance 
Model 
PTnVertVar.wmf 
(a) 
Separation Distance, h, in feet 
0 5000 10000 15000 
Normal-Score Variogram 
0.0 
0.5 
1.0 
1.5 
Data, Az. = 135 
Data, Az. = 45 
a priori Variance 
Model, Az. = 135 
Model, Az. = 45 
PTnHorizVar.wmf 
(b) 
Porosity, as a fraction 
0.0 0.2 0.4 0.6 
0.00 
0.02 
0.04 
0.06 
0.08 
0.10 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
Frequency 
Cumulative Frequency 
Figure 9. Histogram and cumulative distribution function of matrix porosity in the PTn model unit.

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 58 of 150 
laboratory core samples, in which the size of the matrix pores is small enough that water is held in 
them by capillarity under slightly unsaturated (negative pressure) conditions. The difference 
between the two types of porosity measurements is not trivial, as illustrated in Figure 12, a 
comparative down-hole plot of matrix and lithophysal porosity data from drill hole SD-7. 
Lithophysal porosity is indicated by the dark solid curve, whereas the matrix porosity values 
measured for core samples are indicated by the filled-circle symbols. Note the marked divergence 
of the porosity values indicated by these two sets of data in two vertical locations within the drill 
hole. In general, these zones of divergence correspond to the two lithophysal zones (upper and 
lower) defined by Buesch et al. (1996). However, the correspondence is not at all exact, and the 
petrophysical POREF (= lithophysal) porosity curve from downhole geophysics indicates that 
substantial lithophysal cavity development may extend significantly above and below the limits 
Table 14. Variogram Parameters for Spatial Continuity Model of Porosity in the PTn Model Unit 
Nest 
No. 
Model 
Type 
Range 
(ft) 
Sill 
Rotation Angle 
(degrees)1 
Anisotropy 
Ratio1 
Maximum 
(horizontal) 
Intermediate 
Minimum 
(vertical) 
1 2 3 1 2 
-- Nugget -- -- -- 0.01 -- -- -- -- -- 
1 Spherical 300 50 20 0.20 135 135 135 0.167 0.067 
2 Spherical 5,000 2,500 80 0.55 135 135 135 0.500 0.016 
3 Spherical 10,000 7,500 100 0.24 135 135 135 0.750 0.010 
Note: 1. Rotation angles 13 and anisotropy ratios 12 are keyed to input requirements of the SGSIM computer 
code, as documented in Deutsch and Journel 1992, pp. 167 and 22 to 29. 
Figure 11. Histograms and cumulative distribution functions of (a) matrix porosity and (b) lithophysal 
porosity in the TSw model unit. 
y 
Porosity, as a fraction 
0.0 0.2 0.4 0.6 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
TSwM_RHpor.wmf 
(a) 
Porosity, as a fraction 
0.0 0.2 0.4 0.6 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
TSwL_RHpor.wmf 
(b)

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 59 of 150 
Porosity, fraction 
0.0 0.2 0.4 0.6 
Depth, in feet 
400 
500 
600 
700 
800 
900 
1000 
1100 
1200 
1300 
1400 
POREF 
VWC 
Core Porosity 
Tptrn 
Tptrl 
Tptpul 
Tptpmn 
Tptpll 
Tptpv3 
Tptpln 
Tptpv1 
Tptpv2 
Tptbt1 
Tptrv3 
Figure 12. Comparison of different types of porosity data for drill hole USW SD-7. Horizontal dashed lines 
indicate lithostratigraphic units as defined by Buesch et al. (1996).

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 60 of 150 
of the formally named lithophysal zones (Figure 12). A scatterplot of these lithophysal porosity 
values versus the depth-equivalent core RH porosity for the formally named lithophysal-zone 
intervals only is presented in Figure 13, part (a). The region of marked divergence from the 45 
one-to-one correspondence line represents high lithophysal porosities matched on a nearestsample 
basis to the lower core porosity values. 
Note also the third set of data plotted in Figure 12; this curve is identified as volumetric water 
content (equivalent to the amount of water-filled porosity) and is shown by the dashed line 
without symbols. This third curve is observed essentially to overlie the true matrix (= core) 
porosity data throughout much of the drill hole. In locations where the water-filled porosity trace 
does not closely match the core values, it is always observed to indicate markedly lower values 
than the solid lithophysal porosity curve. The near-equivalence of core and VWC values is 
demonstrated in part (b) of Figure 13. The small set of mismatched pairs may be identified in 
Figure 12 as representing the interval between approximate 480 and 550 feet. 
Because many drill holes lack core data from which to obtain matrix porosity for modeling 
purposes, the practice has been adopted (for those non-cored holes only) of using volumetric 
water content as a surogate for matrix porosity. Outside these lithophysae-bearing intervals, 
matrix porosity is set equal to POREF porosity, whereas within these intervals of curve separation, 
matrix porosity is set equal to the VWC values. 
It is clear that this practice is merely a simple heuristic device, and that use of the volumetric water 
content as representing water-filled porosity unquestionably will underestimate the actual matrix 
porosity within the UZ for the simple reason that all the available matrix pore space in the UZ is 
not water filled (any large lithophysal cavities also will not be water filled). However, the 
approach is a reasonable approximation for several reasons. (1) Water saturation throughout much 
of the Topopah Spring Tuff is rather high, typically greater than about 80 percent. (2) The VWC 
p y y 
Core Porosity, as a fraction 
0.0 0.1 0.2 0.3 0.4 
Petrophysical Porosity (POREF), as a fraction 
0.0 
0.1 
0.2 
0.3 
0.4 
Figure 13. Crossplots of (a) petrophysical POREF porosity vs. core RH porosity and (b) petrophysical VWC 
vs. core RH porosity for formally defined lithophysal intervals in drill hole SD-7. Line indicates 
one-to-one correspondence. 
p y y 
Core Porosity, as a fraction 
0.0 0.1 0.2 0.3 0.4 
Petrophysical Porosity (VWC), as a fraction 
0.0 
0.1 
0.2 
0.3 
0.4 
(a) (b)

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Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 61 of 150 
values in zones of significant lithophysal cavity development are much closer to the true matrix 
porosity than are the lithophysal porosity values, which can be observed from Figures 12 and 13 
to be as much as double the matrix (core) porosity values for drill hole USW SD-7. And finally, 
(3) because one of the purposes of modeling the spatial heterogeneity of porosity is to attempt to 
model the variability of saturated hydraulic conductivity using porosity as a surrogate, the 
volumetric water content representing the water-filled porosity (at any in-situ saturation) most 
likely represents essentially all the pore space that is available for the transmission of water under 
unsaturated conditions. 
Note that it is possible to significantly underestimate the whole-rock saturated hydraulic 
conductivity of the Topopah Spring welded interval under true saturated conditions in this 
manner, because the effect of lithophysal cavities on the whole-rock permeability is neglected. 
However, such underestimation is likely to be a non-issue, as this relatively high stratigraphic 
interval almost invariably is present in the unsaturated zone throughout the entire modeled region. 
Additionally, under true saturated conditions, most ground-water flow through the TSw model 
unit would be through fractures (and lithophysae), and not through the matrix. 
Spatial Continuity DataModeled variograms for both matrix and lithophysal porosity in the 
TSw model unit are presented in Figure 14. Parameters for both fitted variogram models are 
presented in Table 15. Details of the variogram modeling exercise may be found in the scientific 
notebook (Rautman and McKenna 1998, pp. 437 to 444 and 459 to 464). 
6.4.4.3 CHn Model Unit 
Porosity DataPorosity values obtained from the Calico Hills nonwelded (CHn) model unit are 
presented graphically in Figure 15; the corresponding statistical summary of these data is 
presented in Table 13. 
Spatial Continuity DataA modeled variogram for matrix porosity in the CHn model unit is 
presented in Figure 16. Parameters of the fitted variogram model are presented in Table 16. 
Details of the variogram modeling exercise may be found in the scientific notebook (Rautman and 
McKenna 1998, pp. 534 to 556). 
6.4.4.4 Tcp Model Unit 
Porosity DataPorosity values obtained from the Prow Pass Tuff (Tcp) model unit are presented 
graphically in histogram format in Figure 17; the corresponding statistical summary of these data 
is presented in Table 13. 
Spatial Continuity DataA modeled variogram for matrix porosity in the Tcp model unit is 
presented in Figure 18. Parameters of the fitted variogram model for porosity in the Tcp model 
unit are presented in Table 17. Details of the variogram modeling exercise may be found in the 
scientific notebook (Rautman and McKenna 1998, pp. 704 to 726).

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6.4.5 Statistical Description of Secondary Material Properties 
The secondary, or derivative, material properties considered in this analysis are matrix saturated 
hydraulic conductivity, thermal conductivity, and bulk density (Section 4.1.3). In general, there 
are insufficient individual measurements of these material properties to determine their spatial 
continuity patterns independently of porosity. Accordingly, they have been modeled under the 
presumption that each variable is coregionalized with porosity. This section contains the basic 
statistical description of each derivative material property, including the correlation of that 
property with corresponding porosity measurements, which is used in the coregionalization 
process. 
6.4.5.1Matr ix S aturated H ydraulic Con ductivity 
The histogram of all available laboratory measurements of matrix saturated hydraulic 
conductivity is presented in Figure 19(a). A scatterplot of these same data against the 
Figure 14. Experimental and fitted model variograms for porosity in the TSw model unit. (a) Matrix porosity, 
stratigraphic vertical and (b) stratigraphic horizontal. (c) Lithophysal porosity, stratigraphic 
vertical and (d) stratigraphic horizontal. 
Separation Distance, in feet 
0 100 200 300 400 500 600 
Normal-Score Variogram 
0.0 
0.5 
1.0 
1.5 
Data 
a priori variance 
Model 
TSwMVertVar.wmf 
(a) 
Separation Distance, h, in feet 
0 5000 10000 15000 20000 25000 
Normal-Score Variogram 
0.0 
0.5 
1.0 
1.5 
Data N-S 
Data E-W 
a priori variance 
Model N-S 
Model E-W 
TSwMHorizVar.wmf 
(b) 
Separation Distance, in feet 
0 100 200 300 400 500 600 
Normal-Score Variogram 
0.0 
0.5 
1.0 
1.5 
Data 
a priori variance 
Model 
TSwLVertVar.wmf 
(c) 
Separation Distance, h, in feet 
0 5000 10000 15000 20000 25000 
Normal-Score Variogram 
0.0 
0.5 
1.0 
1.5 
Data N-S 
Data E-W 
a priori variance 
Model N-S 
Model E-W 
TSwLHorizVar.wmf 
(d)

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corresponding laboratory porosity values is shown in part (b) of the figure, and a statistical 
summary of the data is presented in Table 18. 
Table 15. Variogram Parameters for Spatial Continuity Model of Porosity in the TSw Model Unit 
Nest 
No. 
Model 
Type 
Range 
(ft) 
Sill 
Rotation Angle 
(degrees)1 
Anisotropy 
Ratio1 
Maximum 
(horizontal) 
Intermediate 
Minimum 
(vertical) 
1 2 3 1 2 
TSw Model Unit, Matrix Porosity 
-- Nugget -- -- -- 0.01 -- -- -- -- -- 
1 Spherical 250 250 20 0.19 0 0 0 1.000 0.080 
2 Spherical 2,000 6,500 90 0.25 0 0 0 3.250 0.045 
3 Spherical 29,000 12,500 350 0.55 0 0 0 0.431 0.012 
TSw Model Unit, Lithophysal Porosity 
-- Nugget -- -- -- 0.01 -- -- -- -- -- 
1 Spherical 600 400 15 0.19 0 0 0 0.667 0.025 
2 Spherical 5,000 8,000 175 0.20 0 0 0 1.600 0.035 
3 Spherical 38,000 17,000 200 0.60 0 0 0 0.447 0.006 
Note: 1. Rotation angles 13 and anisotropy ratios 12 are keyed to input requirements of the SGSIM computer 
code, as documented in Deutsch and Journel 1992, pp. 167 and 22 to 29. 
Figure 15. Histogram and cumulative distribution function of matrix porosity in the CHn model unit. 
Porosity as a factor 
0.0 0.2 0.4 0.6 
Frequency 
0.00 
0.05 
0.10 
0.15 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
CHnRHpor.wmf

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Figure 19(a) is distinctively multi-modal, and Figure 19(b) indicates four subpopulations that can 
be identified in the matrix hydraulic conductivity data set. Essentially, cluster A consists of 
samples for which the delta-porosity, computed simply as the arithmetic difference between the 
OD and RH laboratory-measured porosity values, is less than 5 percent (0.05). Cluster A 
corresponds to a continuum of hydraulic conductivity values that are rather strongly correlated to 
porosity, as presented separately in Figure 20. Rautman and McKenna (1997, pp. 37 to 40) present 
an expanded discussion of identifying hydrous-phase mineral alteration in core samples through 
the use of delta-porosity values. 
Cluster B in Figure 19(b) contains samples for which the delta-porosity between the OD and 
RH porosity measurements is greater than 5 percent. These are samples that exhibit significant 
hydrous-phase mineral alteration, as evidenced by the removal of moderately large quantities of 
water during drying at 105C. This subpopulation is plotted separately in Figure 21, and it appears 
largely indistinguishable from a normally distributed (gaussian) population if the small group of 
Table 16. Variogram Parameters for Spatial Continuity Model of Porosity in the CHn Model Unit 
Nest 
No. 
Model 
Type 
Range 
(ft) 
Sill 
Rotation Angle 
(degrees)1 
Anisotropy 
Ratio1 
Maximum 
(horizontal) 
Intermediate 
Minimum 
(vertical) 
1 2 3 1 2 
-- Nugget -- -- -- 0.05 -- -- -- -- -- 
1 Spherical 3,000 3,000 30 0.25 1.000 0.010 
2 Spherical 12,000 5,000 400 0.70 0.417 0.033 
Note: 1. Rotation angles 13 and anisotropy ratios 12 are keyed to input requirements of the SGSIM computer 
code, as documented in Deutsch and Journel 1992, pp. 167 and 22 to 29. 
Figure 16. Experimental and fitted model variograms for matrix porosity in the CHn model unit. 
(a) Stratigraphic vertical; (b) stratigraphic horizontal. 
Separation Distance, in feet 
0 50 100 150 200 250 300 350 
Normal-Score Variogram 
0.0 
0.5 
1.0 
1.5 
Data 
a priori Variance 
Model 
CHnVertVar.wmf 
(a) 
Separation Distance, h, in feet 
0 5000 10000 15000 
Normal-Score Variogram 
0.0 
0.5 
1.0 
1.5 
Data N-S 
Data E-W 
a priori Variance 
Model N-S 
Model E-W 
CHnHorizVar.wmf 
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samples with conductivities greater than 106 m/sec are discounted as potentially misclassified 
samples. 
Cluster C of Figure 19(b) is represents a small subset of the entire population of matrix 
hydraulic conductivity measurements for which the corresponding porosity measurement is very 
low, and for which there appears to be no particular correlation of porosity with conductivity. 
These samples are almost exclusively from two vitrophyric lithostratigraphic units: Tptrv1 and 
Tptpv3, Figure 22(a) and (c). Experimentation indicates that almost the identical subset of 
samples can be extracted from the complete hydraulic conductivity data set simply as those 
samples whose measured porosity is less than 5 percent (0.05). These samples are presented in 
Figure 22(b) and (d). Flint (1998, p. 38) interpreted the relatively uniform-random distribution of 
these matrix hydraulic conductivities as caused by microfracturing within these densely welded 
rock types. 
Figure 17. Histogram and cumulative distribution function of matrix porosity in the Tcp model unit. 
Porosity as a factor 
0.0 0.2 0.4 0.6 
Frequency 
0.00 
0.05 
0.10 
0.15 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
TcpRHpor.wmf 
Figure 18. Experimental and fitted model variograms for matrix porosity in the Tcp model unit. (a) 
Stratigraphic vertical; (b) stratigraphic horizontal. 
Separation Distance, in feet 
0 50 100 150 200 250 300 350 
Normal-Score Variogram 
0.0 
0.5 
1.0 
1.5 
Data 
a priori Variance 
Model 
TcpVertVario.wmf 
(a) 
Separation Distance, h, in feet 
0 5000 10000 15000 
Normal-Score Variogram 
0.0 
0.5 
1.0 
1.5 
Data N-S 
Nata E-W 
a priori Variance 
Model N-S 
Model E-W 
TcpHorizVario.wmf 
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Cluster D of Figure 19(b) represents those core samples for which the matrix saturated 
hydraulic conductivity was below the sensitivity limit of the laboratory permeameter. Note that 
these null values have been ignored in all statistical calculations for this modeling exercise. As 
shown in Figure 19, these no-flow samples have been arbitrarily set equal to 1014 m/sec 
(log10 = 14.0) for plotting purposes, both here and elsewhere in this report. 
In contrast to the discussion of Figures 20 and 21, which involves more or less global 
characteristics of the measured matrix saturated hydraulic conductivity measurements from Yucca 
Mountain, a broader objective of this modeling exercise is to reproduce the material property 
characteristics appropriate for individual model units. The ability to discriminate and identify the 
hydraulic conductivity characteristics of specific vitrophyric rock units essentially by looking 
Table 17. Variogram Parameters for Spatial Continuity Model of Porosity in the Tcp Model Unit 
Nest 
No. 
Model 
Type 
Range 
(ft) 
Sill 
Rotation Angle 
(degrees)1 
Anisotropy 
Ratio1 
Maximum 
(horizontal) 
Intermediate 
Minimum 
(vertical) 
1 2 3 1 2 
-- Nugget -- -- -- 0.05 -- -- -- -- -- 
1 Spherical 6,000 4,000 80 0.40 0.667 0.013 
2 Spherical 15,000 10,000 800 0.55 0.667 0.053 
Notes: 1. Rotation angles 13 and anisotropy ratios 12 are keyed to input requirements of the SGSIM computer 
code, as documented in Deutsch and Journel 1992, pp. 167 and 2229. 
, 
log10 (Ksat, m/sec) 
-14 -12 -10 -8 -6 -4 
Frequency 
0.00 
0.02 
0.04 
0.06 
0.08 
0.10 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
Ksat_alldata_hist.wmf 
Figure 19. (a) Histogram of laboratory-measured matrix saturated hydraulic conductivity from core 
samples and (b) crossplot of hydraulic conductivity vs. matrix porosity for the same samples. 
Porosity, as a fraction 
0.0 0.2 0.4 0.6 
log10(Saturated Hydraulic Conductivity, in m/sec) 
-15 
-10 
-5 
(b) A 
B 
C 
D 
(a)

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solely at their porosity characteristics (e.g., Figure 20 and discussion) is one example. Other 
relevant matrix hydraulic conductivity characteristics for purposes of this report are the by-unit 
statistical distributions of values. These target histograms for the individual simulated models of 
the four modeling units are presented in Figure 23 (a) through (d). 
6.4.5.2 Bulk Density 
A histogram of more than 3,000 relative-humidity-oven-dried bulk density values from all four 
model units is presented in Figure 24(a). The composite histogram is distinctly multimodal, as 
might be expected from aggregation of densely welded tuffs with a collection of non- to partially 
welded ash-flow tuffs and nonwelded air-fall tuffaceous debris. 
Table 18. Statistical Summary of Matrix Saturated Hydraulic Conductivity Measurements 
All Data Unaltered Altered 
Mean -8.9553 -8.6536 -9.6805 
Std.Dev. 1.7317 1.7248 1.5269 
Minimum -11.7086 -11.3360 -11.7086 
Maximum -4.6866 -4.6955 -4.6866 
N 405 286 119 
Note: All values in log10 m/sec except number of samples (N); no-flow 
samples omitted. 
Figure 20. (a) Histogram of laboratory-measured matrix saturated hydraulic conductivity from unaltered 
core samples (identified by delta-porosity) and (b) crossplot of hydraulic conductivity vs. matrix 
porosity for the same samples. Conductivity of non-flowing samples set to 10-14 m/sec for 
plotting only. 
log10 (Ksat, m/sec) 
-14 -12 -10 -8 -6 -4 
Frequency 
0.00 
0.02 
0.04 
0.06 
0.08 
0.10 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
Ksat_unalt_hist.wmf 
(a) 
Porosity, as a fraction 
0.0 0.2 0.4 0.6 
Matrix Saturated Hydraulic Conductivity, 
in log10(m/sec) 
-14 
-12 
-10 
-8 
-6 
-4 
-2 
Unaltered 
Regression 
(-14.0 = null) 
r2 = 0.604 
r = +0.777 
Ksat_unalt_xplot.wmf 
(b)

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Despite the compositing of a group of diverse lithologies (and mineralogies) for Figure 24(a), the 
bulk density data appear to belong to a relatively consistent family of values. A scatter diagram 
showing the relationship between the bulk density values and RH-dried porosity is presented in 
Figure 24(b). Although there is some segregation of the cloud of data points into two overlapping 
subpopulations (which can be demonstrated to relate to hydrous-phase mineral alteration), the 
coefficient of determination (r2) value is a very strong 0.912, indicating only somewhat less than 
one-to-one correspondence. Given the generally low importance of bulk density in most 
performance assessment analyses, it has not been determined to be of sufficient importance to 
analyze altered and unaltered bulk densities separately. Unit-specific histograms that serve as the 
target distributions for the coregionalized bulk density models are presented in Figure 25. Model 
unit genesis is reflected clearly in the four parts of the figure: high-density densely welded tuffs in 
the TSw model unit (part (b)), low-density nonwelded and pumiceous rich materials in the PTn 
unit (part (a)), and intermediate-density nonwelded to only partially welded tuffaceous materials 
in the CHn and Tcp model units (parts (c) and (d)). 
6.4.5.3 Thermal Conductivity 
Thermal conductivity and porosity data have been obtained from a modest number of samples 
collected from the PTn and TSw model units. Figure 26(a) presents a histogram and cumulative 
distribution function for these thermal conductivity values measured at 70C and under 105Cdried 
saturation conditions (note that thermal conductivity is a function of both absolute 
temperature and saturation state). The crossplot of these same values in Figure 26(b) clearly 
Figure 21. (a) Histogram of laboratory-measured matrix saturated hydraulic conductivity from altered core 
samples (identified by delta-porosity) and (b) crossplot of hydraulic conductivity vs. matrix 
porosity for the same samples. Conductivity of non-flowing samples set to 10-14 m/sec for 
plotting only. 
log10 (Ksat, m/sec) 
-14 -12 -10 -8 -6 -4 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
0.25 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
Ksat_altd_hist.wmf 
Porosity, as a fraction 
0.0 0.2 0.4 0.6 
Matrix Saturated Hydraulic Conductivity, 
in log10(m/sec) 
-14 
-12 
-10 
-8 
-6 
-4 
-2 
Altered 
-14.0 = null 
Ksat_altd_xplot.wmf 
(a) (b)

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indicates an inverse relationship of thermal conductivity with porosity. A statistical summary of 
these available thermal conductivity data is presented in Table 19. 
There are two significant difficulties in using the existing thermal conductivity data, which is 
derived from laboratory testing on matrix-sized specimens. First, the in-situ bulk density of the 
Topopah Spring welded unit is most directly related to the lithophysal porosity of this unit, not to 
the matrix porosity. Open cavities too large to be measured as part of the matrix porosity 
laboratory procedure (or its petrophysical equivalent) will significantly reduce the whole rock 
bulk density, leading to lower effective thermal conductivity. Previous discussion of porosity data 
from the TSw model unit (Section 6.4.4.2) indicates that the lithophysal porosity values can be 
greater by a factor of two compared with the depth-equivalent matrix porosity values. Use of this 
factor-of-two porosity difference applied to the regression relationship shown in Figure 26(b) 
Figure 22. Scatterplots of matrix saturated hydraulic conductivity versus matrix porosity for (a) core 
samples from vitrophyric lithostratigraphic units Tptrv1 and Tptpv3 and (b) core samples with 
matrix porosity less than 0.05. (c) and (d) Histograms and cumulative distribution functions for 
samples presented in parts (a) and (b), respectively; no-flow samples omitted. 
Porosity, as a fraction 
0.00 0.05 0.10 0.15 0.20 
log10 Sat. Hydraulic Conductivity, in m/sec 
-14 
-12 
-10 
-8 
-6 
-4 
-2 (a) 
KsatVitroUnitXplot.wmf 
Porosity, as a fraction 
0.00 0.05 0.10 0.15 0.20 
log10 Sat. Hydraulic Conductivity, in m/sec 
-14 
-12 
-10 
-8 
-6 
-4 
-2 (b) 
KsatVitroPorXplot.wmf 
log10 (Ksat, m/sec) 
-14 -12 -10 -8 -6 -4 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
0.25 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 (c) 
KsatVitroUnit.wmf 
log10 (Ksat, m/sec) 
-14 -12 -10 -8 -6 -4 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
0.25 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 (d) 
KsatVitroPor.wmf

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would lead to overprediction errors of roughly 30 to 50 percent for thermal conductivity, 
depending on the actual porosity level considered. Given that the thermal conductivity models 
will be coregionalized using lithophysal porosity in an effort to model the in-situ thermal 
conductivity of the rock mass, the phrase whole-rock thermal conductivity will be used in this 
report. 
A second, and rather severe difficulty with the available thermal conductivity data is that the 
density of sampling is not great (a maximum of 52 samples; see Table 19), and furthermore, those 
samples are highly biased both spatially and toward low-porosity materials, as follows: (1) Two of 
four drill holes that were sampled for thermal conductivity specimens, although located within the 
extended site area, are actually located some distance from the region transected by the main part 
of the ESF (NRG-4, NRG-5; see Figure 5). (2) The sampling vertically within a drill hole is not 
systematic, and in fact, the vertical distribution of samples cannot be considered particularly 
Figure 23. Matrix saturated hydraulic conductivity histograms and cumulative distribution functions for (a) 
the PTn, (b) TSw, (c) CHn, and (d) Tcp model units. 
Saturated Hydraulic Conductivity, in log10 m/sec 
-14 -12 -10 -8 -6 -4 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
0.25 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
PTnKsatHist.wmf 
(a) 
Saturated Hydraulic Conductivity, in log10 m/sec 
-14 -12 -10 -8 -6 -4 
Frequency 
0.00 
0.02 
0.04 
0.06 
0.08 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
TSwKsatHist.wmv 
(b) 
Saturated Hydraulic Conductivity, in log10 m/sec 
-14 -12 -10 -8 -6 -4 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
0.25 
0.30 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
CHnKsatHist.wmf 
(c) 
Saturated Hydraulic Conductivity, in log10 m/sec 
-14 -12 -10 -8 -6 -4 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
0.25 
0.30 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
TcpKsatHist.wmf 
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representative of the entire Topopah Spring welded model unit. (3) The only samples that 
represent the higher porosity values (needed to model the effect of lithophysal cavities on heat 
conduction) are taken from the PTn model unit, and thus represent nonwelded tuffs rather than the 
lithophysal portion of welded materials. 
With respect to the several biases known to exist in the thermal conductivity data, consider 
Figure 27 (a), which is a histogram of the 54 porosity values measured on the thermal 
conductivity test specimens (Table 19). Comparison of this figure with the histogram of all 
lithophysal porosity values measured from the TSw model unit (part (b) of the figure) clearly 
indicates the extent of the sampling bias. First, Figure 27(a) is clearly bimodal, representing as it 
does, samples from both welded and nonwelded rock types. If the group of samples with 
porosities higher than about 40 percent (presumably representing nonwelded tuffs) is discounted, 
the mode corresponding to the welded Topopah Spring samples is strongly skewed toward lower 
porosity values. For example, the approximate modal value in Figure 27(a) is 8 to 10 percent, 
whereas the modal value for the TSw model unit as a whole (Figure 27(b)) is 18 to 20 percent for 
lithophysal porosity. 
An attempt to reduce the impact of these sampling biases has been conducted in the following 
manner. First, the regression relationship presented in the scatterplot of Figure 26(b) is assumed to 
be a valid predictor of thermal conductivity across the range of porosity values appropriate for the 
TSw model unit. A systematic prediction of the nominal thermal conductivity of the TSw model 
unit is then generated using the systematically sampled (nominal 3-ft spacing) porosity data 
available for three drill holes located along the ESF main drift (SD-7, -9, and -12; Figure 29). 
These three sets of predicted values are then aggregated and the appropriate statistical quantities 
and histogram are computed (Figure 28; Table 20). The histogram of Figure 28 will be used as the 
target distribution for the coregionalized models. Note that although the mean thermal 
conductivity for both the 35 measured samples of the Topopah Spring welded unit and the 
Figure 24. (a) Histogram and cumulative distribution function of relative-humidity-oven-dried bulk density 
values from all four modeling units. (b) Scatterplot of bulk density as a function of matrix 
porosity for the same data. 
Porosity, as a fraction 
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 
Bulk Density, in g/cm3 
0
1
2
3 
r  = 0.912 
r = -0.955 
BulkDporXplot.wmf 
(b) 
log10 (Ksat, m/sec) 
0 1 2 3 
Frequency 
0.00 
0.02 
0.04 
0.06 
0.08 
0.10 
0.12 
0.14 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
BulkDhist.wmf 
(a)

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systematically predicted thermal conductivity of the TSw model unit as a whole (Table 20) are 
remarkably similar at 1.2 W/m-K (rounded), the local thermal conductivity of major intervals 
within the unit differ markedly from one another (Figure 29). 
6.4.6 Modeling Techniques 
This section contains a summarized yet logically accurate description of the geostatistical 
modeling techniques used to produce the rock properties models, including reference to the 
various computer codes (Table 1) and software routines (Table 2) used to generate the actual 
models. Sequential gaussian simulation is used to generate the primary porosity models, whereas 
linear coregionalization is used to generate the derivative models of secondary properties. 
Indicator kriging is used to produce the model of hydrous-phase mineral alteration that constrains 
the distribution of the derivative models of saturated hydraulic conductivity in two of the model 
units. 
Figure 25. Bulk density histograms for (a) the PTn, (b) TSw, (c) CHn, and (d) Tcp model units. 
Bulk Density, in g/cm3 
0 1 2 3 
Frequency 
0.00 
0.02 
0.04 
0.06 
0.08 
0.10 
0.12 
0.14 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
PTnBulkdHist.wmf 
(a) 
Bulk Density, in g/cm3 
0 1 2 3 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
TswBulkdHist.wmf 
(b) 
Bulk Density, in g/cm3 
0 1 2 3 
Frequency 
0.00 
0.02 
0.04 
0.06 
0.08 
0.10 
0.12 
0.14 
0.16 
0.18 
0.20 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
CHnBulkdHist.wmf 
(c) 
Bulk Density, in g/cm3 
0 1 2 3 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
TcpBulkdHist.wmf 
(d)

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6.4.6.1Discr etization of the Model Dom ain 
Details of the grid defined for all geostatistical modeling are presented in Table 21. The horizontal 
discretization of 200-m by 200-m is tied directly to the horizontal resolution of the unsaturatedzone 
site-scale flow model across its entire areal extent. Vertical resolution of the geostatistical 
grid is also tied to the unsaturated-zone flow model, particularly within the general repository 
volume. Additionally, the total number of grid nodes in the resulting suite of models was 
computationally tractable. 
Table 19. Statistical Summary of Measured Thermal Conductivity Data from Non-Zeolitic Rock Samples 
Thermal Conductivity 
(W/m-K) at 70C and 105C dry Porosity 
(105C) 
All Data TSw Only 
Mean 1.054 1.241 0.197 
Std.Dev. 0.516 0.427 0.156 
Minimum 0.160 0.620 0.040 
Maximum 2.200 2.200 0.610 
N 52 35 54 
Note: All values in Watts per meter-Kelvin (W/m-K) except number of 
samples. 
Figure 26. (a) Histogram and cumulative distribution function for measured thermal conductivity data. 
(b) Scatterplot of thermal conductivity as a function of matrix porosity. All thermal conductivities 
measured at 70C and 105C-dried conditions. Solid line in (b) is regression fit (used in 
Section 6.4.5.3); dashed lines are 95-percent confidence limits. 
Matrix Porosity, as a fraction 
0.0 0.2 0.4 0.6 
Thermal Conductivity, in W/m-K 
0.0 
0.5 
1.0 
1.5 
2.0 
2.5 
3.0 
Kth = 1.5544 -2.4910 f 
r2 = 0.586 
r = -0.766 
ThKporosXplot.wmf 
(b) 
Matrix Thermal Conductivity, in W/m-K 
0.0 0.5 1.0 1.5 2.0 2.5 3.0 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
ThKhisto.wmf 
(a)

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6.4.6.2 Sequential Gaussian Simulation of Porosity 
Geostatistical simulation comprises a large class of modeling techniques that can produce very 
complex, and presumably therefore highly realistic numerical representations of spatially variable 
properties. Simulation may be thought of as expanding the actual information available in a 
stochastic manner that is also compatible with additional information derived from the data 
ensemble and the spatial context of those data. The process builds on the geologic intuition that 
Figure 27. Histograms and cumulative distribution functions for (a) total porosity measured for thermal 
conductivity test specimens and (b) lithophysal porosity from the TSw model unit (repeated 
from Figure 26(b)). 
Matrix Porosity, as a fraction 
0.0 0.2 0.4 0.6 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
ThKPorosHist.wmf 
Porosity, as a fraction 
0.0 0.2 0.4 0.6 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
Cumulative Frequency 0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
TSwL_RHpor.wmf 
(b) 
(a) 
Figure 28. Histogram and cumulative distribution function for thermal conductivity systematically predicted 
from lithophysal porosity values in drill holes USW SD-7, SD-9, and SD-12 using the regression 
relationship from Figure 26(b). 
Thermal Conductivity, in W / m-K 
0.0 0.5 1.0 1.5 2.0 2.5 3.0 
Frequency 
0.00 
0.05 
0.10 
0.15 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
predThKhist.wmf

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unsampled locations nearby a known value will tend to resemble that value, whereas unsampled 
locations at increasing distances from a known measurement tend progressively to resemble that 
datum less and less. This intuition will be observed statistically across a suite of several 
equiprobable simulations. 
The philosophical framework of simulation is simple. Using concepts of random variables, one 
develops a model of the probability density function (pdf) for a material property of interest at all 
locations in space. By transforming the measured data to their respective positions on the 
probability density function and using simple kriging (Deutsch and Journel 1992, pp. 62 and 137), 
the desired pdfs can be made conditional to a set of measured values. Alternative realizations are 
simply generated by sampling from these pdfs. The variance of individual, location-specific, pdfs 
will vary with the amount of geologic uncertainty. Near conditioning data (Figure 30(c)), the pdf 
associated with an unsampled location will be relatively narrow. Where less information is 
known, such as away from data or in the vicinity of conflicting measurements, the pdf will be 
relatively broad (Figure 30(a-b)), leading to generation of a wide range of likely values across a 
suite of realizations. Because the underlying kriging algorithm used to derive the pdfs is an exact 
interpolator, the pdf degenerates to a spike with probability = 1 at a measured location 
(Figure 30(d)). 
Simulations may be conditional or unconditional. Conditional simulations are numerically 
anchored to a specific set of real-world data, and they exhibit three properties that adds to their 
usefulness in evaluating the effects of geologic uncertainty on physical process models. 
Specifically, conditional simulations: 
1. Reproduce the known data values at the same locations within the model as represented by 
the real-world samples 
Table 20. Statistical Comparison of Measured and 
Predicted Thermal Conductivity Data for 
the TSw Model Unit (see text for 
discussion of prediction methodology) 
Measured 
Thermal 
Conductivity 
@ 70C 
Predicted 
Thermal 
Conductivity 
at 70C 
Mean 1.241 1.183 
Std.Dev. 0.4271 0.1822 
Minimum 0.620 0.676 
Maximum 2.200 1.550 
N 35 6063 
Notes: Units are Watts/meter-Kelvin (W/m-K) except 
for number of values (N). 
1. Also includes effect of measurement errors and 
lithologic variability. 
2. Includes effect of lithologic variability only.

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2. Reproduce the full range of measurement variability, as represented by histogram and 
univariate descriptive statistics of the known data values 
3. Reproduce the bivariate statistics, or two-point spatial correlation structure, of the input 
data. 
Unconditional simulations are similar, except that they are not conditioned to any particular 
spatially anchored data, and thus item 1 does not apply. As simulations with these three 
characteristics cannot be distinguished statistically from the ensemble of data used in their 
construction nor from each other, they serve as alternative, equally likely stochastic realizations of 
an incompletely sampled and measured reality shown conceptually in Figure 3. 
Simulations may be developed using parametric or nonparametric techniques for mechanically 
inducing the desired univariate (item 2 above) and bivariate (item 3) statistical properties. 
Parametric techniques rely upon the predictive power of well-understood multivariate probability 
Figure 29. Downhole variation in predicted thermal conductivity values based on systematically measured 
lithophysal porosity data for drill holes (a) USW SD-7, (b) SD-9, and (c) SD-12. Thermal 
conductivity key: predicted thermal conductivity at 70C and 105C-dried conditions. Porosity 
key: dark linelithophysal porosity from petrophysical logs; light grey line with symbolsmatrix 
porosity from core samples. 
USW SD-7 
Po ros ity, frac tion 
0.0 0.2 0.4 0.6 
300 
400 
500 
600 
700 
800 
900 
10 00 
11 00 
12 00 
13 00 
14 00 
Th erm al Condu c tiv ity , W /m -K 
0 1 2 
Depth , feet 
(a) 
sd7predThK.wmf 
(b)
d9 dThK f 
sd9predThK.wmf 
USW SD-12 
Po rosity , fra ctio n 
0.0 0.2 0 .4 0 .6 
300 
400 
500 
600 
700 
800 
900 
1000 
1100 
1200 
1300 
1400 
Thermal Conductiv ity, W /m -K 
0 1 2 De pth , fee t 
(c) 
sd12predThK.wmf

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functions, almost invariably the multivariate gaussian. A number of algorithms have been 
developed that implement gaussian-related simulation (for example, references in Deutsch and 
Journel, 1992). 
The sequential gaussian simulation program SGSIM (Table 1; see also Deutsch and Journel 1992, 
pp. 123 to 125 and 164 to 167) was used to generate 50 replicate models of porosity at all 
unsampled locations for each of the four model units, conditioned to the observed porosity data 
Table 21. Geostatistical Modeling Grid Specification Parameters 
Corresponding to the Southwest Corner of the Grid 
Grid Dimension 
Midpoint 
(ft/m) 
Spacing 
(ft/m) 
No. of 
Nodes 
Total 
Nodes 
Model X 
(Easting) 
549,895.6 
167,600.0 
656.2 
200.0 
34 -- 
Model Y 
(Northing) 
751,349.0 
229,000.0 
656.2 
200.0 
43 -- 
Model Z 
(Stratigraphic 
Vertical) 
PTn 
3.3333 
1.0159 
6.667 
2.032 
30 43,860 
TSw 
8.2025 
2.5000 
16.405 
5.000 
61 89,182 
CHn 
8.4444 
2.5399 
16.666 
5.080 
24 35,088 
Tcp 
8.4444 
2.5399 
16.666 
5.080 
24 35,088 
Probability 
Property Value 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 
(a) (b) (c) (d) 
Figure 30. Conceptual probability density functions representing the uncertainty associated with 
various unsampled locations. (a) Beyond the range of spatial correlation: pdf is virtually 
identical to the univariate histogram; essentially all that is known about the unsampled 
location is what is known about the population as a whole. (b) Far away from a sample, 
but within the range of spatial correlation: pdf is broad, indicating considerable 
uncertainty; distribution begins to focus on expected value. (c) Nearby a sample value: 
pdf is narrower indicating less uncertainty. (d) Immediately adjacent to a sample value: 
pdf is nearly a spike value corresponding to the adjacent sample datum.

Title: Rock Properties Model (RPM3.1) 
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from the several drill holes. The sequential modeling process is relatively straightforward and is 
implemented as follows. 
1. All data values are converted to positions on a univariate standard-normal (=0, s2=1) 
distribution using the graphical normal-score transform (Figure 31), implemented in 
program NSCORE (Table 1; see also Deutsch and Journel 1992, pp. 138 and 209 to 211). 
This transformation does nothing to the spatial correlation structure because the relative 
positions of all values with respect to each other are preserved (i.e., the transform is 
quantile-preserving). 
2. The spatial correlation structure is identified using the normal-score transformed values 
and modeled using standard variography. 
3. The transformed measured data are mapped into the model volume; samples located (only 
fortuitously) at a node in the stratigraphic-coordinate grid are assigned to that node and the 
node is not simulated. 
4. A sequential random path is defined that will visit each unsampled node once and 
only once. 
5. At each node along this path, a search is conducted for nearby data and any previously 
simulated grid nodes. The search parameters (anisotropic radii; number of data to use) are 
user specified. 
6. The (user-specified) N closest data are identified and weighted by their geological 
distance (in contrast to simply their Euclidean distance), as defined in the stratigraphic 
coordinate system according to the mathematical formulation of the spatial continuity 
model (variogram). Because the normal-score transformed values are effectively relative 
positions on a cumulative distribution function, the resultant value is also effectively a 
relative position on the same cumulative distribution function. 
0.0 0.2 0.4 0.6 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
-3 -2 -1 0 1 2 3 
(b) 
Original Variable Transformed Variable 
(a) 
Figure 31. Graphical representation of the quantile-preserving normal-score transform process using 
cumulative distribution functions. A population with virtually any univariate distribution (a) can 
be transformed to any other univariate distribution (b) (here standard gaussian) in a manner 
represented by the arrows such that the quantile relationships among the data are preserved. 
The reverse transformation is also possible in the same manner.

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7. A value (in normal-score space) is drawn at random from the conditional probability 
distribution defined in step 6 and this value is assigned to represent the porosity at that 
point. The simulation process then moves to the next unsampled location along the 
random path defined in step 4 and the process is repeated beginning with step 5. 
8. After all originally unsampled grid nodes have been simulated using the logic of steps 5 
through 7, the resulting spatial array of normal-score values are back-transformed to the 
original porosity space using the inverse of the normal score transform of step 1 (software 
routine BACKTR, Table 2), and the simulation process is complete. 
Because porosity values are drawn at random for each unsampled grid node, the values obtained 
in different simulation runs will be different. Indeed, the weighting scheme used to develop the 
conditional expectation in each independent simulation will be different as well in that the same 
path through the 3-D grid is not used in successive simulations. Additionally, because the datasearch 
process considers previously simulated grid nodes as well as measured data (non-varying), 
the nearby values used to estimate the conditional expectation will also vary among simulation 
runs. At grid locations that are well constrained by consistent measured data, the variability of the 
simulated values across a suite of simulations will be small, as described by the spatial continuity 
model. However, at grid locations far from any conditioning measured data, or at grid nodes that 
are in the vicinity of conflicting measurements, the spread of porosity values that will be 
generated by the simulation algorithm across different computer runs will be quite broad, 
approaching the univariate variance of the data when considered without regard for spatial 
position. Uncertainty, measured by variability across the suite of simulations is small where much 
is known about the rock mass and progressively greater at longer distances from actual sampled 
values. 
6.4.6.3 Indicator Kriging Using Uncertain Data 
The indicator methodology is most easily understood through the following definition of an 
indicator transformation of a spatially distributed variable, Z:
, (Eq. 3) 
where I(x) is the indicator-transformed variable at spatial location x, Z(x) is the original variable 
also at location x, and Z* is a particular threshold value of interest. In other words, the original 
variable is replaced by the value 1 at all locations where it is less than or equal to the threshold 
and by the value 0 at all locations where it is greater. 
All of this presumes that there is precise knowledge of the original variable of interest, Z(x). 
Should knowledge of Z be less than 100-percent certain, however, it is possible to restate 
Equation 3 to account for the soft probability, p, that Z less than or equal to Z*. Thus: 
. (Eq. 4) 
I x ( ) 
1 Z x ( ) Z* = . 
0 Otherwise . . . .
= 
I x ( ) 
p Z x ( ) Z* = . 
1 p  Otherwise . . . .
=

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Note that it is perfectly legitimate to mix hard and soft indicators in the same analysis, and thus 
the methodology is suitable for combining the relatively definitive XRD indicators of hydrousphase 
mineral alteration with the less-certain-but-spatially-more-abundant petrophysical 
indicators (Sections 4.1.4 and 4.1.5, respectively). It remains to calibrate the appropriate value(s) 
of p, given the petrophysical estimates of bound-water content; this calibration effort is described 
below in Section 6.4.7.1. 
Implementation of indicator kriging process (program IK3D, Table 1; see also Deutsch and Journel, 
1998, pp. 103 to 106) is straightforward enough in concept. 
1. Hard XRD measurements of hydrous-phase mineral content are converted to a set of ones 
and zeros with respect to some threshold concentration judged relevant. 
2. Soft petrophysical measurements of hydrous-phase mineral content are converted to a set 
of values ranging between zero and one in accordance with the calibration exercise (using 
program BICALIB, Deutsch and Journel 1998, pp. 235 to 236). 
3. The spatial continuity structure of the composite hard and soft data set is determined 
through standard variography. 
4. The transformed measured data are mapped into the model coordinate system. 
5. At each desired grid location a search is conducted for nearby indicator data, I(x) (either 
hard or soft). 
6. The nearest N values identified by the search are then weighted according to their relative 
geologic distances, as computed from the variogram model. The weighted average is 
assigned as the appropriate indicator value at that location, and the estimation process 
moves to the next grid node. Steps 5 and 6 are iterated until the grid is complete. 
Note that implicit in Equations 3 and 4 is the probabilistic interpretation that p is the likelihood of 
Z(x) being less than the threshold, Z*. If one is dealing with a binary classification in which the 
rock present at location x is either altered versus unaltered, it is a logical conclusion that: 
7. All grid nodes with a modeled probability of p < 0.5 may be considered unaltered, and that 
those with p > 0.5 may be deemed altered. 
6.4.6.4 Coregionalization Modeling of Derivative Properties 
There are two frequently used methods that have been used to incorporate cross-variable 
correlations of material properties into rock properties models in the presence of undersampling 
of one variable. First, one may assume a coefficient of determination (r2) equal to one and 
simply apply the empirically determined regression equation to predict the secondary 
(undersampled) variable. A second method is to model a randomly distributed error (noise) 
about the regression line. However, neither of these two alternatives is particularly satisfying. In 
many instances, r2 = 1.0 implies a substantially stronger relationship than exists in fact. In the 
second case, a cross-plot of the two resulting variables reproduces the desired cross-variable 
relationship, but any spatial correlation exhibited in nature by the secondary variable is effectively 
destroyed by the addition of spatially uncorrelated noise. Cokriging and cosimulation (Journel 
and Huijbregts 1978, pp. 324 to 326; Deutsch and Journel 1992, pp. 121 to 123) are wellestablished 
algorithms for producing models that reproduce both the observed correlation

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between two variables and the observed spatial correlation structure of each. However, in the 
presence of severe undersampling of the secondary variable, such as is the case at Yucca 
Mountain, there are simply insufficient data from which to infer the necessary auto- and crosscorrelation 
relationships. 
A practical alternative mechanism to cokriging or cosimulation in the presence of undersampling 
involves the assumption of a linear model of coregionalization (Journel and Huijbregts 1978, 
pp.171 to 175 and 516 to 517; Luster 1986; Altman et al. 1996, pp. 54 to 59), which effectively 
states that the spatial continuity of the secondary variable, and of the joint (cross-variable) 
correlation structure, is presumed to be approximately identical to that of the primary variable. 
Although the mathematical relationships involved in the derivation are tedious (e.g. Rautman and 
McKenna 1997, pp. 63 to 66, and references therein), it can be shown that it is possible to 
generate a pair of cross-correlated simulations as a weighted linear combination of two 
independent standard-normal spatially correlated simulations where the weighting factor is 
effectively the cross-variable correlation coefficient, r. What this translates to in practical terms, is 
to take a conditional porosity simulation in standard-normal form, such as is generated in step 7 of 
Section 6.4.6.2, and combine it (software routine COREGPC, Table 2) with an identically generated 
but independent unconditional simulation (these are paired in this activity by run number), also in 
standard-normal form, using r and as the appropriate weighting coefficients. The resulting 
linear combination is also essentially in standard normal form, and it can be back-transformed to 
match the desired distribution of the target secondary variable (software routine TRANS, Table 2). 
If appropriate, the back transformed coregionalized property simulation is post-processed further 
to impart additional relevant characteristics as described below in Section 6.4.8. 
6.4.7 Modeling of Hydrous-Phase Mineral Alteration 
Volcanic glass within the lower two modeling units (CHn and Tcp) has been variably altered to 
(dominantly) zeolite minerals throughout a major portion of the model area. These altered rocks 
exhibit markedly reduced saturated hydraulic conductivity by comparison with unaltered 
materials of approximately the same porosity. The rock properties modeling effort attempted to 
include not only the XRD mineralogic data (described in Section 4.1.4), which provide virtually 
100-percent certain identification of hydrous-phase mineral alteration, but also less accurate but 
more abundant and widely distributed petrophysical indicators of such alteration (Section 4.1.5). 
6.4.7.1Calib rating Soft Ind icators of Hyd rous-Phase M ineral A lteration 
Because the petrophysical data available provide a less-than-100-percent certain identification of 
hydrous-phase alteration, it is necessary to calibrate these values to account for the added 
uncertainty. The calibration effort involved 334 samples from the CHn and Tcp model units for 
which depth-matched pairs (generated using software routine MATCHUP, Table 2) of both XRD 
mineral analyses and petrophysical bound-water contents could be obtained. Petrophysical 
bound-water content was calculated simply as the difference between the POROTOT and POREF 
log traces (see also Section 4.1.5). Core bound-water content was calculated as the difference 
between the OD and RH porosity values (Section 4.1.1), and is initially identical to the deltaporosity 
value described in Section 6.4.5.1. Comparison of depth-matched core and petrophysical 
bound-water data (software routine MATCH, Table 2) indicate that the laboratory core measurement 
1 r2 

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process gave a bound-water content of approximately twice that indicated by the down-hole 
petrophysical measurements; see Figure 32. Although a precise explanation for the discrepant 
measurements is uncertain, the empirical relationship can be used to adjust the core measurements 
to provide a common basis with the petrophysical values. Adjusted values for core bound water 
content have been used in the calibration work that follows. 
Figure 33 presents a scatterplot of total hydrous-phase mineral content vs. adjusted bound-water 
content. In general, an increase in adjusted bound-water content corresponds directly to an 
increase in the total hydrous minerals. The calibration consists of cross-tabulating (software 
routine BICALIB, Table 2) the number of pairs in each of the categories: 
 Hydrous-phase mineral content: 
 Greater than 5 percent 
 Less than or equal to 5 percent. 
 Adjusted bound-water content: 
 Less than or equal to 0.03 
 Greater than 0.03 to less than 0.04 
 Greater than 0.04 to less than 0.05 
 Greater than 0.05. 
Figure 32. Scatterplot of core vs. petrophysically derived bound-water content for 354 depth-matched 
pairs of samples. Regression line (solid, with 95-percent confidence limits, dotted) has 
been forced through the origin and has a slope of 1.74; unconstrained regression has r2 = 
0.67 (r-squared for a constrained line is not meaningful). 
Petrophysical Bound-water Fraction 
0.00 0.02 0.04 0.06 0.08 0.10 
Core Bound-water Fraction (delta f) 
0.00 
0.02 
0.04 
0.06 
0.08 
0.10 
0.12 
0.14 
0.16 
0.18 
0.20 
1:1 
2:1 
Petrophysical Bound-water Content

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The cross-tabulated counts of soft-value pairs were converted to a decimal proportion (software 
routine BICALIB), and these values were taken as the prior probability of obtaining the specified 
total hydrous-phase mineral content given a specified adjusted bound-water content. These soft, 
prior-probability values are presented in Table 22. In contrast, XRD hydrous-phase mineral 
contents were coded as hard probability values of zero or one. 
6.4.7.2 Indicator Kriging of Hydrous-Phase Mineral Alteration 
Both hard and soft indicators of hydrous-phase mineral alteration were combined and supplied as 
input to an indicator kriging exercise (program IK3D; Deutsch and Journel, 1998, pp. 103 to 106). 
Indicator kriging (Section 6.4.6.3) is a variant of ordinary kriging, in which the variable of interest 
is estimated as a weighted linear combination (average) of the available observed values within 
some local neighborhood of influence. In common with ordinary kriging, the weights applied to 
the observed values are calculated in accordance with the spatial continuity model developed 
from the combined indicator data set. Necessarily, alteration in the CHn and Tcp model units was 
Table 22. Prior Probability of Altered vs. Unaltered Rocks as a Function of Bound-Water Content 
Hydrous-Phase Mineral Content 
Bound-Water Content, 
Cumulative Prior Probability 
< 0.03 0.03  0.04 0.04  0.05 > 0.05 
< 5 percent 0.2474 0.6122 .7778 0.8625 
> 5 percent 0.7526 0.3878 0.2222 0.1375 
Figure 33. Scatterplot of total hydrous-phase mineral content vs. adjusted bound-water content for 334 
depth-matched paired samples. Interior lines correspond to the various threshold values used 
in Table 22. 
Petrophysical Bound Water Fraction 
0.00 0.05 0.10 
Total Hydrous Minerals, percent 
0 
20 
40 
60 
80 
100 
Core Data 
Non-core Data 
Petrophysical Bound-water Content

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modeled separately, even though the two units were combined for purposes of estimating the prior 
probability values discussed above. 
CHn Model UnitThe variogram model for hydrous-phase mineral alteration indicators in the 
CHn model unit is presented in Figure 34, and the parameters of the fitted variogram model are in 
Table 23. Details of the variogram modeling exercise may be found in the scientific notebook 
(Rautman and McKenna 1998, pp. 663 to 695). 
Table 23. Variogram Parameters for Spatial Continuity Model, Alteration in the CHn and Tcp Model Units 
Nest 
No. 
Model 
Type 
Range 
(ft) 
Sill 
Rotation Angle 
(degrees) 
Anisotropy 
Ratio 
Maximum 
(horizontal) 
Intermediate 
Minimum 
(vertical) 
1 2 3 1 2 
CHn Model Unit 
-- Nugget -- -- -- 0.005 -- -- -- -- -- 
1 Spherical 4000 1500 30 0.010 0 0 0 0.3750 0.0075 
2 Spherical 7000 4000 500 0.035 0 0 0 0.5714 0.0714 
Tcp Model Unit 
-- Nugget -- -- -- 0.010 -- -- -- -- -- 
1 Spherical 2500 2500 150 0.025 0 0 0 1 0.060 
2 Spherical 15000 15000 150 0.058 0 0 0 1 0.010 
Figure 34. Indicator variogram and fitted model computed for alteration in the CHn model units. (a) 
Stratigraphically vertical and (b) stratigraphically horizontal directions. 
Separation Distance, h, in feet 
0 5000 10000 15000 
Variogram 
0.00 
0.02 
0.04 
0.06 
0.08 
0.10 
Data N-S 
Data E-W 
a priori Variance 
Model N-S 
Model E-W 
CHnHorizAltVario.wmf 
(b) 
Separation Distance, in feet 
0 50 100 150 200 250 300 350 
Variogram 
0.00 
0.02 
0.04 
0.06 
0.08 
0.10 
Data 
a priori Variance 
Model 
CHnVertAltVario.wmf 
(a)

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Tcp Model UnitThe variogram model for hydrous-phase mineral alteration indicators in the Tcp 
model unit is presented in Figure 35. The parameters of the fitted variogram model are given in 
Table 23. Details of the variogram modeling exercise may be found in the scientific notebook 
(Rautman and McKenna 1998, pp. 772 to 786). 
6.4.8 Postprocessing of Simulated Models 
6.4.8.1In corporation of S pecific Attributes into Si mulated M odels 
The actual rocks at Yucca Mountain are the composite result of numerous geologic processes that 
overlap in both space and time. Consequently, rock properties modeling involves more than the 
simple generation of a set of porosity values. This is particularly true for the models of derivative 
material properties that have been generated by coregionalization with porosity. This section 
presents the techniques used to incorporate two specific types of secondary geologic attributes 
into raw simulated property models. 
VitrophyresThe widely variable hydraulic conductivity values associates with densely welded 
vitrophyric core samples of uniformly low porosity from the Topopah Spring Tuff 
(lithostratigraphic units Tptrv1 and Tptpv3) have been described by Flint (1998, p. 38) as 
resulting from microfractures present within these glassy, brittle rocks. Additional consideration 
of these samples (Flint 1998, Figure 12) suggests that vitrophyric samples may independently be 
identified by their uniformly very low porosity (less than approximately 0.05; see Section 6.4.5.1, 
Figure 22). Accordingly, the simulated models of saturated hydraulic conductivity for the 
TSw model unit (only) were post-processed (software routine VITROPHYRE, Table 2) such that if 
the corresponding porosity value was less than 0.05 (simulations paired by run number), 
the coregionalized hydraulic conductivity value was discarded. Under the assumption that such 
low-porosity grid nodes represent vitrophyre or other essentially nonporous brittle materials, a 
value of Ks was generated by random sampling from a uniform population with a range of 10-14 to 
Figure 35. Indicator variogram and fitted model computed for alteration in the Tcp model unit. (a) 
Stratigraphically vertical and (b) both stratigraphically horizontal directions (isotropic). 
Separation Distance, in feet 
0 100 200 300 
Variogram 
0.00 
0.05 
0.10 
0.15 
TcpVertAltVario.wmf 
(a) 
Separation Distance, in feet 
0 5000 10000 15000 
Variogram 
0.00 
0.05 
0.10 
0.15 
TcpHoirzAltVario.wmf 
(b)

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10-6 m/sec as derived from the histogram of Figure 22. A conceptual representation of the logic 
underlying the modeling of vitrophyric rocks is presented in Figure 36. 
Hydrous-Phase Mineral AlterationHydrous-phase mineral alteration is inferred to represent a 
secondary alteration process that affected vitric tuffaceous materials at some particular time after 
formation of the original rock mass, although generally before tectonic faulting and tilting. 
Consequently, there appears to be little or no direct correlation of saturated hydraulic conductivity 
with matrix porosity for altered (zeolitized) samples, see Section 6.4.5.1, Figure 21). Recall also 
from Figure 21 that the histogram of altered hydraulic conductivity values appears virtually 
indistinguishable from a gaussian population, given the relatively small sample size. 
This modeling philosophy has been implemented for the rock properties model by postprocessing 
(software routine ZEOLITE5, Table 2) the initial coregionalized hydraulic conductivity models (for 
both the CHn and Tcp model units) grid node by grid node together with a corresponding 
indicator kriging model (Section 6.4.7.2) indicating the probability of significant hydrous-phase 
mineral alteration. If the grid node under consideration was considered unaltered (palt < 0.50), the 
coregionalized Ks value was retained, and the processing moved to the next grid node. If the node 
was considered altered (palt > 0.50), then the coregionalized Ks value was discarded in favor of a 
Figure 36. Logic diagram for post-processing porosity and hydraulic conductivity simulations to recognize 
vitrophyre rock type. See text for discussion.

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normally distributed random value sampled from a population with the appropriate mean and 
variance. A schematic diagram of this postprocessing procedure is presented in Figure 37. 
6.4.8.2 Uncertainty Modeling 
Geostatistical generation of the material property models is essentially complete at this point. As 
part of the current modeling exercise, 50 replicate, statistically indistinguishable models of 
porosity for each model unit (one set each for matrix and lithophysal porosity in the TSw model 
unit) and 50 replicate models for each one of the derivative properties (bulk density, matrix 
saturated hydraulic conductivity, andfor the TSw model unitthermal conductivity as well) 
have been generated. Each of the replicate simulations honors the measured porosity data at 
sample locations (subject to the discretization limits), exhibits the full range of variability 
captured by the histogram of the relevant property, exhibits the appropriate range of spatial 
correlation (variogram), and (for the derivative properties) exhibits the appropriate correlation 
coefficient with porosity. In effect, there is nothing objective about any one simulated (or 
coregionalized) model to prefer it over any other model of that suite. Indeed, the only meaningful 
distinguishing feature within a suite of replicate models is the arbitrarily selected random number 
seed which initiated the simulation process. 
Figure 37. Logic diagram for post-processing porosity and alteration indicator simulations to recognize 
hydraulic conductivity dependence on alteration state. See text for discussion.

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Because there are few, if any, objective differences to distinguish the members of each suite of 
simulated property models, it thus logically follows that the variability among members of a 
suite represents an empirical estimate of the geologic uncertainty associated with each material 
property. Geologic uncertainty is defined in this context as that which results from less-thanexhaustive 
sampling or other measurement. The difficulty arises, however, as how best to 
represent this space of uncertainty in a simple and concise manner. 
An uncertainty model has been generated (software routine ETYPE; Table 2) for each material 
property-modeling unit combination by computing the node-by-node standard deviations of each 
set of 50 replicate simulated models. This process produces uncertainty models that are 
themselves spatially heterogeneous. By theory and in practice, variability among simulations 
and uncertainty as defined by the standard deviationis small in close proximity to measured 
sample values. Variability among simulations and uncertainty is high at great distances from 
measured data, or in the vicinity of conflicting measured values. Note that there is no particular 
reason other than general reader familiarity for selecting the standard deviation as the measure 
of uncertainty. Values such as the total range of the modeled property or the interquartile range 
could easily be computed during this post-processing step. 
With respect to alternative uncertainty models, it is also important to remember that the best 
measure of geologic uncertainty for the potential nuclear-waste repository at Yucca Mountain is 
the impact of that uncertainty on some relevant measure of repository system performance. 
Potential examples of such global performance measures might be particle-tracking travel times 
or cumulative radionuclide release rates, as suggested by the consequence analysis step shown in 
the conceptual diagram of Figure 3. Development of these types of comprehensive uncertainty 
assessments is beyond the scope of the rock properties modeling effort. 
6.4.8.3 Expected-Value Modeling 
The post-processing step used to generate the standard-deviation uncertainty model for each rock 
property-modeling unit combination described in Section 6.4.8.2 is easily adapted to produce 
some type of summary statistical measure associated with the central-tendency of the 
simulation process. In effect, the geostatistical simulation process develops a 3-D array of 
spatially correlated probability density functions, one distribution for each of the discretizing 
grid nodes within a model unit. Continuing with the probability density function analogy, certain 
rock property values are more likely to exist at a given location than other values. Note, however, 
that more likely to exist can be defined in more than one manner. 
A set of summary expected-value models has been generated (software routine ETYPE; Table 2) 
for each suite of simulated models by calculating the arithmetic mean of the 50 replicate 
simulated values generated at each grid node. Journel (1983, pp. 459 to 461; see also Deutsch 
and Journel 1992, pp. 76 and 225) defined this conditional expectation representation of central 
tendency as the E-type estimate. Note that computing the median (M-type estimate, Journel 
1983, p. 460) of the 50 replicate simulated values would be an equally legitimate measure of 
expectation, although one that is somewhat more computationally intensive.

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Because of the logistical difficulty of presenting the full simulated results for 50 models times 
19 unique material-property/model-unit combinations, the results of this geostatistical modeling 
exercise described in Section 6.5 that follows are presented in terms of the E-type estimate. It is 
important to remember, however, that the three characteristic properties of simulated models 
described as desirable in the first paragraph of Section 6.4.6.2 no longer necessarily apply to 
these summary models. Compare, for example, the statistical nature of the simulated and 
summary models from ISM2, as discussed by Rautman and McKenna (1997, e.g., pp. 99 to 104), 
and in abbreviated form for ISM3 as presented in the discussion of model validation in 
Section 6.7, below. 
The first characteristic, that involving reproduction of the measured (porosity) values at the 
locations of actual measurement, is maintained. However, the ensemble of modeled E-type 
values no longer represents the full range of univariate variability of the measurement ensemble 
(the second characteristic). Additionally, the two-point spatial correlation character (variogram) 
of the E-type model no longer reproduces that of the underlying measurements (the third 
characteristic). Specifically, because of averaging across the replicate simulations, the E-type 
model typically grades relatively smoothly and continuously from one (exactly reproduced) 
measured value to the next (in three dimensions). Thus the apparent spatial continuity of the Etype 
model typically is much greater than that observed for the data themselves. This is the socalled 
smoothing effect that is typical of virtually all interpolation (in contrast to simulation) 
algorithms, including kriging, nearest-neighbor estimation, and inverse-distance-to-a-power 
weighting. 
6.5 RESULTS AND DISCUSSION 
The real results of the rock properties modeling exercise consist of the numerical model files 
containing the replicate Monte Carlo simulated models and the associated summary E-type and 
uncertainty model files for each of the four modeling units and each of the modeled properties. 
Because of the impracticality of presenting and discussing each of these simulated and summary 
models individually, the results presented in this section are illustrative and focus on gross 
heterogeneity features as revealed by the summary E-type models. Each model unit and each 
modeled material property within that model unit is discussed in turn. Discussion of the replicate 
individual simulated models is generally restricted to the section on Model Validation. Again, 
because of the impracticality of validating each and every replicate simulation, the discussion 
in this section will be illustrative. 
Because of technical limitations involving plotting the individual drill holes on some model 
views, refer to Figures 4 though 7 for information regarding the spatial distribution of input 
measurements. Note that the distribution of available drill hole information is unit-specific. Also 
note that although the color-scale legend on each figure generally represents the full range of the 
modeled property present in the underlying numerical file, it is only fortuitous if the highest (or 
lowest) value is actually shown in the particular model view. 

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6.5.1 PTn Model Unit 
Heterogeneity of matrix porosity within the PTn model unit is shown in Figure 38 in both 
stratigraphic and real-world coordinates. As indicated by the projection arrows connecting the 
two halves of the figure, the vertically exaggerated rectangular volume in stratigraphic 
coordinates is back transformed to real-world coordinates, such that the material property values 
assume their correct relative positions within the tilted and faulted strata of Yucca Mountain, 
shown with no vertical exaggeration. Cross-sectional views of porosity heterogeneity are 
presented in Figure 39. 
Porosity values within the PTn model unit are generally high, varying principally from about 30 
to more than 60 percent (0.30 to 0.60). Porosity values appear relatively continuous over 
distances of 5,000 to 10,000 feet, as expected from the input range of spatial continuity. Porosity 
trends are prominently anisotropic from northwest to southeast, also as expected from the 
variogram model (top surface of the block diagram of Figure 38). 
Bulk density (Figure 40) varies spatially approximately inversely with porosity, as expected from 
the strong (r = 0.912) negative correlation coefficient. Bulk density values vary from less than 
1.0 g/cm3 to nearly 2.0 g/cm3. Densities are generally low across the modeled area. Prominent 
regions of higher density are associated with drill hole H-6, shown on the southernmost east-west 
cross section, and particularly with drill hole G-2 near the northern boundary of the modeled 
region at the intersection of the north-south and northernmost east-west cross sections. At the G-2 
locality, density exceeds 1.9 g/cm3 at two horizons, presumably corresponding to the Pah Canyon 
and Yucca Mountain Tuffs, which are described as moderately welded in this part of the model 
area. 
Heterogeneity in matrix saturated hydraulic conductivity values is shown in Figure 41. Hydraulic 
conductivity values are generally between 105 and 107 m/sec (note that in this and following 
similar figures, hydraulic conductivity values are shown in log10 units; i.e., 10-7 m/sec = 7.000). 
Lower conductivities on the order of 108 m/sec are modeled in the vicinities of drill hole H-6 
(not visible in figure) and G-2, coincident with the lower matrix porosities in these regions from 
which the hydraulic conductivity values are coregionalized. 
6.5.2 TSw Model Unit 
Heterogeneity of material properties within the TSw model unit is presented in Figures 42 to 48. 
Note that matrix porosity, as indicated in Figure 42 and 43, is very low, mostly less than 10 to 
15 percent, and relatively constant in magnitude across the entire modeled region. This minimal 
variability is consistent with the definition of this unit as densely welded tuff. However, the front 
face of the block diagram, shown in stratigraphic coordinates in Figure 42, and the cross-section 
views of Figure 43 indicate that increased matrix porosity is associated with the major 
lithophysae-bearing intervals within the unit, and most particularly with what in the GFM would 
be the vapor-phase corroded crystal-rich nonlithophysal interval near the top of the unit. 

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Figure 38. Perspective diagrams showing E-type model matrix porosity in the PTn model unit in both 
stratigraphic and real-world coordinates. Light-grey objects in real-world-coordinate view are 
drill holes and workings of the ESF. Easting and northing values are Nevada state plane 
coordinates in feet. 
ESF 
Nevada State Plane 
Coordinates

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Figure 39. Cross-sectional views showing E-type heterogeneity in matrix porosity in the PTn model unit in 
stratigraphic coordinates. Vertical exaggeration 10x.

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Figure 40. Cross-sectional view showing E-type heterogeneity of bulk density in the PTn model unit in 
stratigraphic coordinates. Vertical exaggeration 10x.

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Figure 41. Cross-sectional views showing E-type heterogeneity in matrix saturated hydraulic conductivity in 
the PTn model unit in stratigraphic coordinates. Vertical exaggeration 10x. 
Approximate Location of G-2 
Approximate 
Location of H-6

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ESF 
Figure 42. Perspective diagrams showing E-type model matrix porosity in the TSw model unit in both 
stratigraphic and real-world coordinates. Light-grey objects in real-world-coordinate view are drill 
holes and workings of the ESF. Easting and northing values are Nevada state plane coordinates 
in feet. Note compressed porosity scale compared with Figure 44. 
Nevada State Plane 
Coordinates

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Figure 43. Cross-sectional views showing E-type heterogeneity of matrix porosity in the TSw model unit in 
stratigraphic coordinates. Vertical exaggeration 10x.

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Figure 44. Perspective diagrams showing E-type model lithophysal porosity in the TSw model unit in both 
stratigraphic and real-world coordinates. Light-grey objects in real-world-coordinate view are 
drill holes and workings of the ESF. Easting and northing values are Nevada state plane 
coordinates in feet. Note expanded porosity scale compared with Figure 42. 
ESF 
Nevada State Plane 
Coordinates

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Figure 45. Cross-sectional views showing E-type heterogeneity of lithophysal porosity in the TSw model 
unit in stratigraphic coordinates. Vertical exaggeration 5x.

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Figure 46. Cross-sectional views showing E-type heterogeneity of bulk density in the TSw model unit in 
stratigraphic coordinates. Vertical exaggeration 5x.

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Figure 47. Cross-sectional views showing E-type heterogeneity of thermal conductivity in the TSw model 
unit in stratigraphic coordinates. Vertical exaggeration 5x.

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Figure 48. Cross-sectional views showing E-type heterogeneity of matrix saturated hydraulic conductivity 
in the TSw model unit in stratigraphic coordinates. Vertical exaggeration 5x.

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The heterogeneity of lithophysal porosity, in contrast to the matrix porosity, is shown in Figure 
44 as perspective views, and in Figure 45 in cross-sectional view. Although even lithophysal 
porosity is generally low compared to the porosity of a nonwelded welded tuff, such as the PTn 
model unit, maximum porosity values within the lithophysal intervals locally exceed 30 to 
35 percent (0.30 to 0.35). Figure 45 clearly indicates two such intervals of high porosity, 
corresponding approximately to the upper and lower lithostratigraphic units (Tptpul and Tptpll), 
separated by a low-porosity (on the order of 10 percent) interval equivalent to the middle 
nonlithophysal lithostratigraphic unit (Tptpmn). Note however, that there is a fairly large amount 
of lateral heterogeneity within each of the elevated porosity intervals. It is the measured porosity 
data themselves, as propagated away from drill hole locations by the spatial continuity model, 
that produce both the apparent layering and the variations within those layers. There are no 
detailed lithostratigraphic (or other) subunits explicitly modeled within the TSw model unit. All 
property heterogeneity in the rock properties model are functions strictly of the measured 
material properties. 
Bulk density heterogeneity, which is coregionalized from lithophysal porosity, is illustrated in 
Figure 46. Density values are typically above 2.0 g/cm3 throughout most of the relatively 
lithophysae-free region. Bulk density is particularly high (approaching 2.5 g/cm3) in the lower 
parts of the TSw model unit, as indicated by the red colors on the figure. A prominent high 
density interval is associated with the lower vitrophyre in the central part of the modeled region 
(approximately corresponding to lithostratigraphic unit Tptpv3). However, bulk-rock density 
values associated with the upper lithophysal horizon in particular may be as low as 1.5 to 1.8 g/ 
cm3. The alternation of lithophysal and nonlithophysal intervals are particularly clearly 
visualized through the bulk density model 
Thermal conductivity is also coregionalized from lithophysal porosity, in an effort to predict the 
thermal conductivity of volumes of rock influenced by the presence of lithophysal cavities one 
decimeter or larger in diameter. Figure 47 presents the E-type model of spatial heterogeneity in 
thermal conductivity. High values of thermal conductivity (greater than approximately 1.3 to 
1.4 W/m-K and shown in yellow and orange tones) are associated with the lower portion of the 
TSw model unit, and with the presumed low-lithophysae middle nonlithophysal 
lithostratigraphic unit (Tptpmn). Particularly high thermal conductivity values, approaching 1.5 
W/m-K, are present at the very base of the TSw unit, presumably associated with the densely 
welded vitric lithostratigraphic unit. In contrast, the most lithophysal portions of the unit, which 
contain lithophysal cavities up to a meter in diameter, appear to be characterized by bulk-rock 
thermal conductivities less than 1.0 W/m-K (blue and blue-green colors in Figure 47). 
Heterogeneity in matrix saturated hydraulic conductivity is presented in Figure 48, and has been 
coregionalized from the matrix porosity model shown in Figures 42 and 43. Matrix 
conductivities are less than 1011 m/sec through much of the lower part of the model unit. As 
expected from the higher matrix porosity values associated with the lithophysae-bearing portions 
of the TSw model unit, matrix hydraulic conductivity values are markedly higher, 109 to 1010 
m/sec (yellow to green tones), in these vapor-phase altered portions of the unit. Some of these 
higher conductivity values may also be associated with vapor-phase corrosion of the welded tuff 
within the crystal-rich nonlithophysal unit. Note, however, that matrix hydraulic conductivity

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does not include conductivity attributable to flow through lithophysal cavities or fractures under 
true saturated conditions. 
6.5.3 CHn Model Unit 
Variations in the matrix porosity of the CHn model unit are presented in Figures 49 and 50. 
Porosity values are generally high at 20 to 40 percent (0.20 to 0.40) throughout the unit, 
particularly in contrast to the low porosity values typical of the overlying TSw model unit (0.10 
to 0.15). Expanding the porosity color scale indicates that a mass of particularly high porosity 
occupies the central portion of the modeled volume. Porosity values locally approach 50 percent 
(0.50) within this region. 
Variations in bulk density in the CHn model unit are presented in Figure 51. Density values vary 
from more than 2.0 g/cm3 to less than 1.3 g/cm3, depending upon location, although the majority 
of this nonwelded unit exhibits limited variation in bulk density at 1.5 to 1.75 g/cm3. Generally 
speaking, bulk density varies inversely with porosity, as anticipated from the coregionalization 
relationship. 
Heterogeneity in matrix saturated hydraulic conductivity for the CHn model unit is illustrated in 
Figure 52. Although hydraulic conductivity is derived by coregionalization with matrix porosity, 
the relationship between the two material properties is not precisely straightforward because of 
the presence of hydrous-phase mineral alteration (predominantly zeolitic) within the unit. Matrix 
conductivities are typically 106 to 107 m/sec (greens to reds) within the unaltered portion of the 
CHn, and typically less than 1011 m/sec elsewhere (blue). The block diagram in the upper part 
of Figure 52 clearly indicates that vitric (to potentially devitrified) materials are limited to the 
upper portion of the model unit, and more particularly to the southwestern portion of the modeled 
volume. The overall impression is of a wedge of vitric (unaltered) material tapering to a feather 
edge toward the northeast. Zeolitic (altered) rocks are shown in tones of blue underlying and 
replacing the green- through red-colored volume to the north. Recall that the saturated hydraulic 
conductivity of altered samples are essentially uncorrelated with matrix porosity. The lower 
portion of Figure 52 presents cross-sectional views of the hydraulic conductivity field within the 
model unit, and attempts to illustrate some of the complex interfingering relationships of altered 
and unaltered rock types. 
6.5.4 Tcp Model Unit 
Figures 53 and 54 present the spatial heterogeneity of matrix porosity within the Tcp model unit. 
Because the Prow Pass Tuff is mostly nonwelded, the porosity values are typically high, varying 
from 20 to nearly 40 percent across large volumes of the model. Lower porosity values, typically 
less than 15 percent (0.15), are present along the northern boundary of the modeled volume, and 
as a poorly defined lobate mass (indicated by the 0.15 porosity isoshell), which may correspond 
to the moderately welded portion of this unit, generally low within the central-eastern part of 
the region. 
Variations in bulk density, shown in Figure 55, substantiate the variations in porosity described in 
the preceding paragraph. Densities well in excess of 2.1 g/cm3 are prominently displayed along

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ESF 
Cross-Block Drift 
Nevada State Plane 
Coordinates 
Figure 49. Perspective diagrams showing E-type model matrix porosity in the CHn model unit in both 
stratigraphic and real-world-coordinates. Light-grey objects in real-world-coordinate view are 
drill holes and workings of the ESF. Easting and northing values are Nevada state plane 
coordinates in feet.

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Figure 50. Cross-sectional views showing E-type heterogeneity of matrix porosity in the CHn model unit in 
stratigraphic coordinates. Vertical exaggeration 10x.

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Figure 51. Cross-sectional views showing E-type heterogeneity of bulk density in the CHn model unit in 
stratigraphic coordinates. Vertical exaggeration 10x.

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Figure 52. Block and cross-sectional views showing E-type heterogeneity of matrix saturated hydraulic 
conductivity in the CHn model unit in stratigraphic coordinates. Vertical exaggeration 10x. 

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ESF 
Cross-Block Drift 
Nevada State Plane 
Coordinates 
Figure 53. Perspective diagrams showing E-type model matrix porosity in the Tcp model unit in both 
stratigraphic and real-world coordinates. Light-grey objects in real-world-coordinate view are 
drill holes and workings of the ESF. Easting and northing values are Nevada state plane 
coordinates in feet.

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Figure 54. Cross-sectional views showing E-type heterogeneity of matrix porosity in the Tcp model unit in 
stratigraphic coordinates. Vertical exaggeration 10x. Note adjusted porosity scale in lower 
figure. Objects extending away from cross sections in lower figure are isoshells enclosing all 
regions of lowest porosity (less than approximately 0.15).

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Figure 55. Cross-sectional views showing E-type heterogeneity of bulk density in the Tcp model unit in 
stratigraphic coordinates. Vertical exaggeration 10x. 
Approximate Location of G-2

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the northern boundary of the model in the vicinity of drill hole G-2. Higher densities on the order 
of 2.0 g/cm3 are also visible in the east-central portion of the block, corresponding to the low 
porosity lobe. Elsewhere across the modeled volume, bulk densities are more typically between 
1.75 and 2.0 g/cm3 and are shown in green colors. 
Heterogeneity in matrix saturated hydraulic conductivity is presented in Figure 56. In a manner 
similar to the overlying CHn model unit, a bimodal distribution of conductivity values, 
corresponding to altered and unaltered rock types, is quite prominent. Lower hydraulic 
conductivity values, typically less than 1010 m/sec are associated with regions affected by 
hydrous-phase mineral alteration. Markedly higher values of hydraulic conductivity, varying 
from 1010 to 107 m/sec, are associated with the vitric-to-devitrified continuum of matrix 
porosity values in regions unaffected by alteration. The block diagram in the upper portion of 
Figure 56 indicates that the upper and lower margins of the Prow Pass Tuff are essentially 
completely altered. Reference to the cross-sectional views in the lower half of the figure indicates 
that the unaltered portions of the unit correspond to the devitrified interior core of the ash flow. 
6.6 UNCERTAINTIES AND LIMITATIONS 
Uncertainty, in the context of a stochastic modeling analysis, assumes a specific meaning as a 
descriptor of ones state of knowledge, in that a quantitative assessment of uncertainty is 
typically one of the explicit objectives of the analysis. This meaning is in contrast to another 
possible definition, which is expressed more precisely as involving limitation or doubt as to the 
accuracy or relevance of a result. This distinction is maintained in this report. This section first 
describes a number of limitations of both methodology and data that detract from the exactness 
or accuracy of the models generated by this analysis. The results of a stochastic uncertainty 
analysis is then presented, which attempts to quantify rigorously the space of geologic 
uncertainty that results from less-than-completely exhaustive site characterization. 
6.6.1 Limitations 
There are a number of factors affecting this analysis that may best be described as limitations of 
the data or of the modeling process itself. These limitations include errors and biases in the 
sample data used in the analysis, the methodological use of porosity as a surrogate for other 
material properties, the combination of numerous lithostratigraphic units into the four major 
modeling units, and the effect of geologic departures from the assumptions inherent in the use of 
the stratigraphic coordinate system. 
6.6.1.1 Errors and Biases in Sample Data 
Stochastic simulation is a statistical-probabilistic methodology, with reproduction of various 
target statistical measures an important part. As such, errors (uncertainties) incorporated into 
the statistical description of the rock mass unquestionably will be propagated through the 
simulation process into the output models. These errors are of two principal types: measurement 
error and systematic bias.

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Figure 56. Block diagram and cross-sectional views showing E-type heterogeneity of matrix saturated 
hydraulic conductivity in the Tcp model unit in stratigraphic coordinates. Vertical exaggeration 
10x.

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Measurement error or analytical uncertainty in the input data is not addressed in these rock 
property models. Philosophically, the underlying assumption is that measurement uncertainty, 
such as would be captured by replicate measurements of a given material property on the same 
physical sample, is small compared to the lateral heterogeneity of the actual rock mass. It is also 
assumed that these measurement types of errors are essentially unbiased, such that some may be 
high whereas others may be correspondingly low. Statistically, this assumption may be stated 
that the errors are of mean zero with a small relative variance. 
Systematic biases, on the other hand, represent a more severe challenge for rock properties 
modeling using a statistical-probabilistic approach. Two examples of systematic bias within the 
data sets used for this modeling activity are known, and have been compensated for to some 
extent during creation of the individual simulated models. These biases are discussed in the 
following paragraphs. 
Measurement Sensitivity LimitsMeasurement of the matrix saturated hydraulic conductivity 
values for core samples appears to have had a lower detection limit of roughly 1012 to 1011 
m/sec. Samples whose hydraulic conductivity are lower than this lower limit are reported in the 
data set as no flow. Omitting these samples entirely would lead to an unrealistically high set of 
modeled hydraulic conductivity values. On the other hand, substituting the no-flow samples with 
an arbitrary low value prior to the simulation process would tend to skew the results towards that 
arbitrary low conductivity. Therefore, as described in Section 6.4.7, the effect of these no-flow 
samples has been simulated explicitly during post-processing by setting the appropriate fraction 
of values equal to the arbitrary value of 1014 m/sec at randomly selected grid nodes within each 
model unit. This fix to approximate the non-negligible number of non-flowing laboratory 
samples assumes that there is no particular spatial correlation among these samples. Some of 
these samples, or additional immediately adjoining samples, more recently have been retested in 
a permeameter with a lower detection limit somewhat less that 1013 m/sec, but these revised 
values for the non-flowing samples have not been incorporated into the current generation of 
rock properties models. 
Preferential Sampling BiasAnother, more pronounced example of preferential bias in the 
target sample population involves the whole-rock thermal conductivity modeling. As described 
originally by Rautman and McKenna (1997, pp. 40 to 43), the laboratory measurements of 
thermal conductivity are systematically biased by preferential sampling of more coherent, 
generally lower-porosity/higher thermal conductivity, core specimens. This bias was identified 
by differences in the histograms of porosity for those laboratory thermal-test specimens (Figure 
27) versus the overall histogram of porosity for the Topopah Spring welded unit. An additional 
confounding influence with respect to thermal conductivity is the effect of larger-than-core-size 
lithophysal cavities on the thermal conductivity of the rock mass as a whole. An attempt was 
made to reduce the impact of this identified sampling bias for thermal conductivity by 
constructing an unbiased reference distribution (see Rautman and McKenna 1997, pp. 40 to 
43) of thermal conductivity values for simulation using a porosity-weighted distribution of 
estimated thermal conductivities (Section 6.4.5.3), where the porosity values were obtained by 
relatively rigorous systematic sampling of the entire TSw model unit. 

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Similar sampling bias also affects matrix hydraulic conductivity determinations, in that 
laboratory testing is skewed slightly toward measurements of the more conductive samples (low 
permeability samples take longer to run) in certain drill holes. This bias was not addressed 
explicitly in this modeling work as the total number of laboratory hydraulic conductivity 
determinations is quite large (400-plus) compared to thermal conductivity (~50 total; 35 for the 
TSw model unit), and several drill holes (especially UZ-16, SD-9) were sampled on a quite 
systematic basis for the hydraulic property (compare, for example, the locations and measured 
values of hydraulic conductivity specimens sampled from SD-9 (Rautman and Engstrom 1996b, 
Figure 11) with the corresponding information for SD-7 (Rautman and Engstrom 1996a, 
Figure 9)). 
6.6.1.2 Porosity as a Surrogate 
A fundamental limitation of the rock properties modeling effort clearly is the use of porosity as a 
surrogate for derivative properties of more general interest to design and performance 
assessment analysts (Section 5). These derivative properties, such as matrix saturated hydraulic 
conductivity, are related to the principal modeled property only through a correlation coefficient, 
generally indicated as r. To the extent that the absolute value of r is less than one (recall that r = 
1.0 implies a perfect inverse relationship), this modeling of a surrogate thus increases the 
uncertainty in the secondary properties. Nevertheless, use of a non-zero correlation coefficient 
combined with incorporation of spatial correlation in the modeling of those secondary properties 
works to decrease uncertainty in those secondary properties. This is in contrast to modeling 
methodologies that discount either or both of these observable statistical characteristics. 
Knowing that a particular region exhibits high porosity values most likely translates to higherthan-
average matrix permeability in the same region (a positive r-value). However, actual 
measured values of derivative properties are not reproduced within the simulated 
(coregionalized) models in the same manner that measured porosity values located at a grid node 
are reproduced by construction. Again, the real issue is whether the modeled uncertainty in 
material properties translates to unacceptable uncertainty in an objective performance measure 
when evaluated over a number of statistically indistinguishable simulated models (Figure 3). 
Another limitation induced by the modeling process into the rock properties models through the 
porosity-as-a-surrogate mechanism involves those hydraulic conductivity values that are not 
correlated with porosity. Flint (1998, Figures 12(a) and (b)) describes a group of low-porosity 
samples that exhibit apparently random permeabilities with respect to their uniformly low 
porosity values, and Flint interprets these samples as exhibiting behavior consistent with the 
existence of microfractures, largely in vitrophyric rocks (lithostratigraphic units Tptrv1 and 
Tptpv3). The implication is that the permeability measured is not truly a matrix property, even 
though microfracture-related flow is measurable at the core scale. These erratic, out-of-porositycharacter 
permeability values have been modeled as a random overprint imposed only on 
extremely low-porosity (< 0.05) grid nodes (interpreted as representing vitrophyre). Because the 
entire sampled population of microfractured vitrophyre-like samples consists of a mere dozen 
or so individuals, it is simply impossible to determine if these values are spatially correlated in 
their own right. However, to the extent that the measured data truly represent vitrophyre as a 
rock type (geologically restricted to the upper (Tptrv1) and lower (Tptpv3) margins of the TSw 
unit), it is thus possible to generate microfractured permeability values at inappropriate spatial

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locations within the TSw model unit. This limitation is presumed to be relatively minor, as the 
restriction of generating these values to extremely low-porosity grid nodes (typically between 
five and seven percent of the TSw grid) suggests that such rocks might be susceptible to 
microfracturing even though they would not belong to the vitrophyre-type small-scale 
lithostratigraphic units (see also Flint 1998, Figures 12(a) and (b)). Additionally, conditioning of 
the interior of the TSw model unit to porosity values substantially in excess of 0.05 produces 
models that are very unlikely to exhibit extremely low porosity values except near the margins 
where measured porosities of this magnitude are observed. 
A somewhat similar limitation affects the modeling of altered hydraulic conductivity values 
within the CHn and Tcp model units. Although the style of hydrous-mineral-phase alteration 
responsible for these reduced matrix permeability values is clearly correlated spatially 
(Section 6.4.7.2), it is unclear whether the permeability values themselves within those altered 
regions are correlated. Adequate, spatially distributed measured Ks data do not exist to provide 
an estimate of the spatial correlation structure of permeability itself in these materials. In any 
event, as there is no reliable relationship between porosity and matrix permeability for these 
altered specimens, it is unclear what would serve as a surrogate for modeling spatial continuity 
for these materials. Accordingly, the spatial distribution of altered permeability has been treated 
as random within the spatial envelope of altered rocks, and the affected grid nodes merely 
assigned values sampled from a normal population with the appropriate mean and variance. To 
the extent that altered permeabilities are, in fact, spatially correlated, this modeling approach 
increases uncertainty. Across the full suite of simulated models, however, the variability of rock 
properties (and presumably of process modeling results as well) is likely to be greater than had 
the properties been spatially correlated, thus allowing a quantitative evaluation of the 
consequences of that increased space of uncertainty. 
6.6.1.3 Underestimation of Porosity and Hydraulic Conductivity in the TSw Model Unit 
Another limitation related somewhat to the use of porosity as a surrogate for hydraulic 
conductivity affects modeling of parts of the TSw model unit. Recall from Section 6.4.4.2 that 
for non-cored drill holes in this model unit, the available petrophysical data were able to provide 
only an estimate of lithophysal porosity, because the density logging tool is sensitive to the total 
amount of void space in the rock mass, including the influence of large lithophysal cavities. 
Accordingly, a surrogate for porosity-as-a-surrogate was adopted whereby the water-filled 
porosity data from the computed VWC trace were inserted into the matrix porosity data files for 
the named lithophysal zones only. Because matrix saturations, particularly in the crystal-rich 
lithophysal zone (Tptrl) and crystal-poor upper lithophysal zone (Tptpul) are less than one where 
these units are present above the static water level, substitution of the VWC data for matrix 
porosity underestimates the true matrix porosity (such as would be obtained from core) of the 
rock (see Figure 12). Coregionalization of matrix saturated hydraulic conductivity from porosity 
models conditioned to these lowered matrix porosity data produces models of Ks that are 
systematically somewhat low in localized regions. 
The impact of this limitation on the overall material property models is probably somewhat 
limited. First, the effect is limited almost exclusively to the upper lithophysal intervals (Tptrl and 
Tptpul), as matrix saturations within the crystal-poor lower lithophysal zone (Tptpll) are

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typically sufficiently high that there is little mismatch between measured core porosity values 
and the water-filled porosity (VWC) measurements (see Figure 12). Second, the matter becomes 
an issue only for areas populated by non-cored drill holes. The immediate Yucca Mountain-ESF 
area is dominated by drill holes for which core samples were obtained (Figure 5). Close within 
the range of influence of these cored holes, the porosity (and hydraulic conductivity) models are 
strongly conditioned by the presence of laboratory measured matrix porosity data. Furthermore, 
examination of Figure 5 indicates that the principal holes lacking core, the WT- series, are 
located primarily in regions near the periphery or surrounding the volume modeled by the rock 
properties model. It is presumed that these regions are of less direct interest in the evaluation of 
the Yucca Mountain site. Third, the additional uncertainty caused by this substitution of VWC 
data for measured matrix porosity values has already been incorporated into the simulated 
models. For regions near the main part of the ESF where non-cored drill holes (such as H-5, 
Figure 5) compete with cored holes (e.g., SD-9), any discordance between the laboratory 
measurements and the VWC substitute will result in the simulation algorithm generating a wider 
range of simulated values (in the appropriate stratigraphic interval) than would be the case in the 
absence of that discordance. The space of uncertainty, as measured across the suite of 
simulations (Figure 3), has been increased, which is a realistic reflection of the state of 
knowledge associated with the limitations imposed by the use of non-core drilling techniques: 
the matrix porosity is unknown. 
6.6.1.4 Use of Major Stratigraphic Units as Modeling Units 
A quite different, but potentially significant limitation of the approach used in development of 
the rock properties model is the use of composite major stratigraphic intervals and an internal 
stratigraphic coordinate system as the geometric basis for modeling. There are only four such 
model units; compare these to the virtual plethora of different lithostratigraphic units tabulated in 
Table 10. To the extent that the stratigraphic coordinate transformation for each of these major 
modeling units does not reposition equivalent parts of the model unit at the same stratigraphic 
position, the model will attempt to simulate continuity (improperly) between rocks formed at 
significantly different pressure-temperature conditions. These attempts will create an increase of 
uncertainty across the suite of replicate simulations as the simulation algorithm tries to resolve 
any inconsistency of the measured material properties in between drill hole locations. 
This limitation is probably of minimal effect within the major ash-flow units at Yucca Mountain, 
particularly for the Topopah Spring welded unit, which was effectively an instantaneous deposit 
of massive proportions. Although the rock unit thins southward away from its source, the same 
physical/chemical conditions responsible for the ultimate physical properties of the rock almost 
certainly varied with relative vertical position within the cooling rock mass. The same logical 
argument applies to a large extent to the Prow Pass Tuff modeling unit, and (to a lesser degree) to 
the multiple-cooling-unit Calico Hills nonwelded interval. 
The justification for treating the PTn modeling interval as a single rock properties unit is 
somewhat weaker, as this modeling unit contains two distinctly different, significant if only 
locally, developed pyroclastic-flow deposits (the Pah Canyon and Yucca Mountain Tuffs), 
separated by intervals of unrelated and even reworked volcanic materials. The decision to model 
a single PTn entity is based on two factors: (1) In general, the properties of the rocks within the

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PTn unit are quite similar (almost all nonwelded tuffaceous materials, particularly within the 
region transected by the main part of the ESF), and especially in comparison with over- and 
underlying materials. (2) The individual genetic units are typically very thin, leading not only to 
a vastly increased bookkeeping task for selecting and tracking sample data butmore 
importantlyto markedly reduced statistical mass relevant to any one unit. Ultimately the 
choice to represent the PTn model unit as a whole was a pragmatic determination, presumably 
suitable for modeling at the site scale, although perhaps not appropriate for more detailed use. 
6.6.1.5 Faulting, Erosion, and the Stratigraphic Coordinate System 
Another limitation related to the use of a stratigraphic coordinate system is that the presence of 
erosional unconformities or within-unit faulting will work to confound the petrologic and 
material-property equivalence of rocks assigned the same stratigraphic (vertical) coordinates. 
Faults are known to affect several of the drill holes at Yucca Mountain, specifically WT-1, 
WT-11, ONC-1, and UZ-7a. Drill hole p#1 is affected by erosion, and Moyer and Geslin (1995, 
pp. 8 to 31) report progressive lateral truncation of inferred depositional units within the Calico 
Hills Formation and Prow Pass Tuff across the model area. The effects of fault displacements 
have been included in the computation of stratigraphic coordinates based on the best available 
information, and in all cases, this compensation involves the same separations and uncertainties 
as the GFM (GFM3). The locations and extents of erosional complexities are probably less well 
constrained than the effects of faulting. However, in all cases, there should be no discontinuities 
between the adjustments to stratigraphic coordinates applied to the rock properties modeling 
effort and the representation of the GFM. 
A factor working to offset uncertainties related to the stratigraphic coordinate transformation is 
that all of the properties modeling activities were conducted within that conceptual and 
mathematical framework. Specifically, the quantitative description of spatial correlation 
behavior (variograms) was conducted after conversion to stratigraphic coordinates. If undetected 
faulting or erosion worked to juxtapose samples of differing rock properties, the observed range 
of spatial correlation should be reduced, and this higher lateral variability would be reflected in 
the simulated property models. For a given set of conditioning data, a lesser degree of spatial 
correlation will also translate into more variability across the suite of realizations, and thus more 
uncertainty is (accurately) reflected in the suite of simulated models. 
6.6.2 Stochastic Uncertainty Assessment 
The entire rock properties modeling effort has been designed as one method for quantifying the 
geologic uncertaintythat which results from less-than-exhaustive site characterizationin the 
material properties used in downstream design and performance assessment analyses. The 
stochastic simulation process is intended to generate an arbitrary number of individual rock 
property models, each one of which reproduces the measured site characterization data and 
exhibits the full range of heterogeneity and spatial continuity observed in those data. This 
uncertainty in material properties then must be propagated into uncertainty in some particular 
performance measure, through some relevant consequence analysis, as depicted in the 
conceptual representation of a Monte Carlo modeling process presented in Figure 3.

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Because the emphasis in a geostatistical modeling analysis such as this one is on the joint 
characteristics of heterogeneity and spatial continuity, it logically follows that estimates of 
uncertainty are spatially variable as well. By theory and intuition, uncertainty as a statement of 
confidence is low in the immediate vicinity of observations, where the effect of conditioning the 
simulated models to measured property values leads to the construction of well-constrained 
probability density functions. At great distances from measured values, the probability density 
functions are less well constrained, which leads to the generation of more disparate values when 
considered across a suite of simulations. The space of uncertainty is greater. However, even at 
these locations, there is the constraint imposed by the statistical character of the data ensemble as 
a whole. At a minimum the unconditional probability density function is effectively equal to the 
histogram of all relevant measured values, in contrast to the uniform distribution of all physically 
possible values. 
The influence of spatial correlation in the modeling process further works to reduce uncertainty, 
regardless of the presence or absence of observed information in the vicinity. Because the 
simulated models are built sequentially, inclusion of previously simulated grid nodes in the local 
search neighborhood used in constructing the probability density function means that low values 
are likely to be generated in the vicinity of other low values and high values are likely to be 
generated near other highs. Note, however, that this relationship is not absolute. Because the 
value at each simulated grid node is derived by random sampling from the relevant probability 
density function, there is a finite chance within any one realization at each node of generating an 
unusual value from the tails of the distribution. Because the properties at any unsampled 
location are, in fact, not known, it is possible that the true property value might be quite different 
from the expectation. Across multiple simulations, it is therefore possible to account 
quantitatively for the performance or design consequences of that uncertainty by propagating 
variations in input properties through numerical process models to describe uncertainty in 
performance measures (Figure 3). 
6.6.2.1 Expectations versus Individual Outcomes 
These comments regarding the representation of spatial uncertainty related to less-thanexhaustive 
site characterization apply to the individual stochastically simulated rock property 
models. In addition to these individual simulations or outcomes, summary type models have 
been created that correspond to the mathematical expectation of a probability distribution. These 
summary models were generated by computing the node-by-node arithmetic mean value of the 
suite of individual simulations (50 in the present case), and these are typically referred to as 
E-type models. 
Note, however, that simply because a value is mathematically the most likely does not mean 
that value is the appropriate value to use for a particular purpose. In fact, the expected value 
may be a very unlikely value for any actual realization or outcome. The mathematical 
expectation of one-half where zero is heads and one is tails does not mean that the result of 
tossing a coin is most likely to be standing on edge. In similar manner, an expected porosity 
value of 0.20 at a particular grid location does not necessarily imply that 0.20 is the value of 
porosity that should be entered into a numerical flow-and-transport model at this location. It 
means that over a (large) number of individual simulated outcomes, the average simulated

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porosity at the location, individual values of which may have varied from, say, 5 to 45 percent, 
was 0.20. What those simulated values were, however, is discarded in the summary process. 
The limitations of E-type models, which are in common with the shortcomings of most 
interpolation-type modeling algorithms in representing the real world, are fairly well known. For 
example, the range of variability is always reduced with respect to variability of the input data 
(the so-called smoothing effect). Modeled values outside the limits of the measured values 
generally are impossible, even though it is rather unlikely that physical sampling has actually 
encountered the absolute highest or lowest value present in the real world. Also, the apparent 
strength of spatial correlation is typically much greater (a consequence of smoothing). And 
finally, the consequences of applying a numerical physical-process algorithm to a smoothed 
input property field may be very different from the results of applying that same algorithm to one 
(or more) of the underlying more realistically varying individual outcome models. This effect 
may be particularly important in performance assessment analyses, for which the expected 
behavior of the physical system is of less interest than high-consequence/low probability events 
representing the tails of a probability density function. Also, the flow consequences of smoothly 
varying (i.e., continuous) material properties may be quite different than the consequences of a 
more heterogeneous property representation. 
6.6.2.2 Summary Uncertainty Models 
Uncertainty in rock material properties should be evaluated rigorously in terms of the 
consequences of that variability on a particular computed performance measure. However, the 
post-processing step that produces the E-type models is easily adapted to generate models of 
spatially distributed variability across the suite of simulations. Such a spatially varying 
representation may be thought of as a first-order uncertainty model. 
This type of summary model has been generated for this modeling activity as the node-by-node 
standard deviations of the 50 individual simulated rock property models. There is no particular 
reason to prefer the standard deviation approach other than general user familiarity. It would also 
be possible to represent in one summary model the variability of individual stochastic 
simulations through use of the inter-quartile range or the tenth-to-ninetieth-percentile difference. 
In almost any such uncertainty model, the magnitude of the spatially varying uncertainty will 
decrease effectively to zero at sample locations and increase to some maximum value at great 
distances from conditioning samples or in close proximity to samples exhibiting conflicting 
values. In all cases, it is important to separate conceptually the difference between spatial 
heterogeneity and uncertainty. 
PTn Model UnitA block view of the PTn model unit in stratigraphic coordinates is presented in 
Figure 57 showing the uncertainty model of porosity for this unit. Uncertainty is generally low 
(shown in blue colors) in the immediate vicinity of drill holes containing conditioning 
measurements (Figure 4), and increases to higher values away from these locations. Uncertainty 
is spatially heterogeneous within the model as well. However, because most drill holes penetrate 
most of each unit, the general pattern of heterogeneity in uncertainty will be that exhibited on the 
top surface of the model unit.

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Figure 57. Uncertainty model showing E-type standard deviation of matrix porosity in the PTn model unit. 
Color scale is in porosity units as a fraction. Vertical exaggeration 10x. 
Legibility of the coordinates can be deduced from Figure 42 on 
page 95 of this document.

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TSw Model UnitBlock models presenting the uncertainty models of matrix and lithophysal 
porosity in the TSw model unit are presented in Figures 58 and 59, respectively. Uncertainty in 
the figures is calculated as the node-by-node standard deviation of the replicate simulated 
material property models. As anticipated, uncertainty is lowest in the vicinity of drill holes 
containing conditioning measurements (Figure 5), and it increases away from those drill hole 
locations. Note that there are slight differences in the uncertainty models for matrix and 
lithophysal porosity, even though drill hole coverage at this stratigraphic level is essentially 
identical. As is typical in many real-world data sets, the variance (standard deviation) is a 
function of the magnitude of the variable under consideration. 
CHn Model UnitThe uncertainty model for matrix porosity in the CHn model unit is presented 
in Figure 60, again as the node-by-node standard deviation of the 50 replicate simulated models of 
this property. Low values of uncertainty are indicated by the shades of blue, and these regions are 
associated with the drill holes containing conditioning data that penetrate this model unit 
(Figure 6). Spatial heterogeneity of uncertainty can be seen on the front face of the block model. 
However, the dominant pattern of uncertainty will be vertically downward associated with the 
vertical drill holes. 
Tcp Model UnitA block view of uncertainty in matrix porosity for the Tcp model unit, as 
computed as the standard deviation of the replicate simulated models, is presented in Figure 61. 
Uncertainty is lowest in the immediate vicinity of the drill holes penetrating this unit (Figure 7), 
and increases away from these locations of conditioning data. It is interesting to note the marked 
increase in uncertainty within the Tcp model unit, in comparison with the uncertainty model for 
the CHn model unit presented previously in Figure 60. This increase is most noticeable in the 
northeast corner of the modeled volume (note also the increase in the maximum value of the 
standard deviation in these two figures, colored red on the color scale). The cause of this marked 
change in uncertainty is the loss of drill hole WT-16 from the Tcp data set (compare Figures 6 
and 7, showing the drill hole locations). Additional increases in modeled uncertainty, 
particularly in the eastern portion of the area, in the Tcp model unit result from the loss of drill 
holes WT-14 and WT-15 (outside the modeled volume) and drill hole ONC-1 (within the 
volume). 
6.7 MODEL VALIDATION 
A fundamental premise of the Monte Carlo simulation approach is that each individual 
realization is a plausible model of the unknown real world and that variation among the different 
stochastic realizations represents a probabilistic distribution of outcomes consistent with all that 
is known. Presumably, the only meaningful difference between realization 1 and realization N is 
that a different random number seed was used to initiate the simulation process (definition of 
random path and initialization of random number generators). Recalling that conditional 
simulations theoretically possess the attributes of data reproduction (including reproduction of 
ensemble statistical character) described in Section 6.4.6.2, it should be possible to test the 
validity of the individual simulated models in terms of statistical similarity to the data, by 
examining the three relevant criteria for simulated models specified in Section 6.4.6.2: 
1. Reproduction of the known data values at the same locations within the model as 
represented by the real-world samples

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Figure 58. Uncertainty model showing E-type standard deviation of matrix porosity in the TSw model unit. 
Color scale is in porosity units as a fraction. Vertical exaggeration 5x. 
Legibility of the coordinates can be deduced from Figure 42 on 
page 95 of this document.

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Figure 59. Uncertainty model showing E-type standard deviation of lithophysal porosity in the TSw model 
unit. Color scale is in porosity units as a fraction. Vertical exaggeration 10x. 
Legibility of the coordinates can be deduced from Figure 42 on 
page 95 of this document.

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Figure 60. Uncertainty model showing E-type standard deviation of matrix porosity in the CHn model unit. 
Color scale is in porosity units as a fraction. Vertical exaggeration 10x. 
Legibility of the coordinates can be deduced from Figure 42 on 
page 95 of this document.

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Legibility of the coordinates can be deduced from Figure 42 on 
page 95 of this document. 
Figure 61. Uncertainty model showing E-type standard deviation of matrix porosity in the Tcp model unit. 
Color scale is in porosity units as a fraction. Vertical exaggeration 10x.

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2. Reproduction of the full range of measurement variability, as represented by the 
univariate descriptive statistics of the known data values (the histogram) 
3. Reproduction of the bivariate statistics, or two-point spatial correlation structure, of the 
input data (the variogram). 
Because of the large number of suites of simulated models generated for the rock properties 
model, it is impractical to present validation statistics for every material property-model unit 
combination. Instead, illustrative examples validating selected simulated suites will be 
presented here. Similar validation exercises for all the material property models constituting 
RPM3 may be found in the scientific notebook covering this modeling activity (Rautman 1999). 
6.7.1 Validation of TSw Lithophysal Porosity and Whole-Rock Thermal Conductivity 
Criterion number 1 (above) for validating a descriptive model consists of reproducing the known 
data values at the same locations within the model as represented by the real-world samples. 
Satisfaction of this criterion can be demonstrated by extracting a vertical profile through the 
modeled volume at a drill hole location and comparing that property profile to the measured 
property values that were used to condition the simulation process. Although this comparison is, 
perhaps, somewhat simple-minded, a numerical property model that does not reproduce 
measured values at the locations of those values can be demonstrated to be a distortion of the 
known reality, and can potentially be considered invalidated. 
In practice, reproduction of measured drill hole data by a material property model is only 
approximate, principally because the model can only represents rock properties at discrete grid 
locations (656-ft/200-m horizontal spacing in RPM3). Depending upon the distance from the 
drill hole to the nearest set of grid nodes, a certain amount of completely expectable variation 
from the actual measured values may be introduced into the comparison. Recall also that a 
simulated model is generated by sampling at random from the locally conditioned probability 
density function appropriate for that grid node. Nevertheless, the model should reproduce fairly 
accurately the major features of the measured values, particularly when several individual 
simulations are considered. An odd property value sampled by chance from a tail of the 
conditional probability density function, even a well constrained one located near a conditioning 
datum, in one stochastic simulation is unlikely to be repeated in multiple simulations. Therefore, 
the summary E-type model, which summarizes the entire suite of simulated models, should 
reproduce the measured values fairly closely, even accounting for a modest mismatch between 
the locations of the drill hole and the vertical grid nodes comprising the profile. 
Figure 62 presents three drill hole profiles extracted from five different simulations of lithophysal 
porosity for the TSw model unit. For each profile, the detailed (nominal 3-ft spacing) measured 
porosity data are shown, as are the discretized model (~16-ft vertical spacing) porosities for 
each different simulation. Also shown for comparison is the E-type porosity model (also 
discretized, but shown as a continuous curve for clarity on the figure). The distance from each 
drill hole to the nearest set of grid nodes is shown on the figure for reference. Note that an 
argument could be made (for the five simulations shown) that the inter-simulation variability 
exhibited at drill hole G-4 (66 ft distant) appears somewhat less than the variation present at drill 
hole SD-7 (332 ft distant). 

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Figure 62. Lithophysal porosity profiles extracted from five simulated models of the TSw model unit, 
showing comparison of results with the measured lithophysal porosity values and with the 
results for the E-type model. (a) SD-7, (b) G-4, (c) H-5. 
Distance to Grid: 332 ft 
Porosity, as a fraction 
0.0 0.2 0.4 0.6 
Stratigraphic Depth 
0 
200 
400 
600 
800 
1000 
(a) Distance to Grid: 259 ft 
Porosity, as a fraction 
0.0 0.2 0.4 0.6 
0 
200 
400 
600 
800 
1000 
Data 
Sim. 03 
Sim. 17 
Sim. 23 
Sim. 34 
Sim. 47 
E-type 
(c) 
G-4: TSw 
Distance to Grid: 66 ft 
Porosity, as a fraction 
0.0 0.2 0.4 0.6 
0 
200 
400 
600 
800 
1000 
(b)

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With respect to validation criterion 2, which deals with reproduction of the ensemble statistical 
character of the data, Figure 63 presents histograms of four different simulations of lithophysal 
porosity (parts (a) through (d)). Also shown for comparison are the histograms of the input 
conditioning data values (part (e) of the figure), and of the summary E-type model (part (f)). The 
figure clearly indicates quite exact reproduction of the input histogram by the several simulated 
models. This is particularly so given that the input histogram is, in fact, only a sampling of all the 
potential measurements of lithophysal porosity that could be obtained from the Yucca Mountain 
site. In contrast, the histogram of the E-type summary model is distinctly more normal in 
character, and the tails of the distribution (both high and low values) are noticeable compressed 
in comparison with the measured data. In fact, reduction of the high-valued tail is quite marked. 
This is despite the fact that the mean porosity of both simulations/data and the E-type model is 
virtually identical at 0.12. 
Figure 64 presents variograms summarizing the spatial continuity pattern of the simulated models 
of lithophysal porosity for the TSw model unit. Reproduction of the bivariate statistical character 
or spatial correlation structure of the measured data is criterion 3 proposed for validation of a 
descriptive model. These figures present the average variogram across all 50 replicate 
simulations, together with the plus/minus one standard deviation values. 
According to the figure, reproduction of the input model variogram (Table 15) is quite excellent 
in the vertical and north-south directions. Reproduction of the input model is somewhat less in 
the east-west direction of minimum horizontal connectivity, with the overall model indicating a 
longer range of correlation in this direction, and therefore less horizontal anisotropy than had 
been modeled. However, note that the average variogram, in fact, approximates the experimental 
variogram derived directly from the data at the longer lag separations, especially those around 
12,000 to 13,000 ft. Presumably there is something about the conditioning data values 
themselves that (1) causes the experimental variogram to decrease from its higher values at 
slightly shorter lag distances and (2) constrains the simulation algorithm to produce a more 
continuous continuity structure in the east-west direction. Note that in each part of Figure 64, the 
computed variogram for the E-type summary model indicates a markedly longer range of 
correlation than either the experimental variogram or the variograms of the simulated models. 
This behavior is typical of E-type models, as the smoothing effect increases the apparent 
continuity of the values. 
6.7.2 Validation of TSw Thermal Conductivity Models 
Validation of the simulated thermal conductivity models for the TSw model unit is complicated 
somewhat by the very nature of these coregionalized representations. Thermal conductivity is 
severely undersampled at Yucca Mountain (the TSw model unit is represented by only 35 
samples (Table 19). Because of the way the coregionalization process has been implemented in 
this modeling exercise, there are no conditioning thermal conductivity data against which one 
can judge the validity of these models via criterion 1. Also, because of the mechanics of the 
coregionalization process itself, the spatial continuity patterns or variogram of the thermal 
conductivity values as a whole will be essentially identical to that of the lithophysal porosity 
models from which the coregionalization was performed. Criterion 3 is thus functionally not 
applicable as well.

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Figure 63. Histograms and summary statistics of four randomly selected individual simulations of 
lithophysal porosity in the TSw model unit (a)(d), compared to the original porosity 
measurements (e) and the E-type summary (f). 
(a) (b) 
(c) (d) 
(e) (f) 
Frequency 
Porosity, as a fraction 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 
0.000 
0.040 
0.080 
0.120 
TSw Lithophysal Porosity; Sim. 18 Number of Data89182 
mean 0.1437 
std. dev. 0.0675 
coef. of var 0.4698 
maximum0.5593 
upper quartile0.1840 
median 0.1390 
lower quartile 0.0940 
minimum0.0002 
Frequency 
Porosity, as a fraction 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 
0.000 
0.040 
0.080 
0.120 TSw Lithophysal Porosity; Sim. 23 Number of Data89182 
mean 0.1432 
std. dev. 0.0695 
coef. of var 0.4856 
maximum 0.5491 
upper quartile0.1850 
median 0.1380 
lower quartile 0.0920 
minimum0.0006 
Frequency 
Porosity, as a fraction 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 
0.000 
0.040 
0.080 
0.120 
TSw Lithophysal Porosity; Sim. 34 Number of Data89182 
mean 0.1425 
std. dev. 0.0686 
coef. of var 0.4814 
maximum0.5502 
upper quartile0.1840 
median 0.1380 
lower quartile 0.0920 
minimum.00001 
Frequency 
Porosity, as a fraction 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 
0.000 
0.040 
0.080 
0.120 
TSw Lithophysal Porosity; Sim. 45 Number of Data89182 
mean 0.1438 
std. dev. 0.0685 
coef. of var 0.4762 
maximum0.5472 
upper quartile0.1850 
median 0.1390 
lower quartile0.0940 
minimum0.0010 
Frequency 
Porosity, as a fraction 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 
0.000 
0.020 
0.040 
0.060 
0.080 
0.100 
TSw Lithoph Poros (POREF) Number of Data11796 
number trimmed235 
mean 0.1462 
std. dev. 0.0757 
coef. of var 0.5180 
maximum0.5510 
upper quartile0.1900 
median 0.1380 
lower quartile0.0900 
minimum0.0010 
Frequency 
Porosity, as a fraction 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 
0.000 
0.040 
0.080 
0.120 
0.160 
TSw Lithoph. Porosity E-type Model Number of Data89182 
mean 0.1423 
std. dev. 0.0471 
coef. of var 0.3311 
maximum0.4214 
upper quartile0.1725 
median 0.1437 
lower quartile0.1100 
minimum0.0035 
TRI-6115-965-0 
TSwLithoporHists.wmf

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Figure 65 addresses criterion 2, and the figure presents histograms and summary statistics for four 
individual coregionalized simulations, plus the target histogram reproduced from Figure 28. 
Again, similar to the case with lithophysal porosity, Figure 65 also presents the histogram and 
statistics of the E-type summary model. As was the case above for the underlying lithophysal 
porosity values, reproduction of the input measurements by the various simulated models is 
excellent. The normalization of the histogram of the E-type summary model (part (f) of the 
figure) is even more pronounced than was the case for the lithophysal porosity. 
One other criterion bears on validation of coregionalized models, such as these for thermal 
conductivity: the cross-variable correlation with the underlying primary property model. 
Figure 66 presents a crossplot of thermal conductivity versus lithophysal porosity for 
Figure 64. Reproduction of input variograms for simulated lithophysal porosity models for the TSw model 
unit: (a) stratigraphic vertical; (b) stratigraphic horizontal, azimuth = 0; (c) stratigraphic 
horizontal, azimuth = 90. Line with error bars is average variogram with plus/minus one 
standard deviation. Heavy solid line without error bars is input model. E-type model 
normalized by variance. 
Vertical Separation, in feet 
0 100 200 300 400 
Gamma 
0.0 
0.5 
1.0 
1.5 
Mean Simulation 
Input Model 
Data 
E-type Model 
(a) 
TSwPorValVario1.wmf 
Separation, in feet 
0 5000 10000 15000 20000 
Gamma 
0.0 
0.5 
1.0 
1.5 
Mean Simulation 
Input Model 
Data 
E-type Model 
(b) 
TSwPorValVario2.wmf 
Separation, in feet 
0 5000 10000 15000 20000 
Gamma 
0.0 
0.5 
1.0 
1.5 
Mean Simulation 
Input Model 
Data 
E-type Model 
(c) 
TSwPorValVario3.wmf

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Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 131 of 150 
Figure 65. Histograms and summary statistics of four randomly selected individual simulations of thermal 
conductivity in the TSw model unit (a)(d), compared to the original thermal conductivity 
measurements (e) and the E-type summary model (f). Note: the identical statistics of parts (a) 
through (d) are correct. 
(a) (b) 
(c) (d) 
(e) (f) 
Frequency 
Thermal Conductivity, W/m-K 
0.00 1.00 2.00 3.00 
0.000 
0.040 
0.080 
0.120 
Simulated TSw Thermal K; Sim. 18 Number of Data89182 
mean 1.1831 
std. dev. 0.1822 
coef. of var 0.1540 
maximum2.1147 
upper quartile1.3285 
median 1.2034 
lower quartile1.0550 
minimum0.0000 
Frequency 
Thermal Conductivity, W/m-K 
0.00 1.00 2.00 3.00 
0.000 
0.040 
0.080 
0.120 
Simulated TSw Thermal K; Sim. 23 Number of Data89182 
mean 1.1831 
std. dev. 0.1822 
coef. of var 0.1540 
maximum2.1147 
upper quartile1.3285 
median 1.2034 
lower quartile 1.0550 
minimum0.0000 
Frequency 
Thermal Conductivity, W/m-K 
0.00 1.00 2.00 3.00 
0.000 
0.040 
0.080 
0.120 
Simulated TSw Thermal K; Sim. 34 Number of Data89182 
mean 1.1831 
std. dev. 0.1822 
coef. of var 0.1540 
maximum 2.1147 
upper quartile1.3285 
median 1.2034 
lower quartile 1.0550 
minimum 0.0000 
Frequency 
Thermal Conductivity, W/m-K 
0.00 1.00 2.00 3.00 
0.000 
0.040 
0.080 
0.120 
Simulated TSw Thermal K; Sim. 45 Number of Data89182 
mean 1.1831 
std. dev. 0.1822 
coef. of var 0.1540 
maximum2.1147 
upper quartile1.3285 
median 1.2034 
lower quartile1.0550 
minimum0.0000 
Frequency 
Thermal Conductivity, W/m-K 
0.00 1.00 2.00 3.00 
0.000 
0.040 
0.080 
0.120 
Simulated TSw Thermal K Number of Data6063 
mean 1.1831 
std. dev. 0.1819 
coef. of var 0.1538 
maximum1.5502 
upper quartile1.3285 
median 1.2032 
lower quartile1.0550 
minimum0 .6761 
Frequency 
Thermal Conductivity, W/m-K 
0.00 1.00 2.00 3.00 
0.000 
0.050 
0.100 
0.150 
0.200 
TSw Thermal Conductivity E-type Model Number of Data89182 
mean 1.1831 
std. dev. 0.0976 
coef. of var 0.0825 
maximum1.5098 
upper quartile1.2500 
median 1.1781 
lower quartile1.1210 
minimum0.7732 
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Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 132 of 150 
one randomly selected coregionalized model. From Figure 26, the target correlation coefficient is 
0.776 (based on an r2 value of 0.586 with a negative slope). As indicated on Figure 66(a), the 
actual correlation coefficient is 0.746, which appears quite good, considering that the target 
value is derived from a correlation of laboratory-sized core specimens whereas the simulated 
model is based on an implied large-scale correlation of lithophysal porosity with whole-rock 
thermal conductivity. Figure 66(b) presents the same cross-variable correlation plot for the E-type 
models of lithophysal porosity and thermal conductivity. For this comparison, the actual 
correlation coefficient is 0.983, markedly in excess of the target value of 0.746. The crosssimulation 
averaging process involved in constructing the E-type models has induced a nearly 
one-to-one correspondence between the two material properties. 
6.7.3 Validation of Matrix Porosity in the CHn Model Unit 
Validation profiles for matrix porosity in the CHn model unit are presented in Figure 67, in order 
to allow evaluation of criterion 1 for this part of the rock properties model. Again, the format is to 
present vertical profiles extracted from 5 different simulated models at drill hole locations, and to 
compare those simulated values with both the measured RH porosity data and with the values 
extracted from the E-type summary model. 
Although there are fewer distinctive features in the porosity data profiles within the CHn model 
unit than there were for the TSw unit, reproduction of both the general magnitude of porosity and 
of what features there are is quite good. Note, particularly, reproduction of the relatively large 
Figure 66. Crossplot showing (a) cross-variable correlation between coregionalized thermal conductivity 
and the underlying lithophysal porosity simulation (5-percent subsample) and (b) cross-variable 
correlation for the equivalent E-type models. Compare Figure 26(b). 
Porosity, as a fraction 
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 
Thermal Conductivity, in W/m-K 
0
1
2
3 
r  = 0.557 
r = -0.746 
ThKlithoPorValid.wmf 
(a) 
Porosity, as a fraction 
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 
Thermal Conductivity, in W/m-K 
0
1
2
3 
r2 = 0.966 
r = -0.983 
ThKlithoPorEtypeValid.wmf 
(b)

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 133 of 150 
Figure 67. Matrix porosity profiles extracted from five simulated models of the CHn model unit, showing 
comparison of results with the measured lithophysal porosity values and with the results for the 
E-type model. (a) SD-7, (b) SD-9, (c) H-5. 
Distance to Grid: 332 ft 
Porosity, as a fraction 
0.0 0.2 0.4 0.6 
Stratigraphic Depth 
0 
100 
200 
300 
400 
(a) Distance to Grid: 259 ft 
Porosity, as a fraction 
0.0 0.2 0.4 0.6 
0 
100 
200 
300 
400 
(b) Distance to Grid: 259 ft 
Porosity, as a fraction 
0.0 0.2 0.4 0.6 
0 
100 
200 
300 
400 
Data 
Sim. 06 
Sim. 13 
Sim. 29 
Sim. 31 
Sim. 42 
E-type 
(c)

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 134 of 150 
wavelength porosity features in drill hole SD-7 (part (a) of Figure 67). Reproduction of shorter 
wavelength features deeper in that same drill hole are not particularly well reproduced. However, 
in this latter case, the wavelength of the porosity excursions is approximately the same as the 
grid discretization (5 m/16 ft). The missing data values (offscale) just below a stratigraphic depth 
of 300 feet in drill hole H-5 (part (c)) provide an interesting, if somewhat subtle, example of 
simulation in the vicinity of a data absence. It appears as though the variability among the 
5 simulations shown right at this stratigraphic elevation is somewhat greater than it is several 
grid nodes higher on the profile. Although it is unclear that any firm conclusions in this regard 
should be drawn from examination of only 5 simulations, the proposed increase in variance at 
this level is consistent with simulation theory. 
Validation criterion 2 is addressed in Figure 68. Examination of the histograms associated with 
the four randomly selected simulated models indicates a very close resemblance to the histogram 
of the measured RH porosity data. The reduction of the tails of the statistical distribution for the 
E-type summary model is quite marked, as is the normalization of the histogram itself. Both of 
these features are consistent with the statistical distortions observed above with respect to 
lithophysal porosity in the TSw model unit. 
Variogram reproduction (validation criterion 3) for the simulated models of matrix porosity in the 
CHn model unit is presented in Figure 69. As was the case with the variogram comparison for the 
TSw model unit, the comparison is with the mean variogram computed over all 50 replicate 
stochastic realizations. Examination of the figure suggests that the input model has been 
reproduced quite well in all three principal directions of continuity. A small mismatch may be 
observed in part (c) of the figure for the minimum horizontal direction of correlation, although 
the degree of mismatch is less than was observed for lithophysal porosity. Again, consideration 
of the experimental (data) variogram with respect to the input model suggests that the simulated 
models may have been conditioned to produce a somewhat longer range of correlation than 
indicated by the mathematical modeling of the experimental data. Also, as was the case with the 
variograms for lithophysal porosity in the TSw model unit (Figure 64), the range of correlation 
exhibited by the E-type model is, in general, markedly longer than that expressed by the data or 
the simulated models. 
6.7.4 Validation of Matrix Saturated Hydraulic Conductivity in the CHn Model Unit 
Validation of the derivative models of matrix saturated hydraulic conductivity in the CHn model 
unit is one step more complicated than the validation of the thermal conductivity models 
discussed in Section 6.7.2. The cause of this additional complication is that the nonwelded tuffs of 
the Calico Hills interval have been partially altered to hydrous-phase minerals, principally 
zeolites. Accordingly, the material properties of this interval partially reflect the original neardepositional 
processes, while in part reflecting the operation of the later-stage diagenetic 
processes of alteration. 
According to the conceptual model used for modeling this unit (and the underlying Prow Pass 
Tuff), porosity is largely unaffected by the alteration process (see Section 6.4.4.3 and 6.4.4.4). 
Presumably then, the statistical character of the matrix porosity models is essentially that of the 
measured data: a situation that was validated by the histograms and variograms shown in

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 135 of 150 
Figure 68. Histograms and summary statistics of four randomly selected individual simulations of matrix 
porosity in the CHn model unit (a)(d), compared to the original porosity measurements (e) and 
the E-type summary model (f). 
(a) (b) 
(c) (d) 
(e) (f) 
Frequency 
Porosity, as a fraction 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 
0.000 
0.040 
0.080 
0.120 
CHn Porosity; Sim 2 Number of Data35088 
mean 0.2612 
std. dev. 0.0724 
coef. of var 0.2772 
maximum0.5241 
upper quartile0.3070 
median 0.2580 
lower quartile0.2200 
minimum0.0007 
Frequency 
Porosity, as a fraction 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 
0.000 
0.040 
0.080 
0.120 
CHn Porosity; Sim 13 Number of Data35088 
mean 0.2599 
std. dev. 0.0696 
coef. of var 0.2676 
maximum0.5400 
upper quartile0.3030 
median 0.2560 
lower quartile0.2200 
minimum0.0010 
Frequency 
Porosity, as a fraction 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 
0.000 
0.040 
0.080 
0.120 
CHn Porosity; Sim 29 Number of Data35088 
mean 0.2624 
std. dev. 0.0725 
coef. of var 0.2762 
maximum0.5120 
upper quartile0.3070 
median 0.2580 
lower quartile0.2200 
minimum0.0010 
Frequency 
Porosity, as a fraction 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 
0.000 
0.040 
0.080 
0.120 
CHn Porosity; Sim 41 Number of Data35088 
mean 0.2609 
std. dev. 0.0705 
coef. of var 0.2703 
maximum0.5365 
upper quartile0.3060 
median 0.2570 
lower quartile 0.2200 
minimum0.0002 
Frequency 
Porosity, as a fraction 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 
0.000 
0.100 
0.200 
0.300 
CHn Porosity E-type Model Number of Data35088 
mean 0.2569 
std. dev. 0.0368 
coef. of var 0.1434 
maximum0.4724 
upper quartile0.2747 
median 0.2529 
lower quartile0.2378 
minimum0.0448 
Frequency 
Porosity, as a fraction 
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 
0.000 
0.040 
0.080 
0.120 CHn POREF and RH data for FY99 Number of Data2711 
number trimmed857 
mean 0.2539 
std. dev. 0.0753 
coef. of var 0.2967 
maximum0.5110 
upper quartile0.3000 
median 0.2520 
lower quartile 0.2130 
minimum0.0010 
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Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 136 of 150 
Figures 68 and 69. However, the statistical character of the derivative property, hydraulic 
conductivity should show a bimodal character (altered vs. unaltered) reflecting its two-stage 
genetic history. 
Figure 70 presents the now-familiar comparison of histograms representing four randomly 
selected coregionalized simulations of matrix saturated hydraulic conductivity for the CHn model 
unit. Also shown on the figure are the equivalent statistical distributions of the measured 
Ks values and the values generated for the E-type summary model. Examination of the figure 
suggests that the essential features of the measured dataa broad spread of high conductivity 
vitric conductivities corresponding to the full range of porosities in the CHn, a cluster of lower 
zeolitic conductivities, and a spike of arbitrarily valued non-flowing grid nodes representing 
the no-flow laboratory sampleshave been well reproduced in the simulated models. The 
Figure 69. Reproduction of input variograms for simulated matrix porosity models for the CHn model unit: 
(a) stratigraphic vertical; (b) stratigraphic horizontal, azimuth = 0; (c) stratigraphic horizontal, 
azimuth = 90. Line with error bars is average variogram with plus/minus one standard 
deviation. Heavy solid line without error bars is input model. E-type model normalized by 
variance. 
Vertical Separation, in feet 
0 100 200 300 400 
Gamma 
0.0 
0.5 
1.0 
1.5 
Mean Simulation 
Input Model 
Data 
E-type Model 
(a) 
CHnPorValVario1.wmf 
Separation, in feet 
0 5000 10000 15000 20000 
Gamma 
0.0 
0.5 
1.0 
1.5 
Mean Simulation 
Input Model 
Data 
E-type Model 
(b) 
CHnPorValVario2.wmf 
Separation, in feet 
0 5000 10000 15000 20000 
Gamma 
0.0 
0.5 
1.0 
1.5 
Mean Simulation 
Input Model 
Data 
E-type Model 
(c) 
CHnPorValVario3.wmf

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 137 of 150 
Figure 70. Histograms and summary statistics of four randomly selected individual simulations of matrix 
saturated hydraulic conductivity in the CHn model unit (a)(d), compared to the original Ks 
measurements (e) and the E-type summary model (f). 
(a) (b) 
(c) (d) 
(e) (f) 
Frequency 
log10 Saturated Hydraulic Conductivity, m/sec 
-15.0 -11.0 -7.0 -3.0 
0.000 
0.050 
0.100 
0.150 
0.200 
0.250 
CHn Zeolitic Ksat; Sim. 2 Number of Data35088 
mean -10.7578 
std. dev. 2.5090 
coef. of var undefined 
maximum -4.0000 
upper quartile -9.9418 
median -10.4019 
lower quartile -14.0000 
minimum -14.0000 
Frequency 
log10 Saturated Hydraulic Conductivity, m/sec 
-15.0 -11.0 -7.0 -3.0 
0.000 
0.050 
0.100 
0.150 
0.200 
0.250 
CHn Zeolitic Ksat; Sim. 13 Number of Data35088 
mean -10.7425 
std. dev. 2.4847 
coef. of var undefined 
maximum -4.0001 
upper quartile -9.9259 
median -10.4009 
lower quartile -14.0000 
minimum -14.0000 
Frequency 
log10 Saturated Hydraulic Conductivity, m/sec 
-15.0 -11.0 -7.0 -3.0 
0.000 
0.050 
0.100 
0.150 
0.200 
0.250 
CHn Zeolitic Ksat; Sim. 29 Number of Data35088 
mean -10.7647 
std. dev. 2.4580 
coef. of var undefined 
maximum -4.0011 
upper quartile -9.9386 
median -10.3998 
lower quartile -14.0000 
minimum -14.0000 
Frequency 
log10 Saturated Hydraulic Conductivity, m/sec 
-15.0 -11.0 -7.0 -3.0 
0.000 
0.050 
0.100 
0.150 
0.200 
0.250 
CHn Zeolitic Ksat; Sim. 41 Number of Data35088 
mean -10.8020 
std. dev. 2.3923 
coef. of var undefined 
maximum -4.0003 
upper quartile -9.9335 
median -10.4034 
lower quartile -14.0000 
minimum -14.0000 
Frequency 
log10 Saturated Hydraulic Conductivity, m/sec log10 Saturated Hydraulic Conductivity, m/sec 
-15.0 -11.0 -7.0 -3.0 
0.000 
0.100 
0.200 
0.300 
CHn Ksat E-type Model Number of Data35088 
mean -10.7911 
std. dev. 1.7067 
coef. of var undefined 
maximum -4.2669 
upper quartile -11.1917 
median -11.4231 
lower quartile -11.6144 
minimum -12.4858 
Frequency 
-15.0 -11.0 -7.0 -3.0 
0.000 
0.050 
0.100 
0.150 
0.200 
0.250 
CHn Measured Ksat Data Number of Data116 
mean -11.0457 
std. dev. 2.2273 
coef. of var undefined 
maximum -4.7959 
upper quartile -10.1600 
median -10.5058 
lower quartile -14.0000 
minimum -14.0000 
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Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 138 of 150 
statistical character of the E-type summary model reflects the bimodal alteration state, although 
the two populations are more clearly separated and more normalized in shape. Also, the spike of 
no-flow grid nodes has been averaged out in the E-type post-processing step, as these nonflowing 
nodes represent a random process superimposed on each model of altered conductivity. 
Because they are neither spatially correlated nor conditioned to measured values, non-flowing 
nodes in one realization rarely are replicated at the same location in other simulations. 
The cross-variable correlation of hydraulic conductivity with matrix porosity in the CHn is 
presented for one representative simulated model in Figure 71(a). Part (b) of the figure represents 
the subset of grid nodes that are associated with unaltered materials, whereas part (c) of the figure 
represents those grid nodes that have been modeled as altered. What can be observed clearly in 
Figure 71(a) is the alteration-related segregation of conductivity values into the two populations 
(three, counting the non-flowing nodes arbitrarily assigned a Ks of 1014 m/sec in part (c) of the 
figure). Dependence of unaltered hydraulic conductivity on porosity is clearly indicated in part 
(b); compare with Figure 20(b). The target r2 value was 0.604, which is somewhat higher than the 
modeled r2 value of 0.419. However, the target value is based on the correlation of measured Ks 
values with porosity for all units, not just for the CHn. The inclusion of other units in the target 
calculation involves a much wider range of porosity values than exhibited by data for the CHn 
model unit. The result of including correlated hydraulic conductivity values beyond the range of 
porosities observed for the CHn is to strengthen the apparent correlation. Note that there are only 
12 unaltered Ks sample values for the CHn model unit, far too few data from which to develop a 
meaningful unit-specific target correlation. 
Figure 71(d) presents a similar cross-variable comparison of the E-type models of matrix porosity 
and saturated hydraulic conductivity for the CHn model unit. Although the resemblance to 
Figure 71(a) is unmistakable, it is also clear that the strength of the correlation between the two 
properties for the unaltered rock type (part (b) of the figure) is markedly greater and that the range 
of variability in porosity across the E-type model has been compressed. Variability of hydraulic 
conductivity has also been compressed for the altered lithology, and the typical or average 
altered conductivity has been decreased at least one log unit (compare the vertical position of the 
horizontal cloud of points with that shown in part (c)). Additionally, the cluster of values 
corresponding to the simulated non-flowing grid nodes in parts (a) and (c) of the figure has been 
eliminated by the averaging process. 
6.7.5 Summary Statement Regarding Validation 
Based on the information presented in Figures 62 through 71, as well as on additional similar 
information presented in the scientific notebook associated with this modeling activity 
(Rautman 1999), it appears reasonable to conclude that the individual simulated rock properties 
models (including the coregionalized models of derivative properties) do meet the criteria that 
have been set out above with respect to model validation, and that the models as entire entities 
do closely resemble the input data used to construct these descriptive models. Specifically, the 
primary porosity models reproduce the input measurements used to condition the simulations 
within the limits imposed by the discretization of the models. Additionally, both the primary 
simulated models and the derivative coregionalized models exhibit the full range of material 
property variability exhibited by the conditioning data ensemble. Furthermore, the simulated

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 139 of 150 
Porosity, as a fraction 
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 
Matrix Saturated Hydraulic Conductivity, 
in log10 m/sec 
-14 
-12 
-10 
-8 
-6 
-4 
-2 (d) 
ZKsEtypeValPorXplot.wmf 
Figure 71. Crossplots showing cross-variable correlation between coregionalized saturated hydraulic 
conductivity and the underlying matrix porosity simulation for (a) entire modeled unit 
regardless of lithology and for (b) the unaltered and (c) altered facies. Simulation 29, 10- 
percent subsample. Compare Figures 20(b) and 21(b). (d) Equivalent crossplot for E-type 
models of matrix porosity and full-field saturated hydraulic conductivity. 
Porosity, as a fraction 
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 
Matrix Saturated Hydraulic Conductivity, 
in log10 m/sec 
-14 
-12 
-10 
-8 
-6 
-4 
-2 
r  = 0.419 
r = +0.647 
ZKs029Unalt_PorXplot.wmf 
(b) 
Porosity, as a fraction 
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 
Matrix Saturated Hydraulic Conductivity, 
in log10 m/sec 
-14 
-12 
-10 
-8 
-6 
-4 
-2 
ZKs029Alt_PorXplot.wmf 
(c) 
Porosity, as a fraction 
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 
Matrix Saturated Hydraulic Conductivity, 
in log10 m/sec 
-14 
-12 
-10 
-8 
-6 
-4 
-2 (a) 
ZKs029ValPorXplot.wmf

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 140 of 150 
models reproduce the bivariate spatial correlation structure (variogram) observed in the data 
ensemble; the coregionalized models will reproduce this structure by construction. For the 
coregionalized models, the correlation coefficient between the derivative property and the 
underlying porosity simulation is reproduced within reasonable limits, given the fact that the 
target correlations are typically based on global correlations (without regard for model unit). 
The summary E-type models also reproduce the input conditioning measurements, but the 
statistical character of the models as a whole departs from the ensemble statistics of the 
underlying data. Univariate variability (histograms) is reduced, with the extreme tails of the 
distribution of values being reduced and the form of the distribution normalized to a greater or 
lesser extent. The spatial correlation structure (variograms) of the E-type models is similarly 
distorted. Continuity is observed to be somewhat greater in the summarized models. 
Additionally, cross-variable correlations appear to be strengthened by the averaging process 
implicit in the E-type models, approaching in some instances a one-to-one correlation. All of 
these three latter characteristics are completely expectable from the mechanics of the summary 
process. 

Title: Rock Properties Model (RPM3.1) 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: 141 of 150 
7. CONCLUSIONS 
The Rock Properties Model (RPM) is one component of the Integrated Site Model, which also 
includes the Geologic Framework Model and the Mineralogic Model. The RPM provides 
exhaustive, three-dimensional, discretized, numerical representations of several important 
hydrologic and thermal rock properties (porosity, bulk density, matrix saturated hydraulic 
conductivity, and thermal conductivity) that are intended for further use in numerical design and 
performance assessment analyses. The four composite modeling units defined for this analysis 
encompass the majority of the rocks within the unsaturated zone throughout the immediate 
vicinity of the potential repository at Yucca Mountain. 
7.1 DESCRIPTIVE RESULTS 
Pre-modeling geostatistical analysis has produced a statistical and spatial continuity description 
of porosity for each of the four modeling units. Spatial correlation patterns are unit-specific and 
are relatively complex; nested variogram models were required to fit the observed continuity 
patterns. Spatial correlation is anisotropic, both vertically and in the stratigraphically horizontal 
plane. For porosity, a significant fraction of the total variability is reached within a distance of 
2,000 to 6,000 feet, although another significant fraction exhibits a maximum range of between 
10,000 and 38,000 feet. The spatial correlation of hydrous-phase mineral alteration was also 
evaluated for the lower two modeling units. Variogram patterns again are unit-specific, and the 
range of maximum correlation is observed to vary between 7,000 and 15,000 feet. Cross-variable 
correlations between porosity and the several secondary material properties have been analyzed 
on a global basis. 
The individual model components have been constructed using geostatistical simulation 
methods, conditioned to drill hole-based measurements of porosity, with the result that the 
individual stochastic models are heterogeneous, spatially correlated, and essentially 
indistinguishable statistically from the set of measured values. These simulated models of 
porosity have been provided as input to a linear coregionalization algorithm, which has been 
used to generate simulated models of the derivative material properties, such as bulk density, 
matrix hydraulic conductivity, and thermal conductivity. These derivative property models are 
also spatially correlated and heterogeneous and are close statistical replicas of the set of 
measured secondary property data. Cross-variable correlations exist, and the strength of these 
correlations is approximately that described by the input sample correlation coefficients. Unitspecific 
post-processing steps have been used to impart additional desired property attributes 
such as microfractured hydraulic conductivity associated with very low-porosity (vitrophyric) 
welded tuffs and different hydraulic conductivities associated with altered and unaltered 
nonwelded tuffs. 
Sets of 50 simulations for each material property in each modeling unit have been post-processed 
to provide spatially varying models of the node-by-node standard deviation of the replicate 
individual models. These representations of the spatially heterogeneous inter-simulation 
variability serve as a first-pass uncertainty model for each material property. The same 
post-processing run has also been used to generate a summary expected-value type (E-type) 
model, defined as the arithmetic mean value of the 50 input replicate simulated models.

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Although the averaging process distorts the statistical character of the conditioning data and 
simulated models, these E-type models are useful for visualizing large-scale heterogeneities in 
material properties across the site area. 
Visual examination of block diagrams and cross-sectional views through the various model 
components indicate that there is substantial, complex internal heterogeneity in all four modeling 
units, although the E-type models reveal material properties broadly compatible with the 
conceptual model of layered volcanic stratigraphy at Yucca Mountain. Features such as highporosity 
lithophysal intervals that correlate approximately with formally named lithophysal 
zones have been generated based solely on measured porosity values. However, it can be 
demonstrated that such high porosity intervals exist outside the formally named zones. Matrix 
porosity is also higher associated with these intervals of high, lithophysal porosity. Major 
heterogeneity of matrix saturated hydraulic conductivity, which reflects principally the 
distribution of hydrous-phase mineral alteration in the CHn and Prow Pass Tuff model units, is 
internally complex. Some interfingering of altered and unaltered material is indicated. 
7.2 MODEL VALIDATION 
A model validation exercise has been conducted in which these exhaustive, descriptive models 
of material properties are compared with the sparse, spatially distributed input properties used to 
generate the models. Emphasis has been placed on examining the following three questions: 
 Do the models reproduce the input data at the locations of those data? 
 Do the models reproduce the full range of variability exhibited by the ensemble of measured 
values? 
 Do the models reproduce the spatial correlation structure exhibited by the data ensemble? 
A fourth question is relevant to the coregionalized models of derivative properties: 
 Do the models reproduce the observed correlation coefficient with porosity? 
The individual simulated models appear to pass these validation criteria, and are thus concluded 
to be good statistical models of the various material properties. The E-type summary models, 
however, although they still reproduce the input data at the locations of those data, are 
demonstrated to reproduce neither the univariate variability nor the observed spatial correlation 
structure of the data. Thus, although they may be useful for some purposes, the E-type summary 
models are deemed statistical distortions of the underlying data used in their construction. 
7.3 UNCERTAINTY AND RESTRICTIONS 
The concept of uncertainty in terms of limitation on the accuracy of the RPM does not 
particularly apply to rock properties models in the usual sense, because the entire intent of the 
rock properties modeling activities is not to make location-specific predictions, but rather to 
provide an entire suite of equally plausible, realistic models that collectively describes the total 
space of uncertainty associated with the relevant material properties. No representation is made 
that the individual simulated models are accurate (except at data locations). However, these

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same individual models are represented as geologically reasonable and consistent with all known 
information, and collectively they have been demonstrated (through validation) to be nearperfect 
replicas of the (geo)statistical character of the data ensemble used in their construction. It 
is fully intended that the consequences of the geologic uncertainty represented by the suites of 
models be evaluated through Monte Carlo-style flow-and-transport calculations or other suitable 
analyses. 
Methodological uncertainties involved in the RPM include those inherent in any statistical study, 
and these relate principally to uncertainties (error or bias) present in the input measurements 
used to condition the modeling algorithms. Measurement errors are presumed to be small in 
comparison with spatial heterogeneity. Two instances of measurement bias have been identified, 
but both have been compensated for to the extent possible. Some increased uncertainty is 
induced in the models of derivative material properties through the use of coregionalization (the 
concept of porosity-as-a-surrogate, based solely on the correlation coefficient) as the modeling 
algorithm (in contrast to conditional cosimulation). However, because of the overall modeling 
focus on defining spaces of uncertainty rather than on locally accurate predictions, the 
variability across a given suite of coregionalized models will be larger than it would otherwise, 
and hence that increased uncertainty is already accounted for. The use of stratigraphic 
coordinates for modeling purposes can act to increase uncertainty in the presence of significant 
erosion within a modeling unit or in the presence of faulted sections. However, instances of these 
confounding geologic features are known to be relatively few in the specific rocks being 
modeled, and the increased precision gained by correlating materials formed under similar 
temperature-pressure conditions afforded by the stratigraphic-coordinate conversion overall 
appear to be well worth the local distortions caused by erosion and/or faulting. 
Restrictions on subsequent use of the rock properties models are minimal and most are 
completely consistent with the Monte Carlo modeling methodology adopted as the conceptual 
framework for this activity. It is the individual simulated models (matched by run number across 
different properties to preserve the joint spatial character) that are intended for subsequent use in 
various relevant consequence analyses. The summary E-type models are not intended for general 
use in downstream analyses, except perhaps for individually justified special cases, because of 
their known distortion of the (geo)statistical character of the measured data. 
Evidently, the models are only useful for the stratigraphic intervals considered. Rocks belonging 
to the welded portion of the Tiva Canyon Tuff, as well as overlying units, were not modeled. 
Neither were deeper rocks, occurring principally in the saturated zone at Yucca Mountain, 
beginning at the stratigraphic level of the Bullfrog Tuff. The models are not valid beyond the 
defined lateral limits of the RPM, although the (geo)statistical descriptions and relevant 
measured values could be used to create other models not subject to these lateral limits. 
However, such extended modeling should be restricted to the outflow facies (in contrast to the 
caldera-margin or intra-caldera facies) of the several ash-flow tuff units involved in the four 
modeling units. 
A final restriction involves the saturated hydraulic conductivity models of the Topopah Spring 
welded modeling unit (only). These hydraulic conductivity models represent matrix permeability 
only, and they do not consider the effect of large lithophysal cavities that may be connected by

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either matrix porosity or by fractures. Thus, the matrix hydraulic conductivity models are 
intended more as the upper permeability limit of the unsaturated hydraulic conductivity function 
at near-full matrix saturation, rather than as representing the permeability of the TSw model unit 
were it present within the saturated zone. As the TSw unit is almost invariably high within the 
unsaturated zone in the immediate vicinity of the potential repository (the modeled area), this 
restriction is of little practical effect. Note that the substitution of water-filled porosity 
(volumetric water content) within the upper lithophysal zone (in particular) for drill holes from 
which no core measurements are available leads to a slight underestimation of the true (fully 
saturated) matrix hydraulic conductivity in those regions. Again, however, the modeled values 
are reasonable estimates of the upper permeability limit of the unsaturated hydraulic 
conductivity function at the ambient matrix saturation. 
This document and its conclusions may be affected by technical product input information that 
requires confirmation. Any changes to the document or its conclusions that may occur as a result 
of completing the confirmation activities will be reflected in subsequent revisions. The status of 
the input information quality may be confirmed by review of the Document Input Reference 
System database. 
Several key inputs to the Rock Properties Model have To Be Verified (TBV) status; however, 
excluding them would prohibit construction of the model. Accordingly, outputs from the Rock 
Properties Model are also TBV. Those TBV data on which the RPM is based currently are being 
evaluated to verify their quality-assurance status. Data identified to be unqualified through this 
verification activity will be subject to an independent qualification process, in accordance with 
AP-2III.2Q, to ensure that those data on which the RPM is based are fully qualified. Because it 
is anticipated that all data on which the RPM is based ultimately will be qualified, there is no 
need at this time to develop criteria, pursuant to AP-3.10Q, by which to assess the impact and 
appropriateness of the use of unqualified data on the applicability or validity of the RPM.

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8. ATTACHMENTS 
ATTACHMENT I. Document Input Reference System (DIRS) - Removed. See electronic 
DIRS database. 
ATTACHMENT II. Sigma Plot Transform STRATC4 
ATTACHMENT III. GSLIB Routine TRANS 
ATTACHMENT IV. Validation of UNCERT Program Vario 
ATTACHMENT V. Validation of UNCERT Program Variofit

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INTENTIONALLY LEFT BLANK

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9. REFERENCES 
9.1 DOCUMENTS CITED 
Altman, S.J.; Arnold, B.W.; Barnard, R.W.; Barr, G.E.; Ho, C.K.; McKenna, S.A.; and Eaton, 
R.R. 1996. Flow Calculations for Yucca Mountain Groundwater Travel Time (GWTT-95). 
SAND96-0819. Albuquerque, New Mexico: Sandia National Laboratories. 
ACC: MOL.19961209.0152. 
Buesch, D.C.; Spengler, R.W.; Moyer, T.C.; and Geslin, J.K. 1996. Proposed Stratigraphic 
Nomenclature and Macroscopic Identification of Lithostratigraphic Units of the Paintbrush 
Group Exposed at Yucca Mountain, Nevada. Open-File Report 94-469. Denver, Colorado: 
U.S. Geological Survey. ACC: MOL.19970205.0061. 
CRWMS M&O (Civilian Radioactive Waste Management System Management and Operating 
Contractor) 1996. Determining Porosity, Balanced Water Content and Other Rock Properties 
from Geophysical Logs for the Modern Borehole Data Set at Yucca Mountain, Nevada, June 
1996. BAAA00000-01717-0200-00013 REV 00. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.19970210.0171. 
CRWMS M&O 1999a. M&O Site Investigations. Activity Evaluation, January 23, 1999. 
Las Vegas, Nevada: CRWMS M&O. ACC: MOL.19990317.0330. 
CRWMS M&O 1999b. M&O Site Investigations. Activity Evaluation, September 28, 1999. 
Las Vegas, Nevada: CRWMS M&O. ACC: MOL.19990928.0224. 
CRWMS M&O 1999c. Analysis and Modeling Report (AMR) Development Plan (DP) for Rock 
Properties Model Version 3.1. TDP-NBS-GS-000023. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.19990917.0187. 
CRWMS M&O 1999d. Combined Porosity from Geophysical Logs. BAA000000-01717-0200- 
00003 REV 00. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.19991208.0437. 
Deutsch, C.V. and Journel, A.G. 1992. GSLIB Geostatistical Software Library and User's 
Guide. New York, New York: Oxford University Press. TIC: 224174. 
Deutsch, C.V. and Journel, A.G. 1998. GSLIB Geostatistical Software Library and User's 
Guide. Second Edition. New York, New York: Oxford University Press. TIC: 240101. 
DOE (U.S. Department of Energy) 1998. Quality Assurance Requirements and Description. 
DOE/RW-0333P, Rev. 8. Washington, D.C.: U.S. Department of Energy, Office of Civilian 
Radioactive Waste Management. ACC: MOL.19980601.0022. 
Dyer, J.R. 1999. Revised Interim Guidance Pending Issuance of New U.S. Nuclear Regulatory 
Commission (NRC) Regulations (Revision 01, July 22, 1999), For Yucca Mountain, Nevada. 
Letter from J. R. Dyer (DOE) to Dr. D.R. Wilkins (CRWMS M&O), September 3, 1999, 
OL&RC:SB-1714, with enclosure, Interim Guidance Pending Issuance of New NRC 
Regulations for Yucca Mountain (Revision 01). ACC: MOL.19990910.0079.

Title: Rock Properties Model (RPM3.1) 
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Flint, L.E. 1998. Characterization of Hydrogeologic Units Using Matrix Properties, Yucca 
Mountain, Nevada. Water-Resources Investigations Report 97-4243. Denver, Colorado: 
U.S. Geological Survey. ACC: MOL.19980429.0512. 
Journel, A.G. 1983. Nonparametric Estimation of Spatial Distributions. Mathematical 
Geology, 15, (3), 445-468. New York, New York: Plenum Publishing Corporation. TIC: 
224736. 
Journel, A.G. and Huijbregts, C.J. 1978. Mining Geostatistics. New York, New York: 
Academic Press. TIC: 210128. 
Luster, G.R. 1986. Raw Materials for Portland Cement: Applications of Conditional Simulation 
of Coregionalization. Ph.D. dissertation. Ann Arbor, Michigan: University Microfilms 
International. TIC: 226080. 
Moyer, T.C. and Geslin, J.K. 1995. Lithostratigraphy of the Calico Hills Formation and Prow 
Pass Tuff (Crater Flat Group) at Yucca Mountain, Nevada. Open-File Report 94-460. Denver, 
Colorado: U.S. Geological Survey. ACC: MOL.19941208.0003. 
Nelson, P.H. 1996. Computation of Porosity and Water Content from Geophysical Logs, Yucca 
Mountain, Nevada. Open-File Report 96-078. Denver, Colorado: U.S. Geological Survey. 
ACC: MOL.19980529.0444. 
Rautman, C. 1999. Scientific Notebook, Geostatistical Modeling of Porosity and Derivative 
Properties (FY 1999). Scientific Notebook SNL-SCI-011. ACC: MOL.19990623.0025. 
Rautman, C.A and Engstrom, D.A. 1996a. Geology of the USW SD-7 Drill Hole Yucca 
Mountain, Nevada. SAND96-1474. Albuquerque, New Mexico: Sandia National Laboratories. 
ACC: MOL.19971218.0442. 
Rautman, C.A. and Engstrom, D.A. 1996b. Geology of the USW SD-12 Drill Hole Yucca 
Mountain, Nevada. SAND96-1368. Albuquerque, New Mexico: Sandia National Laboratories. 
ACC: MOL.19970613.0101. 
Rautman, C.A. and McKenna, S.A. 1997. Three-Dimensional Hydrological and Thermal 
Property Models of Yucca Mountain, Nevada. SAND97-1730. Albuquerque, New Mexico: 
Sandia National Laboratories. ACC: MOL.19980311.0317. 
Rautman, C. and McKenna, S. 1998. Geostatistical Modeling of Porosity and Derivative 
Properties for Fiscal Year 1998. Scientific Notebook SNL-SCI-006. 
ACC: MOL.19981027.0187. 
Sawyer, D.A.; Fleck, R. J.; Lanphere, M.A.; Warren, R.G.; Broxton, D.E.; and Hudson, M.R. 
1994. Episodic Caldera Volcanism in the Miocene Southwestern Nevada Volcanic Field: 
Revised Stratigraphic Framework, 40Ar/39Ar Geochronology, and Implications for Magmatism 
and Extension. Geological Society of American Bulletin, 106, (10), 1304-1318. Boulder, 
Colorado: Geological Society of America. TIC: 222523. 
SNL (Sandia National Laboratories) 1997. 3-D Rock Properties Modeling for FY 1998. Work 
Agreement WA-0344, Rev. 00. Albuquerque, New Mexico: Sandia National Laboratories. 
ACC: MOL.19990823.0276.

Title: Rock Properties Model (RPM3.1) 
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SNL 1999. 3-D Rock Properties Modeling for FY 1999. Work Agreement WA-0358, Rev. 00. 
Albuquerque, New Mexico: Sandia National Laboratories. ACC: MOL.19991001.0158. 
9.2 PROCEDURES 
AP-3.10Q, Rev. 0, ICN 0. Analyses and Models. Washington, D.C.: U.S. Department of 
Energy, Office of Civilian Radioactive Waste Management. ACC: MOL.19990225.0335. 
AP-3.10Q, Rev. 1, ICN 0. Analyses and Models. Washington, D.C.: U.S. Department of 
Energy, Office of Civilian Radioactive Waste Management. ACC: MOL.19990702.0314. 
AP-SI.1Q, Rev. 0, ICN 0. Software Configuration Management. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: MOL.19990505.0125. 
AP-SI.1Q, Rev. 1, ICN 0. Software Configuration Management. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: MOL.19990630.0395. 
AP-SIII.2Q, Rev. 0, ICN 0. Qualification of Unqualified Data and the Documentation of 
Rationale for Accepted Data. Washington, D.C.: U.S. Department of Energy, Office of Civilian 
Radioactive Waste Management. ACC: MOL.19990702.0308. 
QAP-2-0, Rev. 4. Conduct of Activities. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.19971031.0060. 
QAP-2-0, Rev. 5. Conduct of Activities. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.19980826.0209. 
QAP-SIII-3, Rev. 2. Scientific Notebooks. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.19971105.0040. 
SNL QAIP 19-1, Rev. 04. Software Quality Assurance Requirements. Albuquerque, New 
Mexico: Sandia National Laboratories. ACC: MOL.19981103.0547. 
SNL QAIP 20-2, Rev. 01. Scientific Notebooks. Albuquerque, New Mexico: Sandia National 
Laboratories. ACC: MOL.19990224.0438. 
SNL QAIP 20-2, Rev. 02. Scientific Notebooks. Albuquerque, New Mexico: Sandia National 
Laboratories. ACC: MOL.19990224.0508. 
9.3 SOURCE DATA, LISTED BY DATA TRACKING NUMBER 
GS960708312132.002. Porosity, Water Content, Mineralogy and Other Data Derived from 
Geophysical Logs and Cores for 26 Boreholes. Submittal Date: 07/09/1996. 
GS980708312242.010. Physical Properties of Borehole Core Samples, and Water Potential 
Measurements Using the Filter Paper Technique, for Borehole Samples from USW WT-24. 
Submittal Date: 07/27/1998.

Title: Rock Properties Model (RPM3.1) 
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GS980808312242.014. Physical Properties of Borehole Core Samples and Water Potential 
Measurements Using the Filter Paper Technique for Borehole Samples from USW SD-6. 
Submittal Date: 08/11/1998. 
LA9910DB831321.001. Mineralogic Variation in Drill Holes. Submittal date: 10/29/1999. 
MO9510RIB00002.004. RIB ITEM: Stratigraphic Characteristics: Geologic/Lithologic 
Stratigraphy. Submittal Date: 06/26/1996. 
MO9804MWDGFM03.000. A 3-D Geological Framework and Integrated Site Sub-Model 
(GFM3.0) of Yucca Mountain, Nevada. Submittal date: 03/31/1998. 
MO9811MWDGFM03.000. Input Data To Geologic Framework Model GFM3.0. Submittal 
date: 11/30/1998. 
MO9901MWDGFM31.000. Geologic Framework Model. Submittal date: 01/06/1999. 
MO9910POROCALC.000. Combined Porosity from Geophysical Logs. Submittal date: 
10/05/1999. 
MO9911INPUTRPM.000. Core Porosities, Bulk Densities, Particle Densities (RH & OD Values) 
Plus Saturated Hydraulic Conductivities and Associated Porosities. Submittal date: 10/12/1999. 
SNF40060198001.001. Unsaturated Zone Lithostratigraphic Contacts in Borehole USW 
WT-24. Submittal date: 10/15/1998. 
SNF40060298001.001. Unsaturated Zone Lithostratigraphic Contacts in Borehole USW SD-6. 
Submittal Date: 10/15/1998. 
SNL01A05059301.005. Laboratory Thermal Conductivity Data for Boreholes UE25 NRG-4, 
NRG-5; USW NRG-6 and NRG-7/7A. Submittal Date: 02/07/1996. 
SNL01A05059301.007. Calculated Porosities for Thermal Conductivity Specimens from 
Boreholes UE25 NRG-4, UE25 NRG-5, USW NRG-6, and USW NRG-7/7a. 
Submittal Date: 10/14/1998. 
9.4 BASELINED SOFTWARE 
GSLIB V 1.4 SGSIM V 1.4. STN: 10110-1.4MSGSIMV1.40-00. 
GSLIB V 2.0 IK3D V 2.0. STN: 10122-2.0MIK3DV2.0-00. 
GSLIB V 1.4 NSCORE V 1.201. STN: 10109-1.4MNSCOREV1.201-01. 
EARTHVISION V 4.0. STN: 30035 V4.0. 
MATCHUP Version 12/5/98. STN: 10196-12598-00. 
MATCH Version 12/5/98. STN: 10195-12598-00.

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ATTACHMENT I. 
DOCUMENT INPUT REFERENCE SYSTEM (DIRS) 
REMOVED 
See electronic DIRS database

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ATTACHMENT II. 
SIGMA PLOT TRANSFORM STRATC4

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SIGMA PLOT TRANSFORM STRATC4 
1. Software Routine Identification 
Software Name and Version Number: stratc4, ver. 4 
Note: version number was not assigned originally, but was added for documentation to be 
included in the Rock Properties Model Analysis Model Report. However, the digit 4 in 
the routine name was intended to indicate that this is the fourth iteration of a software routine 
to perform a similar function. 
SRR Document Identification Number: none 
SRR Media Number: none 
2. Description and Testing 
Documentation that the software routine or macro provides correct results for a specified 
range of input parameters 
 Description and Equations of Mathematical Models, Algorithms, and Numerical Solution 
Techniques, as Applicable: 
The equation that is implemented in software routine stratc4 to convert drillhole measured 
depths to stratigraphic coordinates, more specifically to stratigraphic depths 
(StratDepth), is as follows (equation 2, p. 55, of this report): 
, 
where SampleDepth is the depth of the relevant sample measurement in a given drill hole, 
UnitTop and UnitBottom are the measured or projected top and bottom contacts of re relevant 
model unit at the drill hole location used to determine the thickness of the unit, and 
NominalThickness is the appropriate unit-specific scaling constant (Table 12 of this 
report). The conversion produces a stratigraphic depth such that the very top of the 
geologic unit in question is at a depth of zero, the very bottom of the unit is at a depth 
equal to the nominal stratigraphic thickness of the unit, and all depths in between are 
scaled proportionately to the nominal thickness. Stratigraphic coordinates are dimensionless. 
 Description of Software Routine Including the Execution Environment 
Software routine stratc4 is a transform implemented within the industry-standard, 
commercial statistical and graphics software package, Sigma Plot (SPSS, Inc.; 233 South 
Wacker Drive, 11th Floor; Chicago, Illinois 60606-6307). The routine is essentially a 
macro (however, see next paragraph). Sigma Plot transform syntax does not appear to 
StratDepth 
SampleDepth UnitTop  
UnitBottom UnitTop  
--------------------------------------------------------------- NominalThickness  = d d

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be version specific, but this routine has been used for the current application within 
Sigma Plot, version 5.00, running under Windows NT, version 4. Use of the transform is 
intimately associated with the spreadsheet mechanics of Sigma Plot. 
Note that a transform in Sigma Plot parlance is different than a macro. A Sigma Plot 
macro consists of a recording of a sequence of mouse-based actions for creating or modifying 
a graph. In contrast, a transform performs one or more mathematical operations on 
a set of input data and provides essentially what amounts to an internal programming language 
for performing those operations. 
The Sigma Plot spreadsheets designed for use with software routine stratc4 are 
intended to contain various sets of core-based and geophysics-based rock property measurements, 
and to present those data values graphically as drillhole profiles displaying the 
selected measurements as a function of depth. Accordingly, the true, measured depths 
associated with each set of property values are arranged in a columnar manner, with four 
blank columns to the right of the true-depth column (to be filled in with stratigraphic 
depths); property values are typically arranged to the right of the four blank columns as a 
logical grouping. Multiple sets of such depth and property data may be present in a single 
spreadsheet. Additionally, a column of top and bottom depth values corresponding to 
the top and bottom of each geologic unit of interest is provided elsewhere in the spreadsheet. 
The numeric identifiers of the true-depth and tops columns are required as manual 
input to the software routine (involves editing the transform listing within Sigma 
Plot). 
The transform is invoked according to Sigma Plot conventions, whereupon the appropriate 
unit tops and bottoms are read from the spreadsheet, and the coordinate-conversion 
equation is computed repeatedly for each depth value present in the specified true-depth 
column, with the results being inserted into the appropriate output columns (presumably 
the four blank colums set up for this purpose). 
 Description of Test Cases 
Any arbitrary set of depth values can be used to test the stratigraphic depth calculations 
performed by software routine stratc4. The only requirement is that some number of 
true-depth values be contained within the top and bottom depths of the geologic 
unit being considered. As an alternative, the following data set, which consists of the 
depths associated with selected laboratory core property measurements taken from drillhole 
USW SD-7 (the property data themselves are irrelevant and are not modified by the 
transform), may be used to validate the software routine. Note that within Sigma Plot, 
these data entries are associated with specific cells identified by row and column numbers. 

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The column headed unit designation is not used by the transform, and it is included 
only for reader reference. 
Tops Depth Unit Designation True-Depth 
316.0000 top PTn 302.8000 
316.0000 306.1000 
308.6000 
384.3000 base PTn 312.1000 
384.3000 top TSw 320.9000 
323.7000 
1308.0000 base TSw 330.1000 
1308.0000 top CH 332.9000 
338.9000 
1621.5000 base CH 341.5000 
1621.5000 top PP 368.0000 
369.0000 
2183.9000 base Prow 371.9000 
2183.9000 top Bullfrog 386.3000 
389.7000 
392.7000 
395.8000 
399.1000 
401.4000 
404.6000 
 Description of Test Results 
The following lines are copied from the Sigma Plot spreadsheet in which the stratigraphic 
coordinate conversion was computed. In the original, each entry is associated with a particular 
cell, identified by row and column numbers. 
True Depth PTn StratD TSw StratD CHn StratD Tcp StratD 
302.8000 -38.6530 -88.2321 -1282.5518 -937.9090 
306.1000 -28.9898 -84.6595 -1278.3413 -935.5619 
308.6000 -21.6691 -81.9530 -1275.1515 -933.7838 
312.1000 -11.4202 -78.1639 -1270.6858 -931.2945 
320.9000 14.3485 -68.6370 -1259.4577 -925.0356 
323.7000 22.5476 -65.6057 -1255.8852 -923.0441 
330.1000 41.2884 -58.6771 -1247.7193 -918.4922 
332.9000 49.4876 -55.6458 -1244.1467 -916.5007 
338.9000 67.0571 -49.1502 -1236.4912 -912.2333 
341.5000 74.6706 -46.3354 -1233.1738 -910.3841 
368.0000 152.2694 -17.6464 -1199.3620 -891.5363 
369.0000 155.1977 -16.5638 -1198.0861 -890.8250 
371.9000 163.6896 -13.4243 -1194.3860 -888.7624 
386.3000 205.8565 2.1652 -1176.0128 -878.5206 
389.7000 215.8126 5.8461 -1171.6746 -876.1024 
392.7000 224.5974 9.0939 -1167.8469 -873.9687

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Several items are of note. First, the input data (first listing, above) represent only a very 
small portion of the relevant drillhole data set. Specifically, the true depths include 
only those associated with the PTn geologic unit, plus a few extra depths both above and 
below for illustrative purposes. As expected, true depths higher in the hole than the top 
of the PTn unit (given above as 316 ft), are converted to meaningless stratigraphic depths 
(PTn StratD) less than zero. Second, depths below the bottom of the PTn unit (given 
above as 384.3 ft) are converted to equally meaningless stratigraphic depths in excess of 
the nominal stratigraphic thickness of the PTn unit, which is 200.0 (dimensionless). 
Third, using similar logic, almost all stratigraphic depths for the TSw geologic unit 
(TSw StratD) are negative (those above the top of the TSw unit at 384.3 ft), as are all of 
the indicated stratigraphic depths for the CHn unit and Tcp unit (CHn StratD and Tcp 
StratD), as none of the measured depths of with this illustrative data set are associated 
with those deeper units. And finally, note as logically consistent, that the lowermost 
valid PTn stratigraphic depth (at a true depth of 371.9 ft) is immediately succeeded by the 
first valid TSw stratigraphic depth (at a true depth of 386.3 ft). Shaded values in the listing 
indicate numbers that are meaningless (though arithmetically correct) for one or 
more of the reasons discusssed above. 
A manual calculation, conducted by calculator (a Hewlett-Packard HP-11C; Hewlett- 
Packard Co.; 3000 Hanover Street; Palo Alto, CA 94304), for the first valid PTn true 
depth value (at 320.9 ft) is as follows: 
, 
which has been rounded up to 14.3485 by the display-format specifier in the results presented 
above (set within Sigma Plot). 
 Range of Input Parameter Values for Which the Results Were Verified 
There are no input parameter values specified by the user, other than the column identifiers 
specifying where to look for the unit tops and bottoms and for the true depths that 
are to be converted. In terms of input data values, any real number recognized by Sigma 
Plot is a mathematically valid entry for both the unit contacts (top and bottom) and for the 
true depths. Whether or not specific values are legitimate values for a particular drillhole 
or sample depth is another issue (discussion above). The user is responsible for providing 
geologically meaningful input values. 
395.8000 233.6750 12.4499 -1163.8915 -871.7639 
399.1000 243.3382 16.0225 -1159.6810 -869.4168 
401.4000 250.0732 18.5125 -1156.7464 -867.7809 
404.6000 259.4436 21.9768 -1152.6635 -865.5050 
True Depth PTn StratD TSw StratD CHn StratD Tcp StratD 
StratDepth 
320.9 316.0  
384.3 316.0  
------------------------------ 200.0 14.34846266 =  =

Title: Rock Properties Model (RPM3.1) Attachment II 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: II-7 of II-10 
 Identification of Any Limitations on Software Routine Applications or Validity 
There are no particular limitations to the software routine, per se. Any valid real number 
recognized by Sigma Plot is acceptable as input. However, the routine does not limit the 
calculation of the stratigraphic depth to the geologic unit of interest. Accordingly, the 
routine may generate statigrahic depths that are outside the legitimate range of zero 
through NominalThickness. Such values, although representing arithmetically correct 
results, are meaningless. The user is responsible for identifying and dealing properly 
with such values in later applications. 
3. Supporting Information 
 Directory Listing of Executable and Data Files 
Because software routine stratc4 is a macro designed to operate inside another software 
package, there is no executable per se. The Sigma Plot tranform capability operates in 
an interpreter mode, compiling and executing each line of the transform at runtime. 
There are also no data files per se. All input data is contained within the composite 
Sigma Plot spreadsheet and graphics file. 
 Computer Listing of Source Code, if Available 
The following listing of the transform code has been annotated (in a different font) to 
illustrate some salient features and required user-input values. 
jsv5D 
;Macro to compute stratigraphic coordinates 
; version 4 
; note: uses contacts of t/m units in spreadsheet 
; bottom of one unit can be NONcoincident with top of 
next 
ctop = 1 ; column with tops <--User Input 
dp = 4 ; true depth column <--User Input 
nc1 = dp + 1 ; column in which to put StratZ for PTn 
nc2 = dp + 2 ; column in which to put StratZ for TSw 
nc3 = dp + 3 ; column in which to put StratZ for CHn 
nc4 = dp + 4 ; column in which to put StratZ for PP 
top1 = cell( ctop,2 ) ; PTn parameters 
bot1 = cell( ctop,4 ) 
nt1 = 200.0 <-- NominalThickness for PTn 
top2 = cell( ctop,5 ) ; TSw parameters 
bot2 = cell( ctop,7 ) 
nt2 = 1000.0 <-- NominalThickness for TSw 
top3 = cell( ctop,8 ) ; CHn parameters

Title: Rock Properties Model (RPM3.1) Attachment II 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: II-8 of II-10 
bot3 = cell( ctop,10 ) 
nt3 = 400.0 <-- NominalThickness for CHn 
top4 = cell( ctop,11) ;PP parameters 
bot4 = cell( ctop,13) 
nt4 = 400 <-- NominalThickness for Tcp 
thk1 = bot1 - top1 
col(nc1 ) = ( col( dp ) - top1 ) / thk1 * nt1 
thk2 = bot2 - top2 
col(nc2 ) = ( col( dp ) - top2 ) / thk2 * nt2 
thk3 = bot3 - top3 
col(nc3 ) = ( col( dp ) - top3 ) / thk3 * nt3 
thk4 = bot4 - top4 
col(nc4 ) = (col( dp ) - top4 ) / thk4 * nt4 
 Computer Listing of Test Data Input and Output, Identifying Software Routine Name and 
Version Number 
A printout (taken from an Acrobat portable-document-format [.pdf] file) of the relevant 
parts of the test Sigma Plot spreadsheet is reproduced below in figure . No software 
names or version numbers are associated with the internal appearance of the spreadsheet. 

Title: Rock Properties Model (RPM3.1) Attachment II 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: II-9 of II-10 
Test Case for "stratc4" 
3dm units FY97 3DM 3 Core Depth PTn StratC TSw StratC CHn StratC Tcp StratC 
1 316.0000 top PTn 302.8000 -38.6530 -88.2321 -1282.5518 -937.9090 
2 316.0000 306.1000 -28.9898 -84.6595 -1278.3413 -935.5619 
3 308.6000 -21.6691 -81.9530 -1275.1515 -933.7838 
4 384.3000 base PTn 312.1000 -11.4202 -78.1639 -1270.6858 -931.2945 
5 384.3000 top TSw 320.9000 14.3485 -68.6370 -1259.4577 -925.0356 
6 323.7000 22.5476 -65.6057 -1255.8852 -923.0441 
7 1308.0000 base TSw 330.1000 41.2884 -58.6771 -1247.7193 -918.4922 
8 1308.0000 top CH 332.9000 49.4876 -55.6458 -1244.1467 -916.5007 
9 338.9000 67.0571 -49.1502 -1236.4912 -912.2333 
10 1621.5000 base CH 341.5000 74.6706 -46.3354 -1233.1738 -910.3841 
11 1621.5000 top PP 368.0000 152.2694 -17.6464 -1199.3620 -891.5363 
12 369.0000 155.1977 -16.5638 -1198.0861 -890.8250 
13 2183.9000 base Prow 371.9000 163.6896 -13.4243 -1194.3860 -888.7624 
14 2183.9000 top Bullfrog 386.3000 205.8565 2.1652 -1176.0128 -878.5206 
15 389.7000 215.8126 5.8461 -1171.6746 -876.1024 
16 392.7000 224.5974 9.0939 -1167.8469 -873.9687 
17 395.8000 233.6750 12.4499 -1163.8915 -871.7639 
18 399.1000 243.3382 16.0225 -1159.6810 -869.4168 
19 401.4000 250.0732 18.5125 -1156.7464 -867.7809 
20 404.6000 259.4436 21.9768 -1152.6635 -865.5050 
Figure II-1. Printed spreadsheet cells from Sigma Plot file containing the test case data and outp 
(reproduced from a .pdf file). Columns are numbered sequentially from the left (see col. 3 
but alphanumeric titles may be entered for user convenience.

Title: Rock Properties Model (RPM3.1) Attachment II 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: II-10 of II-10 
INTENTIONALLY LEFT BLANK

Title: Rock Properties Model (RPM3.1) Attachment III 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: III-1 of 18 
ATTACHMENT III. 
GSLIB ROUTINE TRANS

Title: Rock Properties Model (RPM3.1) Attachment III 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: III-2 of III-18

Title: Rock Properties Model (RPM3.1) Attachment III 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: III-3 of 18 
Software routine TRANS, version 1.3, is used directly from the geostatistical software library, 
GSLIB (Deutsch and Journel 1992, pp. 213214). The routine is intended to convert any 
particular univariate distribution of values to match that of a different reference distribution. 
For the rock properties modeling exercise, TRANS was used to transform coregionalized, 
standard-normal (m=0, s2=1) models to match the target statistics of the desired secondary 
property in order to create the full-field derivative-property models. Documentation of TRANS 
was inadvertently omitted from the scientific notebooks covering this work, and hence this 
material is included as this attachment. 
Source Code Listing 
program trans 
C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%% 
C % 
C Copyright (C) 1992 Stanford Center for Reservoir Forecasting. All % 
C rights reserved. Distributed with: C.V. Deutsch and A.G. Journel. % 
C GSLIB: Geostatistical Software Library and Users Guide, Oxford % 
C University Press, New York, 1992. % 
C % 
C The programs in GSLIB are distributed in the hope that they will be % 
C useful, but WITHOUT ANY WARRANTY. No author or distributor accepts % 
C responsibility to anyone for the consequences of using them or for % 
C whether they serve any particular purpose or work at all, unless he % 
C says so in writing. Everyone is granted permission to copy, modify % 
C and redistribute the programs in GSLIB, but only under the condition % 
C that this notice and the above copyright notice remain intact. % 
C % 
C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%% 
c----------------------------------------------------------------------- 
c
c Univariate Transformation 
c ************************* 
c
c Reads in a reference distribution and a number of other distributions 
c and then transforms the values in each of the second distributions 
c such that their histograms match that of the reference distribution. 
c
c
c INPUT/OUTPUT Parameters: 
c
c distin the input file with the reference distribution 
c ivr,iwt parameters to read in reference distribution 
c tmin,tmax trimming limits 
c datafl the input file with the data to be transformed 
c ivrd,iwtd parameters to read in reference distribution 
c tmin,tmax trimming limits 
c nxyz,nsim number of points to transform at a time and the 
c number of times to expect nxyz in the file 
c outfl the output file for transformed data 
c zmin,zmax minimum and maximum data values

Title: Rock Properties Model (RPM3.1) Attachment III 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: III-4 of III-18 
c ltail,ltpar option to handle values in lower tail 
c utail,utpar option to handle values in upper tail 
c
c
c
c Original: C.V. Deutsch Date: May 1991 
c----------------------------------------------------------------------- 
parameter(MAXREF=25000, MAXDAT=100000, MV=20, EPSLON=1.0e-12, 
+ VERSION=1.300) 
implicit real*8 (a-h,o-z) 
character distin*40,datafl*40,outfl*40,str*40 
real*8 rcdf(MAXREF),rvr(MAXREF),dcdf(MAXDAT),dvr(MAXDAT), 
+ indx(MAXDAT),var(MV),ltpar,utpar 
integer ltail,utail 
logical testfl 
data lin/1/,lout/2/ 
c
c Note VERSION number before anything else: 
c 
write(*,9999) VERSION 
9999 format(/ TRANS Version: ,f5.3/) 
c
c Get the name of the parameter file - try the default name if no input: 
c 
write(*,*) Which parameter file do you want to use? 
read (*,(a40)) str 
if(str(1:1).eq. )str=trans.par  
inquire(file=str,exist=testfl) 
if(.not.testfl) then 
write(*,*) ERROR - the parameter file does not exist, 
write(*,*)  check for the file and try again  
stop 
endif 
open(lin,file=str,status=OLD) 
c
c Find Start of Parameters: 
c 
1 read(lin,(a4),end=97) str(1:4) 
if(str(1:4).ne.STAR) go to 1 
c
c Read Input Parameters: 
c 
read(lin,(a40),err=97) distin 
write(*,*)  reference distribution: ,distin 
read(lin,*,err=97) ivr,iwt 
write(*,*)  columns: ,ivr,iwt 
read(lin,*,err=97) tmin,tmax 
write(*,*)  trimming limits: ,tmin,tmax 
read(lin,(a40),err=97) datafl 
write(*,*)  data file: ,datafl 
read(lin,*,err=97) ivrd,iwtd 
write(*,*)  columns: ,ivrd,iwtd 
read(lin,*,err=97) tmind,tmaxd

Title: Rock Properties Model (RPM3.1) Attachment III 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: III-5 of 18 
write(*,*)  trimming limits: ,tmind,tmaxd 
read(lin,*,err=97) nxyz,nsim 
write(*,*)  number to transform: ,nxyz,nsim 
read(lin,(a40),err=97) outfl 
write(*,*)  output file: ,outfl 
read(lin,*,err=97) zmin,zmax 
write(*,*)  data limits: ,zmin,zmax 
read(lin,*,err=97) ltail,ltpar 
write(*,*)  lower tail option: ,ltail,ltpar 
read(lin,*,err=97) utail,utpar 
write(*,*)  upper tail option: ,utail,utpar 
close(lin) 
c
c Check for error situation: 
c 
if(ltail.ne.1.and.ltail.ne.2) then 
write(*,*) ERROR invalid lower tail option ,ltail 
write(*,*)  only allow 1 or 2 - see manual  
stop 
endif 
if(utail.ne.1.and.utail.ne.2.and.utail.ne.4) then 
write(*,*) ERROR invalid upper tail option ,ltail 
write(*,*)  only allow 1,2 or 4 - see manual  
stop 
endif 
if(utail.eq.4.and.utpar.lt.1.0) then 
write(*,*) ERROR invalid power for hyperbolic tail,utpar 
write(*,*)  must be greater than 1.0! 
stop 
endif 
c
c Read in the reference distribution: 
c 
inquire(file=distin,exist=testfl) 
if(.not.testfl) then 
write(*,*) ERROR: No reference distribution file 
stop 
endif 
open(lin,file=distin) 
c
c Proceed with reading in distribution: 
c 
read(lin,(a),err=98) str 
read(lin,*,err=98) nvari 
do 2 i=1,nvari 
2 read(lin,(),err=98) 
c
c Read as much data as possible: 
c 
ncut = 0 
nt = 0 
tcdf = 0 
3 read(lin,*,end=4,err=98) (var(j),j=1,nvari) 
c

Title: Rock Properties Model (RPM3.1) Attachment III 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: III-6 of III-18 
c Trim this data? 
c 
if(var(ivr).lt.tmin.or.var(ivr).ge.tmax) then 
nt = nt + 1 
go to 3 
endif 
if(iwt.ge.1) then 
if(var(iwt).le.EPSLON) then 
nt = nt + 1 
go to 3 
endif 
endif 
c
c Accept this data: 
c 
ncut = ncut + 1 
if(ncut.gt.MAXREF) then 
write(*,*) ERROR: exceeded available storage for reference 
write(*,*)  have ,MAXREF, available 
stop 
endif 
rvr(ncut) = var(ivr) 
if(iwt.ge.1) then 
rcdf(ncut) = var(iwt) 
else 
rcdf(ncut) = 1.0 
endif 
tcdf = tcdf + rcdf(ncut) 
c
c Go back for another data: 
c 
go to 3 
4 close(lin) 
write(*,*) 
write(*,*)  TRANS: there were ,ncut, reference values 
write(*,*)  trimmed ,nt, values 
write(*,*)  the total weight ,tcdf 
c
c Sort the Reference Distribution and Check for error situation: 
c 
call sortem(1,ncut,rvr,1,rcdf,c,d,e,f,g,h) 
if(ncut.le.1.or.tcdf.le.EPSLON) then 
write(*,*) ERROR: too few data or too low weight 
stop 
endif 
if(utail.eq.4.and.rvr(ncut).le.0.0) then 
write(*,*) ERROR can not use hyperbolic tail with  
write(*,*)  negative values! - see manual  
stop 
endif 
if(zmin.gt.rvr(1)) then 
write(*,*) ERROR zmin should be no larger than smallest 
write(*,*)  refernce value 
write(*,*)  zmin = ,zmin, vr1 ,rvr(1)

Title: Rock Properties Model (RPM3.1) Attachment III 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: III-7 of 18 
stop 
endif 
if(zmax.lt.rvr(ncut)) then 
write(*,*) ERROR zmax should be no less than the largest 
write(*,*)  reference value 
write(*,*)  zmax = ,zmax, vrnt ,rvr(ncut) 
stop 
endif 
c
c Turn the (possibly weighted) distribution into a cdf that is useful: 
c 
oldcp = 0.0 
cp = 0.0 
tcdf = 1.0 / tcdf 
do 5 i=1,ncut 
cp = cp + rcdf(i) * tcdf 
rcdf(i) =(cp + oldcp) * 0.5 
oldcp = cp 
5 continue 
c
c Get median and write some info to the screen: 
c 
half = 0.5 
call locate(rcdf,ncut,half,j) 
gmedian = xlinint(rcdf(j),rcdf(j+1),rvr(j),rvr(j+1),half) 
write(*,*)  the median ,gmedian 
write(*,*) 
c
c Get the output and distribution files ready: 
c 
inquire(file=datafl,exist=testfl) 
if(.not.testfl) then 
write(*,*) ERROR ,datafl, does not exist! 
write(*,*)  you need some distributions to work with 
stop 
endif 
open(lin,file=datafl) 
open(lout,file=outfl) 
read(lin,(a40),err=96) str 
read(lin,*,err=96) nvari 
do 6 i=1,nvari 
6 read(lin,(a40),err=96) str 
write(lout,110) 
110 format(Trans output,/,1,/,transformed variable) 
c
c MAIN Loop over all the increments to transform: 
c 
do 10 isim=1,nsim 
c
c Read in the data values: 
c 
tcdf = 0.0 
num = 0 
do 11 i=1,nxyz

Title: Rock Properties Model (RPM3.1) Attachment III 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: III-8 of III-18 
read(lin,*,end=14,err=98) (var(j),j=1,nvari) 
num = num + 1 
if(num.gt.MAXDAT) then 
write(*,*) ERROR: exceeded storage for data 
write(*,*)  have ,MAXDAT, available 
stop 
endif 
dvr(num) = var(ivrd) 
indx(num) = dble(real(num)) 
if(dvr(num).ge.tmind.and.dvr(num).lt.tmaxd) then 
dcdf(num) = 1.0 
if(iwtd.ge.1) dcdf(num) = var(iwtd) 
tcdf = tcdf + dcdf(num) 
endif 
11 continue 
14 if(tcdf.le.EPSLON) then 
write(*,*) ERROR: no data 
stop 
endif 
c
c Turn the (possibly weighted) data distribution into a useful cdf: 
c 
call sortem(1,num,dvr,2,dcdf,indx,d,e,f,g,h) 
oldcp = 0.0 
cp = 0.0 
tcdf = 1.0 / tcdf 
do 12 i=1,num 
if(dvr(i).ge.tmind.and.dvr(i).lt.tmaxd) then 
cp = cp + dcdf(i) * tcdf 
dcdf(i) =(cp + oldcp) * 0.5 
oldcp = cp 
endif 
12 continue 
c
c Now, get the right order back: 
c 
call sortem(1,num,indx,2,dcdf,dvr,d,e,f,g,h) 
c
c Go through all the data back transforming them to the reference CDF: 
c 
do 13 i=1,num 
if(dvr(i).ge.tmind.and.dvr(i).lt.tmaxd) then 
zval = getz(dcdf(i),ncut,rcdf,rvr,zmin,zmax, 
+ ltail,ltpar,utail,utpar) 
else 
zval = -999.0 
endif 
write(lout,101) zval 
101 format(f9.4) 
13 continue 
c
c END Main loop: 
c 
10 continue

Title: Rock Properties Model (RPM3.1) Attachment III 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: III-9 of 18 
stop 
96 stop ERROR in distribution file! 
97 stop ERROR in parameter file! 
98 stop ERROR in global data file! 
end 
double precision function getz(cdfval,ncut,rcdf,rvr,zmin,zmax, 
+ ltail,ltpar,utail,utpar) 
c----------------------------------------------------------------------- 
c
c Get a Z value for a give CDF 
c **************************** 
c
c Performs specified interpolation in the lower and upper tail. 
c
c
c
c
c
c
c Original: C.V. Deutsch May 1991 
c----------------------------------------------------------------------- 
parameter(EPSLON=1.0e-12,UNEST=-1.0) 
implicit real*8 (a-h,o-z) 
real*8 rcdf(ncut),rvr(ncut),ltpar,utpar,lambda 
integer ltail,utail,cclow,cchigh 
zero = 0.0 
one = 1.0 
c
c Figure out part of distribution 0=lower tail, 1=middle, 2=upper tail: 
c 
ipart = 1 
if(cdfval.le.rcdf(1)) ipart = 0 
if(cdfval.ge.rcdf(ncut)) ipart = 2 
c
c ARE WE IN THE LOWER TAIL? 
c 
if(ipart.eq.0) then 
getz = rvr(1) 
if(ltail.eq.1) then 
c
c Linear interpolation to lower limit zmin: 
c 
getz = powint(zero,rcdf(1),zmin,rvr(1),cdfval,one) 
else if(ltail.eq.2) then 
c
c Power model interpolation to lower limit zmin: 
c 
cpow = 1.0/ltpar 
getz = powint(zero,rcdf(1),zmin,rvr(1),cdfval,cpow) 
endif 
c

Title: Rock Properties Model (RPM3.1) Attachment III 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: III-10 of III-18 
c OR, ARE WE IN THE MIDDLE? 
c 
else if(ipart.eq.1) then 
call locate(rcdf,ncut,cdfval,cclow) 
cchigh = cclow + 1 
getz = xlinint(rcdf(cclow),rcdf(cchigh), 
+ rvr(cclow),rvr(cchigh),cdfval) 
c
c OR, ARE WE IN THE UPPER TAIL? 
c 
else if(ipart.eq.2) then 
c
c Linear interpolation to upper limit zmax? 
c 
if(utail.eq.1) then 
getz = xlinint(rcdf(ncut),one,rvr(ncut), 
+ zmax,cdfval) 
else if(utail.eq.2) then 
cpow = 1.0 / utpar 
getz = powint(rcdf(ncut),one,rvr(ncut), 
+ zmax,cdfval,cpow) 
else if(utail.eq.4) then 
c
c Fit a Hyperbolic Distribution? Figure out lambda: 
c 
lambda = (rvr(ncut)**utpar)*(1.0-rcdf(ncut)) 
getz = (lambda/(1.0-cdfval))**(1.0/utpar) 
endif 
endif 
c
c Check for bounds and return: 
c 
if(getz.lt.zmin) getz = zmin 
if(getz.gt.zmax) getz = zmax 
return 
end 
double precision function xlinint(xlow,xhigh,ylow,yhigh,xval) 
c----------------------------------------------------------------------- 
c
c Linearly interpolates the value of y between (xlow,ylow) and 
c (xhigh,yhigh) for a value of x. 
c
c----------------------------------------------------------------------- 
parameter(EPSLON=1.0e-12) 
real*8 xlow,xhigh,ylow,yhigh,xval 
if((xhigh-xlow).le.EPSLON) then 
xlinint = xlow 
else 
xlinint = ylow + (yhigh-ylow)*(xval -xlow) / (xhigh-xlow) 
end if 
return

Title: Rock Properties Model (RPM3.1) Attachment III 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: III-11 of 18 
end 
double precision function powint(xlow,xhigh,ylow,yhigh,xval,pow) 
c----------------------------------------------------------------------- 
c
c Power interpolate the value of y between (xlow,ylow) and (xhigh,yhigh) 
c for a value of x and a power pow. 
c
c----------------------------------------------------------------------- 
parameter(EPSLON=1.0e-20) 
implicit real*8 (a-h,o-z) 
powint = ylow + (yhigh-ylow)* 
+ (((xval-xlow)/amax1(EPSLON,(xhigh-xlow)))**pow) 
return 
end 
subroutine locate(xx,n,x,j) 
c----------------------------------------------------------------------- 
c
c Given an array xx of length n, and given a value x, this routine 
c returns a value j such that x is between xx(j) and xx(j+1). xx 
c must be monotonic, either increasing or decreasing. j=0 or j=n is 
c returned to indicate that x is out of range. 
c
c Bisection Concept From Numerical Recipes, Press et. al. 1986 pp 90. 
c----------------------------------------------------------------------- 
real*8 xx(n),x 
c
c Initialize lower and upper methods: 
c 
jl = 0 
ju = n 
c
c If we are not done then compute a midpoint: 
c 
10 if(ju-jl.gt.1) then 
jm = (ju+jl)/2 
c
c Replace the lower or upper limit with the midpoint: 
c 
if((xx(n).gt.xx(1)).eqv.(x.gt.xx(jm))) then 
jl = jm 
else 
ju = jm 
endif 
go to 10 
endif 
c
c Return with the array index: 
c

Title: Rock Properties Model (RPM3.1) Attachment III 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: III-12 of III-18 
j = jl 
return 
end 
subroutine sortem(ib,ie,a,iperm,b,c,d,e,f,g,h) 
c----------------------------------------------------------------------- 
c
c Quickersort Subroutine 
c ********************** 
c
c This is a subroutine for sorting a real array in ascending order. This 
c is a Fortran translation of algorithm 271, quickersort, by R.S. Scowen 
c in collected algorithms of the ACM. 
c
c The method used is that of continually splitting the array into parts 
c such that all elements of one part are less than all elements of the 
c other, with a third part in the middle consisting of one element. An 
c element with value t is chosen arbitrarily (here we choose the middle 
c element). i and j give the lower and upper limits of the segment being 
c split. After the split a value q will have been found such that 
c a(q)=t and a(l)<=t<=a(m) for all i<=l<q<m<=j. The program then 
c performs operations on the two segments (i,q-1) and (q+1,j) as follows 
c The smaller segment is split and the position of the larger segment is 
c stored in the lt and ut arrays. If the segment to be split contains 
c two or fewer elements, it is sorted and another segment is obtained 
c from the lt and ut arrays. When no more segments remain, the array 
c is completely sorted. 
c
c
c INPUT PARAMETERS: 
c
c ib,ie start and end index of the array to be sorteda 
c a array, a portion of which has to be sorted. 
c iperm 0 no other array is permuted. 
c 1 array b is permuted according to array a 
c 2 arrays b,c are permuted. 
c 3 arrays b,c,d are permuted. 
c 4 arrays b,c,d,e are permuted. 
c 5 arrays b,c,d,e,f are permuted. 
c 6 arrays b,c,d,e,f,g are permuted. 
c 7 arrays b,c,d,e,f,g,h are permuted. 
c >7 no other array is permuted. 
c
c b,c,d,e,f,g,h arrays to be permuted according to array a. 
c
c OUTPUT PARAMETERS: 
c
c a = the array, a portion of which has been sorted. 
c
c b,c,d,e,f,g,h =arrays permuted according to array a (see iperm) 
c
c NO EXTERNAL ROUTINES REQUIRED:

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c
c----------------------------------------------------------------------- 
implicit real*8 (a-h,o-z) 
dimension a(*),b(*),c(*),d(*),e(*),f(*),g(*),h(*) 
c
c The dimensions for lt and ut have to be at least log (base 2) n 
c 
integer lt(64),ut(64),i,j,k,m,p,q 
c
c Initialize: 
c 
j = ie 
m = 1 
i = ib 
iring = iperm+1 
if (iperm.gt.7) iring=1 
c
c If this segment has more than two elements we split it 
c 
10 if (j-i-1) 100,90,15 
c
c p is the position of an arbitrary element in the segment we choose the 
c middle element. Under certain circumstances it may be advantageous 
c to choose p at random. 
c 
15 p = (j+i)/2 
ta = a(p) 
a(p) = a(i) 
go to (21,19,18,17,16,161,162,163),iring 
163 th = h(p) 
h(p) = h(i) 
162 tg = g(p) 
g(p) = g(i) 
161 tf = f(p) 
f(p) = f(i) 
16 te = e(p) 
e(p) = e(i) 
17 td = d(p) 
d(p) = d(i) 
18 tc = c(p) 
c(p) = c(i) 
19 tb = b(p) 
b(p) = b(i) 
21 continue 
c
c Start at the beginning of the segment, search for k such that a(k)>t 
c 
q = j 
k = i 
20 k = k+1 
if(k.gt.q) go to 60 
if(a(k).le.ta) go to 20 
c
c Such an element has now been found now search for a q such that a(q)<t

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c starting at the end of the segment. 
c 
30 continue 
if(a(q).lt.ta) go to 40 
q = q-1 
if(q.gt.k) go to 30 
go to 50 
c
c a(q) has now been found. we interchange a(q) and a(k) 
c 
40 xa = a(k) 
a(k) = a(q) 
a(q) = xa 
go to (45,44,43,42,41,411,412,413),iring 
413 xh = h(k) 
h(k) = h(q) 
h(q) = xh 
412 xg = g(k) 
g(k) = g(q) 
g(q) = xg 
411 xf = f(k) 
f(k) = f(q) 
f(q) = xf 
41 xe = e(k) 
e(k) = e(q) 
e(q) = xe 
42 xd = d(k) 
d(k) = d(q) 
d(q) = xd 
43 xc = c(k) 
c(k) = c(q) 
c(q) = xc 
44 xb = b(k) 
b(k) = b(q) 
b(q) = xb 
45 continue 
c
c Update q and search for another pair to interchange: 
c 
q = q-1 
go to 20 
50 q = k-1 
60 continue 
c
c The upwards search has now met the downwards search: 
c 
a(i)=a(q) 
a(q)=ta 
go to (65,64,63,62,61,611,612,613),iring 
613 h(i) = h(q) 
h(q) = th 
612 g(i) = g(q) 
g(q) = tg 
611 f(i) = f(q)

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f(q) = tf 
61 e(i) = e(q) 
e(q) = te 
62 d(i) = d(q) 
d(q) = td 
63 c(i) = c(q) 
c(q) = tc 
64 b(i) = b(q) 
b(q) = tb 
65 continue 
c
c The segment is now divided in three parts: (i,q-1),(q),(q+1,j) 
c store the position of the largest segment in lt and ut 
c 
if (2*q.le.i+j) go to 70 
lt(m) = i 
ut(m) = q-1 
i = q+1 
go to 80 
70 lt(m) = q+1 
ut(m) = j 
j = q-1 
c
c Update m and split the new smaller segment 
c 
80 m = m+1 
go to 10 
c
c We arrive here if the segment has two elements we test to see if 
c the segment is properly ordered if not, we perform an interchange 
c 
90 continue 
if (a(i).le.a(j)) go to 100 
xa=a(i) 
a(i)=a(j) 
a(j)=xa 
go to (95,94,93,92,91,911,912,913),iring 
913 xh = h(i) 
h(i) = h(j) 
h(j) = xh 
912 xg = g(i) 
g(i) = g(j) 
g(j) = xg 
911 xf = f(i) 
f(i) = f(j) 
f(j) = xf 
91 xe = e(i) 
e(i) = e(j) 
e(j) = xe 
92 xd = d(i) 
d(i) = d(j) 
d(j) = xd 
93 xc = c(i) 
c(i) = c(j)

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c(j) = xc 
94 xb = b(i) 
b(i) = b(j) 
b(j) = xb 
95 continue 
c
c If lt and ut contain more segments to be sorted repeat process: 
c 
100 m = m-1 
if (m.le.0) go to 110 
i = lt(m) 
j = ut(m) 
go to 10 
110 continue 
return 
end 
Parameter File for TRANS 
The following lines are the input parameter file for TRANS. This file must be edited using a 
standard ASCII text editor to specify the appropriate quantities for the problem under 
consideration. 
Parameters for TRANS 
******************** 
START OF PARAMETERS: 
../../data/true.dat \file with ref distribution 
1 0 \iv, iwt 
-1.0e21 1.0e21 \tmin, tmax 
../../data/cluster.dat \file with uncorrected dists 
3 0 \ivr, iwt 
-1.0e21 1.0e21 \tmin, tmax 
1000 1 \nxyz, nsim 
trans.out \file for revised bistributions 
0.0 250.0 \zmin, zmax 
1 1.0 \lower tail: option, parameter 
4 1.5 \upper tail: option, parameter 
Validation Exercise for TRANS 
The following activities were conducted as a validation exercise for software routine TRANS. A 
distribution of values was selected (the choice of distribution is arbitrary). Specifically, a 
standard-normal distribution was chosen, coregionalized after matrix porosity in the CHn model 
unit (number of values, N = 35,088). Note, however, that the spatial information is never used in 
the transformation process. This arbitrary univariate distribution was processed through TRANS 
using the univariate distribution of bulk density values obtained from laboratory measurements on 
core samples (N = 510) as the reference distribution. Again, the specific choice of a reference 
distribution is arbitrary. At the end of processing, the transformed distribution is virtually 
identical in form to that of the reference distribution, and the validation exercise is complete. Note

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Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: III-17 of 18 
that the maximum and minimum values (and therefore the total range) of the transformed 
distribution are not limited by the necessarily limited and incomplete set of measured values. 
The following statistical and graphical observations indicate that the transformation has been 
accomplished properly (Table III-1): 
1. The transformation is one-to-one, with the lowest input value corresponding to the lowest 
transformed value, the next highest input value corresponding to the next highest 
transformed value, and so on (monotonically increasing; Figure III-1.) 
2. The initial input and transformed output distributions are, in fact, different (Figure III-2.) 
3. The transformed output distribution is essentially identical to the target reference 
distribution in that the two curves overlie one another exactly (Figure III-3.). 
Table III-1. Comparative Statistics for Input, Transformed, and Reference Distributions 
Input Transformed Reference 
Mean 0.0950 1.6812 1.6814 
Std.Dev. 0.8821 0.1534 0.1525 
Minimum -3.8911 0.8081 1.3590 
Maximum 3.4005 2.3987 2.3110 
N 35,088 35,088 510 
Original Variable, 
Normal Score 
-4 -2 0 2 4 
Transformed Variable, 
Bulk Density, in g/cm3 
0.0 
0.5 
1.0 
1.5 
2.0 
2.5 
3.0 
transVxplot.wmf 
Figure III-1.Crossplot of the transformed variable as a function of the input variable indicating a one-to-one 
monotonically increasing (but nonlinear) relationship

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Initial Distribution 
Original Variable, 
Normal Score 
-4 -2 0 2 4 
Frequency 
0.00 
0.02 
0.04 
0.06 
0.08 
0.10 
0.12 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
transVhist1.wmf 
(a) 
Transformed Distribution 
Transformed Variable, 
Bulk Density, in g/cm3 
1.0 1.5 2.0 2.5 3.0 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
transVhist2.wmf 
(b) 
Figure III-2. Histograms and cumulative distribution functions for (a) input standard-normal distribution 
and (b) transformed distribution where N = 35,088 (both figures). 
Target Variable, 
Bulk Density, in g/cm3 
1.0 1.5 2.0 2.5 3.0 
Frequency 
0.00 
0.05 
0.10 
0.15 
0.20 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
transVhist3.wmf 
Comparison of CDFs 
Porosity, as a fraction 
0.0 0.5 1.0 1.5 2.0 2.5 3.0 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
Transformed 
Target 
transVcdf.wmf 
Figure III-3. (a) Histogram and cumulative distribution function for the target reference distribution; 
compare with Figure III-2.(b) where N = 510. (b) Comparison of cumulative distribution 
functions for the transformed [Figure 2(b)] and target distributions [Figure 3(a)].

Title: Rock Properties Model (RPM3.1) Attachment IV 
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ATTACHMENT IV. 
VALIDATION OF UNCERT PROGRAM VARIO

Title: Rock Properties Model (RPM3.1) Attachment IV 
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Title: Rock Properties Model (RPM3.1) Attachment IV 
Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: IV-3 of IV-6 
Background 
Program VARIO, versions 1.16 and 1.20, which is part of the industry-standard geostatistical 
software package UNCERT, is intended to compute a simple experimental variogram based on 
measured data spatially distributed in (up to) three-dimensions. The program was available to the 
Yucca Mountain Project as a compiled Unix executable. Accordingly, a source listing is not 
available. 
The algebraic formula for computation of the variogram is extremely simple, and is essentially 
equivalent to that for a variance. The variogram value, gamma (g), is specified simply as one-half 
the average squared difference of all pairs of points separated by a specified vector distance, h: 
(Eq. IV-1) 
where Zx is the value at spatial location, x, Z(x+h) is the value at a location a vector h distant, and 
Nh is the number of such pairs that can be identified. The variogram value is computed for a 
number of different separation values, and the results are plotted as a function of h. 
In practice, because the input data locations are not generally located on a regular grid, the 
separation vector is typically taken as a nominal distance plus-or-minus some tolerance value, 
usually set equal to one-half the lag spacing of the nominal values. The actual average 
separation distance is the h value used in plotting the variogram. Additionally, the orientation of 
the separation vector is typically specified as some nominal direction plus-or-minus a halfangle 
tolerance value. An omnidirectional variogram computed without regard for orientation 
of the vector, h, is specified using a half-angle tolerance of 90 degrees. A bandwidth distance 
value, computed normal to the nominal vector orientation, may be used in conjunction with the 
angular tolerance value to limit the sample locations selected for inclusion in the computation. 
The search parameters in VARIO are user specified. 
Procedure 
Because of the near-infinite number of lag spacing-angular orientation and tolerance-bandwidth 
combinations that are possible for all possible pairs of values of a large data set in three 
dimensions, the trick for validating a variogram program, such as VARIO, is to design a synthetic 
data set that is computationally tractable for manual calculation. The data set for which the 
locations are shown in Figure IV-1 is specifically designed to test the search capabilities of VARIO 
and to allow manual reproduction of the variogram value for one lag distance. The calculations 
are easily conducted in a spreadsheet program, such as Excel 97. 
One subset of the data set appears as the east-trending series of points shown in Figure IV-1(a). 
These locations consist of 50 randomly generated data values located at 500 (arbitrary) grid 
units apart along a line with the y-coordinate equal to zero. The second subset again consists of 
another 50 randomly generated values located at positions described by x- and y-coordinates 
regularly increasing by 200 arbitrary units. This paired-coordinate scheme produces a 45-degree 
line with a sample spacing of 200 = 282.843 units. The third subset of data consists of 
gh 
1 
2Nh 
--------- Z x ( ) Z x h + ( )  [ ]2 
n 1 = 
Nh
=
2

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Document Identifier: MDL-NBS-GS-000004 REV 00 ICN 01 Page: IV-4 of IV-6 
50 additional randomly generated values equally spaced at 100-unit intervals in the z-coordinate 
direction. 
The object of the validation exercise is to specify the relevant search parameters in each different 
direction with a very small tolerance (e.g. N45E plus-or-minus 5-degrees or a bandwidth of plusor-
minus 5 units), such that the search routines of VARIO locate only the samples belonging to 
each subset separately. This is the step that allows manual calculation of the corresponding 
values in Excel. The use of markedly different lag spacings for each subset allows identification 
of mixing of samples from the different subsets, something that would invalidate the simplistic 
manual computation. For example, if VARIO identify only the 500-unit-spaced values located 
along the x-axis. Because all data spacings are 500 units, the average lag distance, h, for the first 
lag should be precisely equal to 500.0 units. If the search locates pairs of points, one member of 
which belongs to another data subset, the average lag distance reported will differ from 500. The 
same logic applies in the other two directions. 
As a further (although perhaps less-definitive) check of the search strategy portion of VARIO, the 
randomly generated data values were scaled differently for each subset of data. The 500-unit 
lag set was scaled between 0 and 1, the 200-unit lag set between 0 and 5, and the 100-unit lag set 
between 0 and 10. Although this means of checking the search results is less definitive than 
examination of the average lag spacing, the different magnitudes provide the opportunity for 
improperly identified pairs to influence the VARIO-computed gamma value disproportionately in 
comparison to the simple manual calculation. Random data values are appropriate, in that there 
is no particular spatial structure required for the validation exercise. It is sufficient to confirm 
that the algebraic calculation of Equation IV-1 is being carried out correctly. 
If the search routine executed internally within VARIO properly identifies the members of each 
data subset separately, and if the mathematical computation of Equation IV-1 is executed 
properly, then the gamma value returned for the first lag of each directional variogram should 
Figure IV-1. Locations of sample values for the test case data set: (a) horizontal plane, (b) vertical plane. 
Individual points may overlap at the scale shown 
Horizontal Coords 
X-Coordinate 
0 5000 10000 15000 20000 25000 30000 
Y-Coordinate 
0 
5000 
10000 
15000 
20000 
25000 
30000 
N90E transect, 500-ft spacing 
N45E transect, 282.843-ft spacing 
200 ft in each x and y) 
(a) 
Vertical Coords 
X-Coordinate 
-1 0 1 2 
Z-Coordinate 
0 
1000 
2000 
3000 
4000 
5000 
6000 
Vertical transect, 100-ft spacing 
(b)

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essentially be identical to the value of Equation IV-1 computed manually for the pairs of the data 
set considered as the tines on a comb (Figure IV-2). Such an ordered computation of squared 
differences is easily implemented using the cell-based arithmetic capabilities of Excel. 
The validation criterion is essentially identical results computed by the two methods. 
Results 
Table IV-1 presents the gamma values calculated by VARIO for the first lag for each directional 
variogram, as well as the actual average lag spacing, h, corresponding to each of the three data 
subsets. Also presented in the table are the results of the manual calculation conducted using 
the arithmetic capabilities of Excel. 
Examination of the table indicates two things: (1). the average lag spacing is precisely identical 
to the nominal spacing of the input data values. This indicates that the search algorithm has 
restricted the computation of the variogram value to only the pairs involved in each data subset. 
(2) The gamma values reported by the two calculation methods are effectively identical. 
Observed differences are limited to the fourth decimal place and are non-meaningful. 
Accordingly, the conclusion is that VARIO is computing the experimental variogram values as 
desired. 
Table IV-1. Validation Results 
Data Subset VARIO Results Excel Results 
Orientation Nominal h Average h Gamma Gamma 
N0E 500 500.0000 0.0828 0.0828 
N45E 282.843 282.8427 11.1223 11.1222 
Vertical 100 100.0000 1.8289 1.8289 
Figure IV-2. Ordered computation of squared differences between sequential values 
implemented in the manual calculation using Excel 97. Gamma is computed as 
one-half the average squared difference 
h h h h h h 
Z2 Z1 Z5 Z4 Z6 Z3 Z7 
(Z1 - Z2)2 
}}}}}} 
(Z4 - Z5)2 (Z5 - Z6)2 (Z6 - Z7)2 (Z3 - Z4)2 (Z2 - Z3)2 + + + + + ....

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ATTACHMENT V. 
VALIDATION OF UNCERT PROGRAM "VARIOFIT

Title: Rock Properties Model (RPM3.1) Attachment V 
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Title: Rock Properties Model (RPM3.1) Attachment V 
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Background 
Program VARIOFIT version 1.16, which is part of the industry-standard geostatistical software 
package UNCERT, is a simple program intended to compute and plot any of a number of 
algebraically defined variogram models for comparison with an experimental variogram derived 
from measured data. The program plots the underlying experimental variogram (computed 
separately with program vario) to the screen and overlays the theoretical model calculation on 
that screen image. The program can also create a Postscript output file containing the screen 
image for printing and write a .out file containing various information related to the modeled 
variogram. The program was available for Yucca Mountain Project use as a compiled Unix 
executable. Accordingly, a source listing is not available. 
Procedure 
The validation approach adopted is as follows: 
1. A model variogram with arbitrary parameters is created using a dummy input variogram 
file to initialize the program (plotting of the dummy plot is turned off, and the input file is 
never used in the variogram model calculations). 
2. The model variogram information is written to a .out file for plotting in a separate 
graphics package capable of simple mathematical calculations (SIGMAPLOT ver. 5). 
3. A second model variogram is computed in the second graphics package using the same 
input parameters. 
4. The two models are plotted on the same graph using different symbols/line types and a 
visual comparison is made. 
Validation has been conducted for the spherical variogram model (Deutsch and Journel 1998), 
which is the only of current interest. The formula for the spherical model is as follows: 
(Eq. V-1) 
where c is the sill value associated with the model, h is the lag spacing under consideration and a 
is the range of the variogram model. A nugget component, c0, may. be added to the formula for 
the spherical model. Spherical models may be nested by adding two (or more) functions of this 
form, each with its own sill and range values. 
The validation criterion is identical results by visual comparison. 
Results 
Figure V-1 presents a replicate of the screen image from VARIOFIT after entry of the variogram 
parameters and calculation of the model variogram. The model consists of two nested spherical 
structures plus a nugget effect. The parameters are indicated on the figure as: c0=2, c1=10, 
a1=1000, c2= 25, and a2=5000. The units for the range are arbitrary. 
g 
c 1.5h
a -
- 0.5h3 
a3 
-----  h a    
c h a >       
=

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Figure V-2 presents the replotted variogram model from VARIOFIT plus the independently 
computed model using the same parameters, generated using the graphics/spreadsheet package, 
SIGMAPLOT. Note that the two models appear to overlie one another precisely. 
Figure V-1. Reproduced screen image of an arbitrary nested variogram model generated using the 
UNCERT program, VARIOFIT 
Model Parameters 
Nest 
Range 
C 
Model 
2 
5000 
25 
Spherical 
1 
1000 
10 
Spherical 
Nugget 
2 
0 
500 
1000 
1500 
2000 
2500 
3000 
3500 
4000 
4500 
5000 
5500 
6000 
0.0 
5.0 
10.0 
15.0 
20.0 
25.0 
30.0 
35. 
0 
40.0 
45.0 
50.0 
Variofi 
t Test Case 
X 
Y 
Figure V-2. Comparison of model variograms generated by program VARIOFIT and by independent 
computation using SIGMAPLOT 
Separation, h 
0 1000 2000 3000 4000 5000 6000 
Gamma 0 
10 
20 
30 
40 
50 
"variofit" Output 
Sigma Plot Calculation 
g = 2 + 10 Sph(1000) + 25 Sph(5000)

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Conclusion 
Based on the nearly exact correspondence between the variogram models computed by the two 
different methods (the maximum difference in gamma is 0.0005 compared to a total sill value of 
37.0), we conclude that VARIOFIT is validated for use with the spherical model equation. A similar 
exercise could be conducted for other variogram model types, if necessary. 
Listing of SigmaPlot Transform 
;transform to compute nested spherical variograms 
c0 = 2.0 
c1 = 10. a1 = 1000 
c2 = 25. a2 = 5000 
n = 8 ; column in which to start variogram 
col(n) = data( 0, 7000, 35) ;lag distances to compute variogram for 
; intermediate computational results: first nugget, then nest 1, then nest 2 
col(n+2) = c0 
col(n+3) = if( col(n) < a1 , c1*( 1.5*col(n) / a1 - 0.5*(col(n)^3) / (a1^3) ) , c1 ) 
col(n+4) = if( col(n) < a2 , c2*( 1.5*col(n) / a2 - 0.5*(col(n)^3) / (a2^3) ) , c2 ) 
; output model and preservation of input parameters Output is sum of 3 cols 
col(n+1) = col(n+2) + col(n+3) + col(n+4) 
cell(18,1) = c0 
cell(18,3) = c1 
cell(18,4) = a1 
cell(18,6) = c2 
cell(18,7) = a2 
; compute difference between two methods 
col(7) = col(6) - col(9) 
; preserve maximum delta gamma 
cell(18,9) = max(col(7) )

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