ASTM D5922-18

Standard Guide for Analysis, Interpretation, and Modeling of Spatial Variation in Geostatistical Site Investigations

SIGNIFICANCE AND USE
5.1 Whether for the sake of simplicity or because of a lack of information, geotechnical engineers regularly assume that soil and rock properties are the same throughout a particular location, even though they realize that the use of averaged parameter values can result in soil parameters that are significantly different from the actual parameters.  
5.2 Considering the spatial distribution of soil and rock mass properties, the use of geostatictics in site investigations should be considered as it will provide a more accurate estimation of the soil and rock properties based on the available input information.  
5.3 This guide is intended to encourage consistency in the analysis, interpretation, and modeling of spatial variation in geostatistical site investigations.  
5.4 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).2  
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, health, and environmental 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.  
1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 14-Dec-2018
• ICS: 07.060 - Geology. Meteorology. Hydrology
• Technical Committee: D18 - Soil and Rock
• Drafting Committee: D18.01 - Surface and Subsurface Investigation

Relations

• Replaces: ASTM D5922-96(2010) - Standard Guide for Analysis of Spatial Variation in Geostatistical Site Investigations
• Effective Date: 15-Dec-2018
• Refers: ASTM D5549-19 - Standard Guide for Contents of Geostatistical Site Investigation Report
• Effective Date: 01-May-2019
• Refers: ASTM D5924-18 - Standard Guide for Selection of Simulation Approaches in Geostatistical Site Investigations
• Effective Date: 15-Jul-2018
• Refers: ASTM D653-14 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Aug-2014
• Refers: ASTM D653-11 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Sep-2011
• Refers: ASTM D5923-96(2010) - Standard Guide for Selection of Kriging Methods in Geostatistical Site Investigations
• Effective Date: 01-May-2010
• Refers: ASTM D5924-96(2010) - Standard Guide for Selection of Simulation Approaches in Geostatistical Site Investigations
• Effective Date: 01-May-2010
• Refers: ASTM D653-09 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Jan-2009
• Refers: ASTM D653-08a - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Dec-2008
• Refers: ASTM D653-08 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Nov-2008
• Refers: ASTM D653-07f - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 15-Dec-2007
• Refers: ASTM D653-07e - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Nov-2007
• Refers: ASTM D653-07d - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Aug-2007
• Refers: ASTM D653-07c - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Jul-2007
• Refers: ASTM D653-07b - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-May-2007

Overview

ASTM D5922-18: Standard Guide for Analysis, Interpretation, and Modeling of Spatial Variation in Geostatistical Site Investigations offers comprehensive guidance for geotechnical and environmental professionals on analyzing, interpreting, and modeling the spatial variation of regionalized variables. Developed by ASTM International, this guide serves as a foundational document for applying geostatistical methods to soil, rock, and contained fluid properties, improving the accuracy and reliability of site investigations. The standard advocates for the consideration of natural spatial distribution rather than using overly simplified averaged values, thereby supporting better decision-making in engineering projects.

Key Topics

• Spatial Variation Analysis
  The standard emphasizes the use of geostatistics-particularly variograms and correlograms-to assess the spatial patterns and dependencies present in geotechnical and environmental data sets. These tools help quantify how properties vary and correlate over distance.

• Interpretation of Results
  Guidance is provided on integrating qualitative and quantitative site information, including geological context, data configuration, and univariate statistics, for a comprehensive understanding of spatial variation. The guide also discusses handling issues such as nugget effect, anisotropy, data skewness, and trends/drifts.

• Modeling Spatial Patterns
  Recommendations are made for developing mathematical models that reflect observed spatial behavior. These models should account for aspects like short-scale variability, anisotropy (directional dependence), and periodic features. Model validity is confirmed by fitting experimental observations, ensuring consistency with physical or chemical site understanding.

• Best Practice Principles
  Users are encouraged to utilize professional judgment, considering project-specific variables and site-specific data characteristics. The standard does not prescribe a single approach but rather presents structured options and considerations to promote consistency and rigor in geostatistical site investigations.

Applications

• Geotechnical Site Investigations
  The standard is widely used in characterizing the variability of soil and rock properties at construction, mining, and environmental remediation sites. Understanding spatial variation informs risk assessments and design margins for earthworks, foundations, and underground structures.

• Environmental Assessments
  Application of geostatistics supports mapping and modeling of contamination, groundwater quality, and other spatially variable environmental factors. This guide improves precision in estimates and scenario simulations for remediation strategies.

• Data-Driven Decision Making
  By providing robust frameworks for spatial data analysis, the guide enhances the interpretation of laboratory and field data, enabling more confident site characterization, resource estimation, and project planning.

• Simulation and Prediction
  Tools and models described in the standard are valuable for predictive mapping, simulating plausible spatial scenarios, and informing the placement of additional sampling locations.

Related Standards

• ASTM D5549 – Guide for the Contents of Geostatistical Site Investigation Report
• ASTM D5923 – Guide for Selection of Kriging Methods in Geostatistical Site Investigations
• ASTM D5924 – Guide for Selection of Simulation Approaches in Geostatistical Site Investigations
• ASTM D653 – Terminology Relating to Soil, Rock, and Contained Fluids

Practical Value

Implementing ASTM D5922-18 in site investigations helps practitioners:

• Achieve more accurate parameter estimation by accounting for spatial variability
• Apply appropriate statistical tools such as variograms and correlograms
• Develop and validate reliable mathematical models tailored to site-specific conditions
• Ensure consistency and rigor in reporting and analysis across projects

Keywords: geostatistics, spatial variation, variogram, correlogram, site investigations, geotechnical, environmental, modeling, spatial analysis, ASTM D5922-18.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: D5922 − 18
Standard Guide for
Analysis, Interpretation, and Modeling 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.
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 recommendations for analyzing,
document means only that the document has been approved
interpreting, and modeling spatial variation of regionalized
through the ASTM consensus process.
variablesingeotechnicalandenvironmentalsiteinvestigations.
1.6 This international standard was developed in accor-
1.2 The measures of spatial variation discussed in this guide
dance with internationally recognized principles on standard-
include variograms and correlograms; these are fully described
ization established in the Decision on Principles for the
in Refs. (1-4).
Development of International Standards, Guides and Recom-
1.3 This guide is intended to assist those who are already
mendations issued by the World Trade Organization Technical
familiar with the geostatistical tools discussed herein and does
Barriers to Trade (TBT) Committee.
not provide introductory information on the analysis,
2. Referenced Documents
interpretation, and modeling of spatial variation.
1.4 This standard does not purport to address all of the 2.1 ASTM Standards:
safety concerns, if any, associated with its use. It is the D653 Terminology Relating to Soil, Rock, and Contained
responsibility of the user of this standard to establish appro- Fluids
priate safety, health, and environmental practices and deter- D5549 Guide for The Contents of Geostatistical Site Inves-
mine the applicability of regulatory limitations prior to use. tigation Report (Withdrawn 2002)
1.5 This guide offers an organized collection of information D5923 GuideforSelectionofKrigingMethodsinGeostatis-
or a series of options and does not recommend a specific tical Site Investigations
course of action. This document cannot replace education or D5924 Guide for Selection of Simulation Approaches in
experienceandshouldbeusedinconjunctionwithprofessional Geostatistical Site Investigations
judgment. Not all aspects of this guide may be applicable in all
3. Terminology
circumstances. This ASTM standard is not intended to repre-
sent or replace the standard of care by which the adequacy of
3.1 Definitions:
a given professional service must be judged, nor should this
3.1.1 For definitions of common technical terms in this
standard, refer to Terminology D653.
3.2 Definitions of Terms Specific to This Standard:
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 Dec. 15, 2018. Published December 2018. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 1996. Last previous edition approved in 2010 as D5922–96(2010). Standards volume information, refer to the standard’s Document Summary page on
DOI: 10.1520/D5922-18. 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 − 18
3.2.1 anisotropy, n—in geostatistics, a property of the var- situations. Other methods exist and may enhance the develop-
iogram or covariance stating that different spatial variation ment of an appropriate model of spatial variation.
structures are observed in different directions.
4.3 For the interpretation of spatial variation, this guide
3.2.2 correlogram, n—a measure of spatial variation ex-
emphasizes the importance of site-specific quantitative and
pressing the coefficient of correlation between two variables as qualitative information. Quantitative information includes the
a function of the lag separating their locations.
number and configuration of the available data, their precision,
and their univariate statistics; qualitative information includes
3.2.3 drift, n—in geostatistics, a systematic spatial variation
items such as local geology and geomorphology, site usage,
of the local mean of a variable, usually expressed as a
and history. All of these are necessary for a sound interpreta-
polynomial function of location coordinates.
tion of spatial variation.
3.2.4 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.
3.2.5 geometric anisotropy, n—a form of anisotropy in
whichthevariogramrangechangeswithdirectionwhilethesill 5. Significance and Use
remains constant.
5.1 Whether for the sake of simplicity or because of a lack
3.2.6 lag, n—in geostatistics, the vector separating the
of information, geotechnical engineers regularly assume that
locations of two variables, as used in measures of spatial
soil and rock properties are the same throughout a particular
variation.
location, even though they realize that the use of averaged
parameter values can result in soil parameters that are signifi-
3.2.7 nugget effect, n—the component of spatial variance
cantly different from the actual parameters.
unresolvedbythesamplespacingincludingthevariancedueto
measurement error.
5.2 Considering the spatial distribution of soil and rock
mass properties, the use of geostatictics in site investigations
3.2.8 range, n—in geostatistics, the maximum distance over
should be considered as it will provide a more accurate
which a variable exhibits spatial correlation in a given direc-
estimationofthesoilandrockpropertiesbasedontheavailable
tion.
input information.
3.2.9 regionalized variable, n—a measured quantity or a
5.3 This guide is intended to encourage consistency in the
numerical attribute characterizing a spatially variable phenom-
analysis, interpretation, and modeling of spatial variation in
enon at a location in the field.
geostatistical site investigations.
3.2.10 sill, n—in geostatistics, a stable level of spatial
5.4 This guide should be used in conjunction with Guides
variation observed for lags greater than the range.
D5549, D5923, and D5924.
3.2.11 simulation, n—in geostatistics, a Monte-Carlo proce-
dure for generating realizations of fields based on the random
6. Analysis of Spatial Variation
function model chosen to represent a regionalized variable. In
6.1 Theprincipaltoolsforanalyzingspatialvariationarethe
addition to honoring a random function model, the realizations
variogram and the correlogram; whenever possible, both
may also be constrained to honor data values observed at
should be used.
sampled locations.
NOTE 1—Features that appear on both the variogram and correlogram
3.2.12 structure, n—in geostatistics, a source of spatial
are usually worthy of interpretation and should be reflected in the
variability with a characteristic length scale.
mathematical model for spatial variation. Features that appear on one but
not the other may reflect artifacts of the calculation or peculiarities of the
3.2.13 variogram, n—a measure of spatial variation defined
available data and their configuration; such features generally warrant
asonehalfthevarianceofthedifferencebetweentwovariables
further investigation before a decision can be made on whether they
and expressed as a function of the lag; it is also sometimes
should be reflected in the mathematical model for spatial variation.
referred to as the semi-variogram.
6.2 If univariate data analysis has revealed that the data
3.2.14 zonal anisotropy, n—a form of anisotropy in which
have a skewed distribution or if study objectives demand that
the variogram sill changes with direction.
the data be transformed, then the analysis of spatial variation
should be performed on an appropriate transform of the data.
4. Summary of Guide
NOTE2—Oneofthemostimportantaspectsofamathematicalmodelof
4.1 This guide presents advice on three separate but related spatial variation is the direction and degree of anisotropy. This is often
much better revealed by variograms and correlograms of transformed data
components of the study of spatial variation: the analytical
values, such as logarithms or normal scores. Even if the study ultimately
tools that are used, the interpretation of the results, and the
makes use of the original data values in estimation or simulation, the
development of an appropriate mathematical model.
analysis of spatial variation on transformed data values often leads to the
development of a more appropriate model of spatial variation.
4.2 For the analysis of spatial variation, this guide empha-
sizes the use of variograms and correlograms on both trans- 6.3 The choice of lag spacing and tolerance should take into
formed and untransformed variables since these are the most account the data configuration, particularly the minimum
common and successful analytical tools in most practical spacing between the available data and the average spacing
D5922 − 18
between the available data. Whenever possible, the choices of then the experimental variogram should not influence the
lag spacing and tolerance should be such that at least 20 paired interpretation of spatial continuity.
data values will be available for each lag.
NOTE 5—With data sets in which there is intentional clustering of
additional samples in areas with high data values, the variance of the most
NOTE3—Withdataconfigurationsthatarepseudo-regular,itiscommon
closely spaced data pairs is often much higher than that of the overall data
to use the spacing between the columns and rows of th
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: D5922 − 96 (Reapproved 2010) D5922 − 18
Standard Guide for
Analysis Analysis, Interpretation, and Modeling 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
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 safety, health, and healthenvironmental 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.
1.6 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
D653 Terminology Relating to Soil, Rock, and Contained Fluids
D5549 Guide for The Contents of Geostatistical Site Investigation Report (Withdrawn 2002)
This guide is under the jurisdiction of ASTM Committee D18 on Soil and Rock and is the direct responsibility of Subcommittee D18.01 on Surface and Subsurface
Characterization.
Current edition approved May 1, 2010Dec. 15, 2018. Published September 2010December 2018. Originally approved in 1996. Last previous edition approved in 20042010
as D5922–96(2004).D5922–96(2010). DOI: 10.1520/D5922-96R10.10.1520/D5922-18.
The boldface numbers in parentheses refer to a list of references at the end of the text.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
The last approved version of this historical standard is referenced on www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5922 − 18
D5923 Guide for Selection of Kriging Methods in Geostatistical Site Investigations
D5924 Guide for Selection of Simulation Approaches in Geostatistical Site Investigations
3. Terminology
3.1 Definitions of Terms Specific to This Standard:
3.1.1 anisotropy, n—in geostatistics, a property of the variogram or covariance stating that different spatial variation structures
are observed in different directions.
3.1.2 correlogram, n—a measure of spatial variation expressing the coefficient of correlation between two variables as a
function of the lag separating their locations.
3.1.3 drift, n—in geostatistics, a systematic spatial variation of the local mean of a variable, usually expressed as a polynomial
function of location coordinates.
3.1.4 estimation, n—a procedure by which the value of a variable at an unsampled location is predicted using a weighted average
of sample values from the neighborhood of that location.
3.1.5 experimental variogram, n—an experimental measure of spatial variation usually calculated as one half the average
squared difference between all pairs of data values within the same lag.
3.1.6 geometric anisotropy, n—a form of anisotropy in which the variogram range changes with direction while the sill remains
constant.
3.1.7 lag, n—in geostatistics, the vector separating the locations of two variables, as used in measures of spatial variation.
3.1.8 nugget effect, n—the component of spatial variance unresolved by the sample spacing including the variance due to
measurement error.
3.1.9 range, n—in geostatistics, the maximum distance over which a variable exhibits spatial correlation in a given direction.
3.1.10 regionalized variable, n—a measured quantity or a numerical attribute characterizing a spatially variable phenomenon
at a location in the field.
3.1.11 sill, n—in geostatistics, a stable level of spatial variation observed for lags greater than the range.
3.1.12 simulation, n—in geostatistics, a Monte-Carlo procedure for generating realizations of fields based on the random
function model chosen to represent a regionalized variable. In addition to honoring a random function model, the realizations may
also be constrained to honor data values observed at sampled locations.
3.1.13 structure, n—in geostatistics, a source of spatial variability with a characteristic length scale.
3.1.14 variogram, n—a measure of spatial variation defined as one half the variance of the difference between two variables and
expressed as a function of the lag; it is also sometimes referred to as the semi-variogram.
3.1.15 zonal anisotropy, n—a form of anisotropy in which the variogram sill changes with direction.
3.1 For definitions of other terms used in this guide, refer to Terminology D653 and Guides D5549, D5923, and D5924. A
complete glossary of geostatistical terminology is given in Ref (5).Definitions:
3.1.1 For definitions of common technical terms in this standard, refer to Terminology D653.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 anisotropy, n—in geostatistics, a property of the variogram or covariance stating that different spatial variation structures
are observed in different directions.
3.2.2 correlogram, n—a measure of spatial variation expressing the coefficient of correlation between two variables as a
function of the lag separating their locations.
3.2.3 drift, n—in geostatistics, a systematic spatial variation of the local mean of a variable, usually expressed as a polynomial
function of location coordinates.
3.2.4 experimental variogram, n—an experimental measure of spatial variation usually calculated as one half the average
squared difference between all pairs of data values within the same lag.
3.2.5 geometric anisotropy, n—a form of anisotropy in which the variogram range changes with direction while the sill remains
constant.
3.2.6 lag, n—in geostatistics, the vector separating the locations of two variables, as used in measures of spatial variation.
3.2.7 nugget effect, n—the component of spatial variance unresolved by the sample spacing including the variance due to
measurement error.
3.2.8 range, n—in geostatistics, the maximum distance over which a variable exhibits spatial correlation in a given direction.
3.2.9 regionalized variable, n—a measured quantity or a numerical attribute characterizing a spatially variable phenomenon at
a location in the field.
3.2.10 sill, n—in geostatistics, a stable level of spatial variation observed for lags greater than the range.
D5922 − 18
3.2.11 simulation, n—in geostatistics, a Monte-Carlo procedure for generating realizations of fields based on the random
function model chosen to represent a regionalized variable. In addition to honoring a random function model, the realizations may
also be constrained to honor data values observed at sampled locations.
3.2.12 structure, n—in geostatistics, a source of spatial variability with a characteristic length scale.
3.2.13 variogram, n—a measure of spatial variation defined as one half the variance of the difference between two variables and
expressed as a function of the lag; it is also sometimes referred to as the semi-variogram.
3.2.14 zonal anisotropy, n—a form of anisotropy in which the variogram sill changes with direction.
4. Summary of Guide
4.1 This guide presents advice on three separate but related components of the study of spatial variation: the analytical tools
that are used, the interpretation of the results, and the development of an appropriate mathematical model.
4.2 For the analysis of spatial variation, this guide emphasizes the use of variograms and correlograms on both transformed and
untransformed variables since these are the most common and successful analytical tools in most practical situations. Other
methods exist and may enhance the development of an appropriate model of spatial variation.
4.3 For the interpretation of spatial variation, this guide emphasizes the importance of site-specific quantitative and qualitative
information. Quantitative information includes the number and configuration of the available data, their precision, and their
univariate statistics; qualitative information includes items such as local geology and geomorphology, site usage, and history. All
of these are necessary for a sound interpretation of spatial variation.
4.4 For the modeling of spatial variation, this guide recommends attention to the short-scale behavior of the mathematical model
of spatial variation and to its anisotropy as reflected in the directional changes in the range.
5. Significance and Use
5.1 Whether for the sake of simplicity or because of a lack of information, geotechnical engineers regularly assume that soil
and rock properties are the same throughout a particular location, even though they realize that the use of averaged parameter
values can result in soil parameters that are significantly different from the actual parameters.
5.2 Considering the spatial distribution of soil and rock mass properties, the use of geostatictics in site investigations should be
considered as it will provide a more accurate estimation of the soil and rock properties based on the available input information.
5.3 This guide is intended to encourage consistency in the analysis, interpretation, and modeling of spatial variation.variation
in geostatistical site investigations.
5.4 This guide should be used in conjunction with Guides D5549, D5923, and D5924.
6. Analysis of Spatial Variation
6.1 The principal tools for analyzing spatial variation are the variogram and the correlogram; whenever possible, both should
be used.
NOTE 1—Features that appear on both the variogram and correlogram are usually worthy of interpretation and should be reflected in the mathematical
model for spatial variation. Features that appear on one but not the other may reflect artifacts of the calculation or peculiarities of the available data and
their configuration; such features require generally warrant further investigation before a decision can be made on whether they should be reflected in
the mathematical model for spatial variation.
6.2 If univariate data analysis has revealed that the data have a skewed distribution or if study objectives requiredemand that
the data be transformed, then the analysis of spatial variation should be performed on an appropriate transform of the data.
NOTE 2—One of the most important a
...