ASTM D5924-96e1

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e1
Designation: D 5924 – 96
Standard Guide for
Selection of Simulation Approaches in Geostatistical Site
Investigations
This standard is issued under the fixed designation D 5924; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
e NOTE—Paragraph 1.5 was added editorially October 1998.
INTRODUCTION
Geostatistics is a framework for data analysis, estimation, and simulation in media whose
measurable attributes show erratic spatial variability yet also possess a degree of spatial continuity
imparted by the natural and anthropogenic processes operating therein. The soil, rock, and contained
fluids encountered in environmental or geotechnical site investigations present such features, and their
sampled attributes are therefore amenable to geostatistical treatment. Geostatistical simulation
approaches are used to produce maps of an attribute that honor the spatial variability of sampled
values. This guide reviews criteria for selecting a simulation approach, offering direction based on a
consensus of views without recommending a standard practice to follow in all cases.
1. Scope document be applied without consideration of a project’s many
unique aspects. The word “Standard” in the title of this
1.1 This guide covers the conditions that determine the
document means only that the document has been approved
selection of a suitable simulation approach for a site investi-
through the ASTM consensus process.
gation problem. Alternative simulation approaches considered
here are conditional and nonconditional, indicator and Gauss-
2. Referenced Documents
ian, single and multiple realization, point, and block.
2.1 ASTM Standards:
1.2 This guide describes the conditions for which the use of
D 653 Terminology Relating to Soil, Rock, and Contained
simulation is an appropriate alternative to the use of estimation
Fluids
in geostatistical site investigations.
D 5549 Guide for Reporting Geostatistical Site Investiga-
1.3 This guide does not discuss the basic principles of
tions
geostatistics. Introductions to geostatistics may be found in
2 D 5922 Guide for Analysis of Spatial Variation in Geostatis-
numerous texts including Refs (1), (2), and (3).
tical Site Investigations
1.4 This guide is concerned with general simulation ap-
D 5923 Guide for Selection of Kriging Methods in Geo-
proaches only and does not discuss particular simulation
statistical Site Investigations
algorithms currently in use. These are described in Refs (4),
(5), and (6).
3. Terminology
1.5 This guide offers an organized collection of information
3.1 Definitions of Terms Specific to This Standard:
or a series of options and does not recommend a specific
3.1.1 drift, n—in geostatistics, a systematic spatial variation
course of action. This document cannot replace education or
of the local mean of a variable, usually expressed as a
experience and should be used in conjunction with professional
polynomial function of location coordinates.
judgment. Not all aspects of this guide may be applicable in all
3.1.2 field, n—in geostatistics, the region of one-, two- or
circumstances. This ASTM standard is not intended to repre-
three-dimensional space within which a regionalized variable
sent or replace the standard of care by which the adequacy of
is defined.
a given professional service must be judged, nor should this
3.1.3 indicator variable, n—a regionalized variable that can
have only two possible values, zero or one.
1 3.1.4 kriging, n—an estimation method where sample
This guide is under the jurisdiction of ASTM Committee D-18 on Soil and
weights are obtained using a linear least-squares optimization
Rock and is the direct responsibility of Subcommittee D18.01 on Surface and
Subsurface Characterization.
Current edition approved April 10, 1996. Published June 1996.
2 3
The boldface numbers in parentheses refer to a list of references at the end of Annual Book of ASTM Standards, Vol 04.08.
the text. Annual Book of ASTM Standards, Vol 04.09.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
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D5924–96
procedure based on a mathematical model of spatial variability approaches yield maps that preserve the spatial variability of
and where the unknown variable and the available sample the regionalized variable.
values may have a point or block support.
5.1.1 If mapped values of the regionalized variable are
3.1.5 nugget effect, n—the component of spatial variance
required to provide an estimate of actual values at unsampled
unresolved by the sample spacing and the additional variance
points, then an estimation approach such as kriging is appro-
due to measurement error.
priate.
3.1.6 point, n—in geostatistics, the location in the field at
5.1.2 If mapped values of the regionalized variable are to
which a regionalized variable is defined. It also commonly
preserve the spatial variability of values at unsampled points,
refers to the support of sample-scale variables.
then simulation rather than estimation should be used.
3.1.7 realization, n—an outcome of a spatial random func-
tion or a random variable.
NOTE 1—Preservation of in-situ spatial variability is important if
3.1.8 regionalized variable, n—a measured quantity or a
mapped values of the regionalized variable are to be entered in a
numerical attribute characterizing a spatially variable phenom- numerical model of a dynamic process and therefore simulation should
generally be used. For example, mapped values of transmissivity to be
enon at a location in the field.
entered in a numerical model of ground water flow should be generated by
3.1.9 simulation, n—in geostatistics, a numerical procedure
simulation (8). However, if the numerical process model is insensitive to
for generating realizations of fields based on the random
spatial variations of the regionalized variable, then an estimation approach
function model chosen to represent a regionalized variable.
may also be used.
3.1.10 conditional simulation, n—a simulation approach
5.2 Conditional Versus Nonconditional Simulation—
where realizations of the random function model are con-
strained by values at sampled locations. Geostatistical simulation methods are able to produce maps of
3.1.11 nonconditional simulation, n—a simulation approach a regionalized variable that honor values observed at sampled
where realizations of the random function model are uncon-
points, a selected univariate distribution model, and a selected
strained by sample data. model of spatial variation. The univariate distribution model
3.1.12 smoothing effect, n—in geostatistics, the reduction in
may be that of the observed sample values or a model that is
spatial variance of estimated values compared to true values.
deemed more appropriate. The model of spatial variation may
3.1.13 spatial average, n—a quantity obtained by averaging
be that of observed sample values or a model of spatial
a regionalized variable over a finite region of space.
variation that is deemed more appropriate.
3.1.14 support, n—in geostatistics, the spatial averaging
5.2.1 If the simulated field need honor only a univariate
region over which a regionalized variable is defined, often
distribution model and a spatial variability model, then a
approximated by a point for sample-scale variables.
nonconditional simulation approach is sufficient.
3.2 Definitions of Other Terms—For definitions of other
5.2.2 If the
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