第29回日本情報地質学会講演会 講演要旨集 017-018頁 2018年

Effectiveness of Geostatistical Simulation for Sparse Geologic Dataset
Vitor Ribeiro de Sá* and Katsuaki Koike**Graduate School of Engineering, Kyoto University, Katsura C1–2–215, Kyoto 615–8540, Japan.
E–mail: koike.katsuaki.5x@kyoto–u.ac.jp (K. Koike)Key words: Geostatistics, Stochastic simulation, Turning Bands simulation, Sequential
Gaussian simulation, Metal concentration

1. Introduction
Geostatistics is founded on its pioneer methods
developed by Krige and Matheron in 1950’s and 1960’s,
whose works aimed to estimate values of randomvariables in unknown locations using spatial linear
regression approaches, called kriging techniques (Olea,2003). These methods provide the most likely value atevery cell in the model as their outcome. Such methods
are known to smooth the data because the kriged values
have less variability than the original data from which
they were calculated (Deutsch, 2002). Stochastic
methods have been turned out to bring light to aspects
which traditional geostatistical techniques do notproperly cover, such as the assessment of uncertainty
innate to their proposed models. Uncertainty may beunderstood as the error associated with the model. Thesemethods yield numerous equiprobable realizations as
their results and the data variance tend to be honored
and are preferable approaches to deal withheterogeneous environments.
Based on those background, this study aims tocompare the effectiveness of two different stochastic
methods, Sequential Gaussian Simulation (SGS) andTurning Bands Simulation (TBSIM), for a spatialmodeling of metal concentration in a hydrothermal area.
Both methods are conditional simulations, i.e., theoriginal data values can be reproduced at their location.
SGS is regarded as fast and straightforward due to themodeling of a Gaussian conditional cumulative
distribution function (ccdf) at each location and the needof solving only a single cokriging system there (Chilèsand Delfiner, 1999), whereas TBSIM simulates thevariable along 1-D lines and then combined into a 3-D
model: one of its main advantages is to handle with
non-stationary data which SGS does not consider(Deutsch, 2002). Since stochastic methods provide
several equiprobable scenarios, the modeler must selectone or few of them to present as reality’s illustration. To
make the best informed decision, this professional may
use the assessment of uncertainty of each realizationand its expected spatial distribution, once a conceptualmodel, also known as Empirical model, of the geologic
structure of target area was previously designed. These
criteria are also applied not only to decide which the bestmodel of each conditional simulation methods fits betterbut also which method is more indicated for the current
study area, a volcanogenic massive sulfide (VMS) deposit
type in the seafloor under survey. This type of deposits

account for important source of economic mineral, to wit:
Zn, Cu, Pb, Ag, and Au.
Due to their capacity to quantitively characterize thespatial distribution of grades and physical parameters oflithotypes, the importance of numerical models intargeting potential areas for mineral exploration cannot
be overstated.

2. Model Domain and Dataset
Fig. 1 depicts the 250mx700mx300m model’s domain
located around 1500m below sea level (mbsl). This area
is rich in Ba-Zn-Pb according to previous geochemicalstudies. Logarithm values of Pb concentration are used
as input data for implementing SGS and TBSIM, whichwere sampled from six boreholes (black dots) practically
distributed along the E-W direction, with variable
lengths from 46m (borehole 1) to 180m (borehole 3).
The borehole 1 was drilled in a mound and isconsidered as a discharge zone of the hydrothermalsystem, whereas borehole 6 presented few evidences ofsulfide and altered material in its sample coredescriptions and geochemical analysis, being more likely
a recharge zone. Core descriptions were used to identify
shear zones, such as presence of breccias and lack ofhydrothermally altered materials.

3.Methods
The same semivariogram model was set for bothconditional simulations. However, in order to reach thebest cross-validation score and preserve the datavariance, different search neighborhoods were adjusted.
The following subsections briefly describe the main
characteristics under SGS and TBSIM.
3.1. Sequential Gaussian Simulation (SIS)As Olea (1999) succinctly describe, SIS method
consists of generating a partial realization using
multivariable normal random function where its kernel
dwells in drawing from this multivariate distribution
and drawing from a sequence of univariate distributions
are conditioned to univariate realizations. That is, its
principle is to sequentially draw the value at each new
simulated point from the conditional distribution
through the data and the values simulated previously(Chilès and Delfiner, 1999).
3.2. TBSIM
The principle of TBSIM is to produce a non-conditional
simulation at first. That is, yielding a map that reflects

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the variogram, but the data is not honored. Afterwards,
in order to correct it, a map is obtained by interpolating
the experimental error between the measured data andnon-conditional simulated value at each data point(Chilès and Delfiner, 1999).

5. Conclusion
Both methods have their own merits. SGS isstraightforward and not a time-intensive method.
Conversely, sequential simulations tend to yieldsmoothed outcomes. TBSIM may be considered as a
powerful tool to depict the spatial distribution of metal
concentrations in a deposit, once TBSIM broadly
preserves the characteristics of original data.
Acknowledgement: We sincerely thank Dr. Tatsuo
Nozaki and Dr. Yutaro Takaya for providing the chemical
analysis data obtained by D/V Chikyu.

Fig. 1: Dimension of study area and its spatial distribution ofboreholes (black dots).

3.3. Method Evaluations
To assess which method, SGS or TBSIM, is moresuitable for the current study area, the best model must
fit to empirical model and its uncertainty. The former
can be based entirely on facts, such as field observations,geochemical and geophysical data, or theoretical basedon conceptual ideas generally borne out of experienceand knowledge, and extrapolation from known mineral
districts (Pirajno, 2009). Regarding the latter, suchmodel must reproduce the first- and second-order
statistics of the conditioning data, the histogram, andvariogram of the samples (Deutsch and Journel, 1998).

4. Results and Discussion
The
setsemivariogramisconsideredasomnidirectional along XY with a normal component tothis reference plane. Applying the spherical model, its
nugget effect is 0.3186. Considering the plane XY, its
range and sill are 100 m and 0.34, respectively, while, for
its normal component, its range is 112m and sill is fixed
to 1.32. As Chilès and Delfiner (1999) asserts SGS tends
to show much shorter range than the domain, asuggested and followed solution was to set a larger
neighbourhood. In spite of the cross-validation scores forboth SGS and TBSIM reached similar values, 0.80 and0.82, respectively, increasing the neighbourhood implies
a higher risk of estimating the mean values of thesamples, which decreases the variability of realization
outcomes. Even cautiously setting all parameters, SGS’
outcome realizations presented lesser variability and are
not consistent with the first- and second-order statisticsof the original data contrasting with their TBSIM’scounterparts.
Fig. 2 illustrate three cross-sections along E-W, where
the conceptual model (Fig. 2A) shows the expected
lithotypes distribution, and Figs. 2B and 2C represent
the spatial distribution of log (Pb) of SGS’ and TBSIM’srealizations respecting the assessment of their outcomes.
SGS method depicts better the concentration of higher
values in the sulfide layers as well as in the mound. On
the other hand, TBSIM properly reflects locations withlower values of the random variable.

Fig. 2: Cross-sections along E-W in which (A) illustrates theconceptual model of study area, and (B) and (C) depict spatial
distributions of log (Pb) using Sequential Gaussian Simulation(SGS) and Turning Bands Simulations (TBSIM), respectively.

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