ASTM D5922-96(2010)
(Guide)Standard Guide for Analysis of Spatial Variation in Geostatistical Site Investigations
Standard Guide for Analysis of Spatial Variation in Geostatistical Site Investigations
SIGNIFICANCE AND USE
This guide is intended to encourage consistency in the analysis, interpretation, and modeling of spatial variation.
This guide should be used in conjunction with Guides D5549, D5923, and D5924.
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 Refs. (1-4).
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.
1.5 This guide offers an organized collection of information or a series of options and does not recommend a specific course of action. This document cannot replace education or experience and should be used in conjunction with professional judgment. Not all aspects of this guide may be applicable in all circumstances. This ASTM standard is not intended to represent or replace the standard of care by which the adequacy of a given professional service must be judged, nor should this document be applied without consideration of a project's many unique aspects. The word “Standard” in the title of this document means only that the document has been approved through the ASTM consensus process.
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Designation: D5922 − 96 (Reapproved 2010)
Standard Guide for
Analysis of Spatial Variation in Geostatistical Site
Investigations
This standard is issued under the fixed designation D5922; 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 (´) indicates an editorial change since the last revision or reapproval.
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 a given professional service must be judged, nor should this
document be applied without consideration of a project’s many
1.1 This guide covers recommendations for analyzing,
unique aspects. The word “Standard” in the title of this
interpreting, and modeling spatial variation of regionalized
document means only that the document has been approved
variablesingeotechnicalandenvironmentalsiteinvestigations.
through the ASTM consensus process.
1.2 The measures of spatial variation discussed in this guide
include variograms and correlograms; these are fully described
2. Referenced Documents
in Refs. (1-4).
2.1 ASTM Standards:
1.3 This guide is intended to assist those who are already
D653 Terminology Relating to Soil, Rock, and Contained
familiar with the geostatistical tools discussed herein and does
Fluids
not provide introductory information on the analysis,
D5549 Guide for The Contents of Geostatistical Site Inves-
interpretation, and modeling of spatial variation.
tigation Report (Withdrawn 2002)
1.4 This standard does not purport to address all of the D5923 GuideforSelectionofKrigingMethodsinGeostatis-
safety concerns, if any, associated with its use. It is the tical Site Investigations
responsibility of the user of this standard to establish appro- D5924 Guide for Selection of Simulation Approaches in
priate safety and health practices and determine the applica- Geostatistical Site Investigations
bility of regulatory limitations prior to use.
3. Terminology
1.5 This guide offers an organized collection of information
or a series of options and does not recommend a specific
3.1 Definitions of Terms Specific to This Standard:
course of action. This document cannot replace education or
3.1.1 anisotropy, n—in geostatistics, a property of the var-
experience and should be used in conjunction with professional
iogram or covariance stating that different spatial variation
judgment. Not all aspects of this guide may be applicable in all
structures are observed in different directions.
circumstances. This ASTM standard is not intended to repre-
3.1.2 correlogram, n—a measure of spatial variation ex-
sent or replace the standard of care by which the adequacy of
pressing the coefficient of correlation between two variables as
a function of the lag separating their locations.
This guide is under the jurisdiction ofASTM Committee D18 on Soil and Rock
and is the direct responsibility of Subcommittee D18.01 on Surface and Subsurface
Characterization. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved May 1, 2010. Published September 2010. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1996. Last previous edition approved in 2004 as D5922–96(2004). Standards volume information, refer to the standard’s Document Summary page on
DOI: 10.1520/D5922-96R10. the ASTM website.
2 4
The boldface numbers in parentheses refer to a list of references at the end of The last approved version of this historical standard is referenced on
the text. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5922 − 96 (2010)
3.1.3 drift, n—in geostatistics, a systematic spatial variation common and successful analytical tools in most practical
of the local mean of a variable, usually expressed as a situations. Other methods exist and may enhance the develop-
polynomial function of location coordinates. ment of an appropriate model of spatial variation.
3.1.4 estimation, n—a procedure by which the value of a
4.3 For the interpretation of spatial variation, this guide
variableatanunsampledlocationispredictedusingaweighted
emphasizes the importance of site-specific quantitative and
average of sample values from the neighborhood of that
qualitative information. Quantitative information includes the
location.
number and configuration of the available data, their precision,
and their univariate statistics; qualitative information includes
3.1.5 experimental variogram, n—an experimental measure
items such as local geology and geomorphology, site usage,
of spatial variation usually calculated as one half the average
and history. All of these are necessary for a sound interpreta-
squared difference between all pairs of data values within the
tion of spatial variation.
same lag.
4.4 For the modeling of spatial variation, this guide recom-
3.1.6 geometric anisotropy, n—a form of anisotropy in
mendsattentiontotheshort-scalebehaviorofthemathematical
whichthevariogramrangechangeswithdirectionwhilethesill
model of spatial variation and to its anisotropy as reflected in
remains constant.
the directional changes in the range.
3.1.7 lag, n—in geostatistics, the vector separating the
locations of two variables, as used in measures of spatial
5. Significance and Use
variation.
5.1 This guide is intended to encourage consistency in the
3.1.8 nugget effect, n—the component of spatial variance
analysis, interpretation, and modeling of spatial variation.
unresolvedbythesamplespacingincludingthevariancedueto
measurement error. 5.2 This guide should be used in conjunction with Guides
D5549, D5923, and D5924.
3.1.9 range, n—in geostatistics, the maximum distance over
which a variable exhibits spatial correlation in a given direc-
6. Analysis of Spatial Variation
tion.
6.1 Theprincipaltoolsforanalyzingspatialvariationarethe
3.1.10 regionalized variable, n—a measured quantity or a
variogram and the correlogram; whenever possible, both
numerical attribute characterizing a spatially variable phenom-
should be used.
enon at a location in the field.
NOTE 1—Features that appear on both the variogram and correlogram
3.1.11 sill, n—in geostatistics, a stable level of spatial
are usually worthy of interpretation and should be reflected in the
variation observed for lags greater than the range.
mathematical model for spatial variation. Features that appear on one but
3.1.12 simulation, n—in geostatistics, a Monte-Carlo proce-
not the other may reflect artifacts of the calculation or peculiarities of the
available data and their configuration; such features require further
dure for generating realizations of fields based on the random
investigation before a decision can be made on whether they should be
function model chosen to represent a regionalized variable. In
reflected in the mathematical model for spatial variation.
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
3.1.13 structure, n—in geostatistics, a source of spatial
should be performed on an appropriate transform of the data.
variability with a characteristic length scale.
NOTE2—Oneofthemostimportantaspectsofamathematicalmodelof
3.1.14 variogram, n—a measure of spatial variation defined
spatial variation is the direction and degree of anisotropy. This is often
asonehalfthevarianceofthedifferencebetweentwovariables
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
referred to as the semi-variogram. makes use of the original data values in estimation or simulation, the
analysis of spatial variation on transformed data values often leads to the
3.1.15 zonal anisotropy, n—a form of anisotropy in which
development of a more appropriate model of spatial variation.
the variogram sill changes with direction.
6.3 The choice of lag spacing and tolerance should take into
3.2 For definitions of other terms used in this guide, refer to
account the data configuration, particularly the minimum
Terminology D653 and Guides D5549, D5923, and D5924.A
spacing between the available data and the average spacing
complete glossary of geostatistical terminology is given in Ref
between the available data. Whenever possible, the choices of
(5).
lag spacing and tolerance should ensure that at least 20 paired
data values will be available for each lag.
4. Summary of Guide
NOTE3—Withdataconfigurationsthatarepseudo-regular,itiscommon
4.1 This guide presents advice on three separate but related
to use the spacing between the columns and rows of the sampling grid as
components of the study of spatial variation: the analytical
the lag spacing and to use half of this distance as the lag tolerance. If the
tools that are used, the interpretation of the results, and the
data configuration is irregular, then the lag spacing and tolerance may also
development of an appropriate mathematical model.
need to be irregular (see Refs (3), and (6)).
4.2 For the analysis of spatial variation, this guide empha- 6.4 Spatial variation should be analyzed in different direc-
sizes the use of variograms and correlograms on both trans- tions; the choice of directions and directional tolerances should
formed and untransformed variables since these are the most reflect the configuration of the available data and should also
D5922 − 96 (2010)
take into account qualitative information about the physical 7.3 The nugget effect shown by the experimental variogram
and chemical characteristics of the regionalized variable being and correlogram should be consistent with the precisi
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