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 D 5549, D 5923, and D 5924.
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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Publication Date
30-Jun-2004
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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation:D5922–96 (Reapproved 2004)
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 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
variablesingeotechnicalandenvironmentalsiteinvestigations.
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 D653 Terminology Relating to Soil, Rock, and Contained
in Refs. (1-4).
Fluids
1.3 This guide is intended to assist those who are already
D5549 Guide for The Contents of Geostatistical Site Inves-
familiar with the geostatistical tools discussed herein and does
tigation Report
not provide introductory information on the analysis, interpre-
D5923 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
D5924 Guide for Selection of Simulation Approaches in
safety concerns, if any, associated with its use. It is the
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
3.1.2 correlogram, n—a measure of spatial variation ex-
judgment. Not all aspects of this guide may be applicable in all
pressing the coefficient of correlation between two variables as
circumstances. This ASTM standard is not intended to repre-
a function of the lag separating their locations.
sent or replace the standard of care by which the adequacy of
3.1.3 drift, n—in geostatistics, a systematic spatial variation
a given professional service must be judged, nor should this
of the local mean of a variable, usually expressed as a
document be applied without consideration of a project’s many
polynomial function of location coordinates.
This guide is under thejurisdictionofASTMCommittee D18 onSoilandRock
and is the direct responsibility of Subcommittee D18.01 on Surface and Subsurface For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Characterization. contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Current edition approved July 1, 2004. Published August 2004. Originally Standards volume information, refer to the standard’s Document Summary page on
´1
approved in 1996. Last previous edition approved in 1996 as D5922 - 96 . DOI: the ASTM website.
10.1520/D5922-96R04. Withdrawn.
2 5
The boldface numbers in parentheses refer to a list of references at the end of Withdrawn. The last approved version of this historical standard is referenced
the text. on www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D5922–96 (2004)
3.1.4 estimation, n—a procedure by which the value of a and their univariate statistics; qualitative information includes
variableatanunsampledlocationispredictedusingaweighted items such as local geology and geomorphology, site usage,
average of sample values from the neighborhood of that and history. All of these are necessary for a sound interpreta-
location. tion of spatial variation.
3.1.5 experimental variogram, n—an experimental measure 4.4 For the modeling of spatial variation, this guide recom-
of spatial variation usually calculated as one half the average mendsattentiontotheshort-scalebehaviorofthemathematical
squared difference between all pairs of data values within the model of spatial variation and to its anisotropy as reflected in
same lag. the directional changes in the range.
3.1.6 geometric anisotropy, n—a form of anisotropy in
5. Significance and Use
whichthevariogramrangechangeswithdirectionwhilethesill
5.1 This guide is intended to encourage consistency in the
remains constant.
analysis, interpretation, and modeling of spatial variation.
3.1.7 lag, n—in geostatistics, the vector separating the
5.2 This guide should be used in conjunction with Guides
locations of two variables, as used in measures of spatial
D5549, D5923, and D5924.
variation.
3.1.8 nugget effect, n—the component of spatial variance
6. Analysis of Spatial Variation
unresolvedbythesamplespacingincludingthevariancedueto
6.1 Theprincipaltoolsforanalyzingspatialvariationarethe
measurement error.
variogram and the correlogram; whenever possible, both
3.1.9 range, n—in geostatistics,themaximumdistanceover
should be used.
which a variable exhibits spatial correlation in a given direc-
tion.
NOTE 1—Features that appear on both the variogram and correlogram
3.1.10 regionalized variable, n—a measured quantity or a
are usually worthy of interpretation and should be reflected in the
numerical attribute characterizing a spatially variable phenom- mathematical model for spatial variation. Features that appear on one but
not the other may reflect artifacts of the calculation or peculiarities of the
enon at a location in the field.
available data and their configuration; such features require further
3.1.11 sill, n—in geostatistics, a stable level of spatial
investigation before a decision can be made on whether they should be
variation observed for lags greater than the range.
reflected in the mathematical model for spatial variation.
3.1.12 simulation, n—in geostatistics, a Monte-Carlo pro-
6.2 If univariate data analysis has revealed that the data
cedureforgeneratingrealizationsoffieldsbasedontherandom
have a skewed distribution or if study objectives require that
function model chosen to represent a regionalized variable. In
the data be transformed, then the analysis of spatial variation
addition to honoring a random function model, the realizations
should be performed on an appropriate transform of the data.
may also be constrained to honor data values observed at
sampled locations.
NOTE 2—Oneofthemostimportantaspectsofamathematicalmodelof
3.1.13 structure, n—in geostatistics, a source of spatial
spatial variation is the direction and degree of anisotropy. This is often
much better revealed by variograms and correlograms of transformed data
variability with a characteristic length scale.
values, such as logarithms or normal scores. Even if the study ultimately
3.1.14 variogram, n—a measure of spatial variation defined
makes use of the original data values in estimation or simulation, the
asonehalfthevarianceofthedifferencebetweentwovariables
analysis of spatial variation on transformed data values often leads to the
and expressed as a function of the lag; it is also sometimes
development of a more appropriate model of spatial variation.
referred to as the semi-variogram.
6.3 The choice of lag spacing and tolerance should take into
3.1.15 zonal anisotropy, n—a form of anisotropy in which
account the data configuration, particularly the minimum
the variogram sill changes with direction.
spacing between the available data and the average spacing
3.2 For definitions of other terms used in this guide, refer to
between the available data. Whenever possible, the choices of
Terminology D653 and Guides D5549, D5923, and D5924.A
lag spacing and tolerance should ensure that at least 20 paired
complete glossary of geostatistical terminology is given in Ref
data values will be available for each lag.
(5).
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.
If the data configuration is irregular, then the lag spacing and tolerance
components of the study of spatial variation: the analytical
may also need to be irregular (see Refs (3), and (6)).
tools that are used, the interpretation of the results, and the
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. Quant
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