ASTM D5922-96e1
(Guide)Standard Guide for Analysis of Spatial Variation in Geostatistical Site Investigations
Standard Guide for Analysis of Spatial Variation in Geostatistical Site Investigations
SCOPE
1.1 This guide covers recommendations for analyzing, interpreting, and modeling spatial variation of regionalized variables in geotechnical and environmental site investigations.
1.2 The measures of spatial variation discussed in this guide include variograms and correlograms; these are fully described in (1), (2), (3), and (4).
1.3 This guide is intended to assist those who are already familiar with the geostatistical tools discussed herein and does not provide introductory information on the analysis, interpretation, and modeling of spatial variation.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: D 5922 – 96
Standard Guide for
Analysis of Spatial Variation in Geostatistical Site
Investigations
This standard is issued under the fixed designation D 5922; 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. This guide is concerned with the
analysis, interpretation, and modeling of spatial variation. The purpose of this guide is to offer
guidance based on a consensus of views but not to establish a standard practice to follow in all cases.
1. Scope unique aspects. The word “Standard” in the title of this
document means only that the document has been approved
1.1 This guide covers recommendations for analyzing, in-
through the ASTM consensus process.
terpreting, and modeling spatial variation of regionalized
variables in geotechnical and environmental site investigations.
2. Referenced Documents
1.2 The measures of spatial variation discussed in this guide
2.1 ASTM Standards:
include variograms and correlograms; these are fully described
2 D 653 Terminology Relating to Soil, Rock, and Contained
in (1), (2), (3), and (4).
Fluids
1.3 This guide is intended to assist those who are already
D 5549 Guide for Reporting Geostatistical Site Investiga-
familiar with the geostatistical tools discussed herein and does
tions
not provide introductory information on the analysis, interpre-
D 5923 Guide for Selection of Kriging Methods in Geo-
tation, and modeling of spatial variation.
statistical Site Investigations
1.4 This standard does not purport to address all of the
D 5924 Guide for the Selection of Simulation Approaches
safety concerns, if any, associated with its use. It is the
in Geostatistical Site Investigations
responsibility of the user of this standard to establish appro-
priate safety and health practices and determine the applica-
3. Terminology
bility of regulatory limitations prior to use.
3.1 Definitions of Terms Specific to This Standard:
1.5 This guide offers an organized collection of information
3.1.1 anisotropy, n—in geostatistics, a property of the
or a series of options and does not recommend a specific
variogram or covariance stating that different spatial variation
course of action. This document cannot replace education or
structures are observed in different directions.
experience and should be used in conjunction with professional
3.1.1.1 geometric anisotropy, n—a form of anisotropy in
judgment. Not all aspects of this guide may be applicable in all
which the variogram range changes with direction while the sill
circumstances. This ASTM standard is not intended to repre-
remains constant.
sent or replace the standard of care by which the adequacy of
3.1.1.2 zonal anisotropy, n—a form of anisotropy in which
a given professional service must be judged, nor should this
the variogram sill changes with direction.
document be applied without consideration of a project’s many
3.1.2 correlogram, n—a measure of spatial variation ex-
pressing the coefficient of correlation between two variables as
1 a function of the lag separating their locations.
This guide is under the jurisdiction of ASTM Committee D-18 on Soil and
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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D5922–96
3.1.3 drift, n—in geostatistics, a systematic spatial variation and history. All of these are necessary for a sound interpreta-
of the local mean of a variable, usually expressed as a tion of spatial variation.
polynomial function of location coordinates. 4.4 For the modeling of spatial variation, this guide recom-
3.1.4 estimation, n—a procedure by which the value of a mends attention to the short-scale behavior of the mathematical
variable at an unsampled location is predicted using a weighted model of spatial variation and to its anisotropy as reflected in
average of sample values from the neighborhood of that the directional changes in the range.
location.
5. Significance and Use
3.1.5 lag, n—in geostatistics, the vector separating the
locations of two variables, as used in measures of spatial 5.1 This guide is intended to encourage consistency in the
variation. analysis, interpretation, and modeling of spatial variation.
3.1.6 nugget effect, n—the component of spatial variance 5.2 This guide should be used in conjunction with Guides
unresolved by the sample spacing including the variance due to D 5549, D 5923, and D 5924.
measurement error.
6. Analysis of Spatial Variation
3.1.7 range, n—in geostatistics, the maximum distance over
which a variable exhibits spatial correlation in a given direc-
6.1 The principal tools for analyzing spatial variation are the
tion.
variogram and the correlogram; whenever possible, both
3.1.8 regionalized variable, n—a measured quantity or a
should be used.
numerical attribute characterizing a spatially variable phenom-
NOTE 1—Features that appear on both the variogram and correlogram
enon at a location in the field.
are usually worthy of interpretation and should be reflected in the
3.1.9 sill, n—in geostatistics, a stable level of spatial
mathematical model for spatial variation. Features that appear on one but
variation observed for lags greater than the range.
not the other may reflect artifacts of the calculation or peculiarities of the
3.1.10 simulation, n—in geostatistics, a Monte-Carlo pro- available data and their configuration; such features require further
investigation before a decision can be made on whether they should be
cedure for generating realizations of fields based on the random
reflected in the mathematical model for spatial variation.
function model chosen to represent a regionalized variable. In
addition to honoring a random function model, the realizations 6.2 If univariate data analysis has revealed that the data
may also be constrained to honor data values observed at have a skewed distribution or if study objectives require that
sampled locations. the data be transformed, then the analysis of spatial variation
3.1.11 structure, n—in geostatistics, a source of spatial should be performed on an appropriate transform of the data.
variability with a characteristic length scale.
NOTE 2—One of the most important aspects of a mathematical model of
3.1.12 variogram, n—a measure of spatial variation defined
spatial variation is the direction and degree of anisotropy. This is often
as one half the variance of the difference between two variables
much better revealed by variograms and correlograms of transformed data
and expressed as a function of the lag; it is also sometimes
values, such as logarithms or normal scores. Even if the study ultimately
makes use of the original data values in estimation or simulation, the
referred to as the semi-variogram.
analysis of spatial variation on transformed data values often leads to the
3.1.12.1 experimental variogram, n—an experimental mea-
development of a more appropriate model of spatial variation.
sure of spatial variation usually calculated as one half the
average squared difference between all pairs of data values 6.3 The choice of lag spacing and tolerance should take into
within the same lag. account the data configuration, particularly the minimum
3.2 For definitions of other terms used in this guide, refer to spacing between the available data and the average spacing
Terminology D 653 and Guides D 5549, D 5923, and D 5924. between the available data. Whenever possible, the choices of
A complete glossary of geostatistical terminology is given in lag spacing and tolerance should ensure that at least 20 paired
Ref (5). data values will be available for each lag.
NOTE 3—With data configurations that are pseudo-regular, it is com-
4. Summary of Guide
mon to use the spacing between the columns and rows of the sampling
4.1 This guide presents advice on three separate but related
grid as the lag spacing and to use half of this distance as the lag tolerance.
components of the study of spatial variation: the analytical
If the data configuration is irregular, then the lag spacing and tolerance
tools that are used; the interpretation of the results; and the may also need to be irregular (see Refs (3), and (6)).
development of an appropriate mathematical model.
6.4 Spatial variation should be analyzed in different direc-
4.2 For the analysis of spatial variation, this guide empha-
tions; the choice of directions and directional tolerances should
sizes the use of variograms and correlograms on both trans-
reflect the configuration of the available data and should also
formed and untransformed variables since these are the most
take into account qualitative information about the physical
common and successful analytical tools in most practical
and chemical characteristics of the regionalized variable being
situations. Other methods exist and may enhance the develop-
studied.
ment of an appropriate model of spatial variation.
NOTE 4—Omni-directional variograms or correlograms often are ap-
4.3 For the interpretation of spatial variation, this guide
propriate for refining decisions on lag spacing and lag tolerance; they also
emphasizes the importance of site-specific quantitative and
provide preliminary insight into the range of correlation and the short-
qualitative information. Quantitative information includes the
scale variability of the data. However, omni-directional calculations of
number and configuration of the available data, their precision,
spatial variation do not constitute a thorough analysis of spatial variation
and their univariate s
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