**Summary of the onCALCULATION methods used in dbSEABED **

**Chris Jenkins **

Institute of Arctic & Alpine Research (INSTAAR),

University of Colorado at Boulder,

Boulder CO, 80309-0450

09Jun2004 (rev. 15May2005)

The module onCALCULATE performs a small amount of modeling to extend the
outputs of dbSEABED to reasonable estimates of seafloor properties. This
is particularly useful for geoacoustic and other physical properties
which have no practical mappable data distribution based on actual
analyses. The modeling is based on theoretical or empirical relations
that are documented below. The chosen relationships may be replaced by
others in the future as further physical properties research is
published and as validation of the onCALCULATION results is done. Users
of dbSEABED may choose whether to use these lower accuracy estimates in
mappings or to work with map data coverages that are less reliable
because they contain less data.

A couple of principles have guided the selection of relationships and
their implementation: (a) that the methods should be transparent and
well-documented, not complex, (b) they may be built on extracted or
parsed parameter inputs, but not on values that are themselves
onCALCULATED, (c) they might apply only to certain sections of the input
parameter range, (d) they preferably are published relationships, but if
not then (e) should be supported by the analysis of a substantial amount
of data from a wide range of sediments.

The methods that are currently implemented are:

-   1\. [Grain size / Sorting from Gravel:Sand:Silt:Clay and
    Gravel:Sand:Mud Ratios ]{.underline}

Gvl:Snd:Slt:Cly and Gvl:Snd:Mud [(GSSC, GSM) ]{.underline}ratios are in
effect short grain size-fraction histograms for the sediments. An
estimate of AV and SD grain size can be made from them as follows. Each
class is assigned a central grain size value based on examinations of
large USGS and other datasets in EXCEL. These GSSC(M) class central
values result: -3, 2, 5, 7, (8) in phi.

A weighted mean and weighted standard deviation are formed across the
GSSC or GSM classes, leading to an estimate of the average grain size
and sorting of the sediment. A method of validation and uncertainty
calculation is available by comparison of the results for samples where
a mean/sorting is already measured.

-   2\. [Hydrographic Chart Bottom Type code ]{.underline}

This code, described in UKHO (2005) and NOS (1997), has the form
"Cy.S.Co". It is essentially the same as the US NOS codes. The
calculation is mostly a matter of assigning textural classes in
front-significant order based on the GSSC(M) ratios, but also with
special classes "R", "Wd" where rock and weed memberships are
significant. Thus, the output codes are minimal codes.

-   3\. [Folk and Shepard Classifications ]{.underline}

These have been implemented following the schemes in Poppe and Polloni
(2000).

-   4\. [P-wave Velocities for Consolidated Materials Based on
    Time-Average Model ]{.underline}

This calculation is performed only where there is an indication of
cementation or consolidation in the material, usually expressed by
measured or parsed Shear Strength \>50 kPa or porosity \<35%, and where
the porosity has been measured. Then:

mVp = (1 - Poros) / VelSol + Poros / VelFlu

where Poros is the fractional porosity of the material and VelSol and
VelFlu are the solid and fluid phase p-wave velocities. The constants
are: VelSol = 5000, VelFlu = 1520 (these are measured values, different
from those optimized for models such as Biot Theory; see Thorsos et al,
(2001)). The relation is associated with data over the whole range of
porosities (Fig. 1). The time average model is attributed to Wyllie, et
al, (1963).

*Fig. 1. The distribution of sediments by their Porosity and P- and
S-wave Velocity values. Several separate populations are apparent. For
P-wave velocities, the loose sediments with low velocities from 34%
porosity and following the Gassman function; consolidated sediments
following the Time-average relation; apparently cemented sediments with
anomalously high velocities for the porosity. The S-wave populations
have yet to be explained. *

-   5\. [Porosity Based on Mud Content of Loose Sediments ]{.underline}

A compilation of many published analysis (Fig 2) results supports the
empirical relationship:

mPor = 0.4 \* mud + 43

for mud% \> 7%. It appears to hold equally for terrigenous and carbonate
sediments. Figure 3 illustrates the relationship for sediments of the
Mississippi-Alabama-Florida (MAFLA) shelf.

*Fig. 2. Empirical data supporting the Mud%-Porosity relation where mud
fraction is \>7%. The plotted data is a mix of terrigenous, carbonate,
loose and consolidated samples, Mississippi-Alabama-Florida (MAFLA)
shelf. *

-   6\. [Porosity Based on Average Grain size ]{.underline}

Richardson and Briggs (1993) proposed a relationship between porosity
and average grain size (AvGrsz, phi units) based on their measurements
of muddy and sandy sediments. The relation is inverted for the
on-calculation, and is applied only in the range AvGrsz \> 0 phi:

Por = 26.92 + 5.92 \* AvGrsz

The form is less accurate than methods where the percent of mud is
known, and is not used in those cases.

-   7\. [Coarse Fraction and the P-wave Velocity ]{.underline}

Related to the porosity-mud fraction function is another between coarse
fraction and Vp:

mVp = 0.0009 \* SpG^3^ + -0.14 \* SpG^2^ + 8.56 \* SpG + 1512.76

where SpG is the percent coarse fraction. This polynomial is a poor fit
and further work is required.

-   8\. [Wood-Gassman Equation for P-wave Velocity in Loose Sediments
    ]{.underline}

This method of estimating Vp ie applied to sediments with no evidence of
consolidation. It depends on assumed values for some acoustic constants
of the sediments: (a) the Bulk Moduli K for solid, fluid, frame(Ko1Sol,
Ko1Flu and Ko1Fra 3.6E+10, 2E+09 and 4E+08, MKS units); and (b) the
Rigidities for solids and frame (RigidSol, RigidFra 2.2E+07, 1E+07).

The sediment Bulk Modulus and Density are:

Ko1 = (1-fPor)/Ko1Sol + fPor/Ko1Flu

SedDens = (1-fPor)\*DenSol + fPor\*DensFlu .

And the p-wave velocity is calculated as:

[Qgass=Ko1Flu\*(Ko1Sol-Ko1Fra) ]{.underline}

(fPor\*(Ko1Sol-Ko1Flu))

Kgass=Ko1Sol\*(Ko1Fra+Qgass)/(Ko1Sol-Qgass)

VPgass=√(Kgass+4/3\*RigidFra )/SedDens)

Gassman (1951). VPgass is output as the estimate of Vp.

The Wood-Gassman relation is one of several that have been proposed
between porosity and the acoustic velocities. As can be seen on Fig. 1,
the relation has an associated population of data ranging only between
35-80% porosity. In the dbSEABED on-calculation it is applied only where
porosity is known and \>35% and where there is no indication of
consolidation.

-   9\. [Roughness from Grain Protrusion for Gravels and Coarser
    ]{.underline}

Kirchner and others (1990) offer a method for the calculation of grain
protrusion (PnKir) above a sediment surface:

EnKir=0.5\*(DnKir-D50Kir+(DnKir+D50Kir)\*cos(F100nKir))

PnKir=EnKir+pi\*D50Kir/12

where D50Kir and DnKir are the median and nth percentile grain sizes,
and F100nKir is the Friction angle with a test grain of the 100-nth
grain size percentile. In on-calculation the estimation is done only
using the central and the coarsest grain sizes (CSESTsz; either PRS or
EXT) for D50Kir and DnKir. PnKir is output as an estimate of roughness.

-   10\. [Roughness Metric from Outsized Clasts ]{.underline}

This metric was employed as an early measure of seabed roughness; it is
based on an idealized arrangement of the sediment clasts and particles.
The coarsest grain size is logged from previous processing of grain size
analysis and descriptive data inputs, or is estimated from the average
plus 2 times the SD (sorting) where both are known. The vertical
roughness is estimated as half the clast size (D) with allowance for
natural oblateness:

dZ=0.5 \* D \* CSF

where CSF is the Corey Shape Factor to account for non-sphereicity. (In
naturally worn materials CSF is about 0.7; e.g., Jimenez & Madsen 2003.)
The spacing of the clast grain size is assessed as half the repeat
distance implied by the fractional linear abundance P~^L^~ of the
outsized clast with size D. Linear abundance is related to areal and
volume (most common) abundances P~^A^~ and P~^V^~ as:
P~^L^~=P~^A^~^1/2^, P~^L^~=P~^V^~^1/3^ . The clast protrusion and
half-spacing are output as the vertical and horizontal roughness scales.

-   11\. [Critical Shear Stress ]{.underline}

If the material shows evidence of consolidation, then the Critical Shear
Stress (CSS, N/m^2^) is set equal to the reported Shear Strength (kPa).
Whitehouse et al. (2000, p. 27) discuss the relationship, which is
interim in the on-calculation.

For loose sediments, the functions related to grain size (AvGRZ) were
investigated based on data from many studies (Fig. 3). This work was
done in conjunction with IOW, in Germany. The conclusions were: (i) with
fine grained loose sediments where density or porosity are known, use
the relationship of Mitchener, et al, (1996, in Whitehouse, et al,
(2000)); (ii) else for those sediments use a generalized value of 0.5
N/m^2^; (iii) for loose coarse grained sediments use a log-linear
relationship as shown in Fig. 3, log10(CSS)=log10\[1.04-AvGRZ\*0.6\].

Bioturbation and bioconsolidation were not recognized in the estimation
process for fine sediments, though they can be important (see Black, et
al, (2002)). A correction of minor importance compared to the overall
uncertainties is applied in the on-calculation.

*Fig. 3. A compilation of Critical Shear Stress results by sediment
grain size over the gravel to clay range. Over 24 references were used
referring to marine and river sediments, field and laboratory
experiments, on unaltered and manipulated natural sediments. *

[References Cited ]{.underline}

Black, K.S., Tolhurst, T.J., Paterson, D.M., and Hagerthey, S.E., 2002,
Working with natural cohesive sediments: J. Hydraul. Engng, v. 128, no.
1, p. 2-8.

Gassmann, F., 1951, Elastic waves through a packing of spheres:
Geophysics, v. 16, no. 673-685.

Jimenez, J.A., and Madsen, O.S., 2003, A simple formula to estimate
settling velocity of natural sediments: J. of Waterway, Port, Coastal
and Ocean Engineering, v. March/April 2003, p. 70-78.

Kirchner, J.W., Dietrich, W.E., Iseya, F., and Ikeda, H., 1990, The
variability of critical shear stress, friction angle, and grain
protrusion in water-worked sediments: Sedimentology, v. 37, p. 647-672.

National Ocean Service (NOS), 1997, Chart no. 1, United States of
America, Nautical chart symbols, abbreviations and terms, US National
Ocean Service \[Chart\].

Poppe, L.J., and Polloni, C.F., 2000, USGS East-Coast sediment analysis:
Procedures, database, and georeferenced displays: U.S. Geological Survey
Open-file Report 00-358.

Richardson, M.D., and Briggs, K.B., 1993, On the use of acoustic
impedance values to determine sediment properties: Proc. Inst.
Acoustics, v. 15, no. 2, p. 15-24.

Thorsos, E.I., Williams, K.L., Jackson, D.R., Richardson, M.D., Briggs,
K.B., and Tang, D., 2001, An experiment in high-frequency sediment
acoustics: SAX99: IEEE J. Oceanic Eng, v. 26, p. 4-25.

UK Hydrographic Office (UKHO), 2005, Chart symbols & abbreviations,
Chart BA 5011 \[Booklet\], UK Hydrographic Office, 38 p.

Whitehouse, R., Soulsby, R., Roberts, W., and Mitchener, H., 2000,
Dynamics of estuarine muds. A manual for practical applications: London,
Thomas Telford Publ., 209 p.

Wyllie, M., Gardner, G., and Gregory, A., 1963, Studies of elastic wave
attenuation in porous media: Geophysics, v. 27, p. 569-589.