1、Designation: D5922 96 (Reapproved 2010)D5922 18Standard Guide forAnalysis Analysis, Interpretation, and Modeling of SpatialVariation in Geostatistical Site Investigations1This standard is issued under the fixed designation D5922; the number immediately following the designation indicates the year of
2、original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.INTRODUCTIONGeostatistics is a framework for data analysis, estimation,
3、 and simulation in media whosemeasurable attributes show erratic spatial variability yet also possess a degree of spatial continuityimparted by the natural and anthropogenic processes operating therein. The soil, rock, and containedfluids encountered in environmental or geotechnical site investigati
4、ons present such features, and theirsampled attributes are therefore amenable to geostatistical treatment. This guide is concerned with theanalysis, interpretation, and modeling of spatial variation. The purpose of this guide is to offerguidance based on a consensus of views but not to establish a s
5、tandard practice to follow in all cases.1. Scope1.1 This guide covers recommendations for analyzing, interpreting, and modeling spatial variation of regionalized variables ingeotechnical and environmental site investigations.1.2 The measures of spatial variation discussed in this guide include vario
6、grams and correlograms; these are fully described inRefs. (1-4).21.3 This guide is intended to assist those who are already familiar with the geostatistical tools discussed herein and does notprovide introductory information on the analysis, interpretation, and modeling of spatial variation.1.4 This
7、 standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilityof the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine theapplicability of regulatory limitations prior to
8、use.1.5 This guide offers an organized collection of information or a series of options and does not recommend a specific courseof 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
9、 in all circumstances. This ASTM standard is not intended to represent or replacethe standard of care by which the adequacy of a given professional service must be judged, nor should this document be appliedwithout consideration of a projects many unique aspects. The word “Standard” in the title of
10、this document means only that thedocument has been approved through the ASTM consensus process.1.6 This international standard was developed in accordance with internationally recognized principles on standardizationestablished in the Decision on Principles for the Development of International Stand
11、ards, Guides and Recommendations issuedby the World Trade Organization Technical Barriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:3D653 Terminology Relating to Soil, Rock, and Contained FluidsD5549 Guide for The Contents of Geostatistical Site Investigation Report (Withdra
12、wn 2002)41 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 SubsurfaceCharacterization.Current edition approved May 1, 2010Dec. 15, 2018. Published September 2010December 2018. Originally approved in 19
13、96. Last previous edition approved in 20042010as D592296(2004).D592296(2010). DOI: 10.1520/D5922-96R10.10.1520/D5922-18.2 The boldface numbers in parentheses refer to a list of references at the end of the text.3 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Custo
14、mer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.4 The last approved version of this historical standard is referenced on www.astm.org.This document is not an ASTM standard and is intended only to pr
15、ovide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit 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 versionof th
16、e standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1D5923 Guide for Selection of Kriging Methods in Geostatistical Site InvestigationsD5924 Guide for Selection of S
17、imulation Approaches in Geostatistical Site Investigations3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 anisotropy, nin geostatistics, a property of the variogram or covariance stating that different spatial variation structuresare observed in different directions.3.1.2 corr
18、elogram, na measure of spatial variation expressing the coefficient of correlation between two variables as afunction of the lag separating their locations.3.1.3 drift, nin geostatistics, a systematic spatial variation of the local mean of a variable, usually expressed as a polynomialfunction of loc
19、ation coordinates.3.1.4 estimation, na procedure by which the value of a variable at an unsampled location is predicted using a weighted averageof sample values from the neighborhood of that location.3.1.5 experimental variogram, nan experimental measure of spatial variation usually calculated as on
20、e half the averagesquared difference between all pairs of data values within the same lag.3.1.6 geometric anisotropy, na form of anisotropy in which the variogram range changes with direction while the sill remainsconstant.3.1.7 lag, nin geostatistics, the vector separating the locations of two vari
21、ables, as used in measures of spatial variation.3.1.8 nugget effect, nthe component of spatial variance unresolved by the sample spacing including the variance due tomeasurement error.3.1.9 range, nin geostatistics, the maximum distance over which a variable exhibits spatial correlation in a given d
22、irection.3.1.10 regionalized variable, na measured quantity or a numerical attribute characterizing a spatially variable phenomenonat a location in the field.3.1.11 sill, nin geostatistics, a stable level of spatial variation observed for lags greater than the range.3.1.12 simulation, nin geostatist
23、ics, a Monte-Carlo procedure for generating realizations of fields based on the randomfunction model chosen to represent a regionalized variable. In addition to honoring a random function model, the realizations mayalso be constrained to honor data values observed at sampled locations.3.1.13 structu
24、re, nin geostatistics, a source of spatial variability with a characteristic length scale.3.1.14 variogram, na measure of spatial variation defined as one half the variance of the difference between two variables andexpressed as a function of the lag; it is also sometimes referred to as the semi-var
25、iogram.3.1.15 zonal anisotropy, na 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. Acomplete glossary of geostatistical terminology is given in Ref (5).Definitio
26、ns: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, nin geostatistics, a property of the variogram or covariance stating that different spatial variation structuresare observed in differen
27、t directions.3.2.2 correlogram, na measure of spatial variation expressing the coefficient of correlation between two variables as afunction of the lag separating their locations.3.2.3 drift, nin geostatistics, a systematic spatial variation of the local mean of a variable, usually expressed as a po
28、lynomialfunction of location coordinates.3.2.4 experimental variogram, nan experimental measure of spatial variation usually calculated as one half the averagesquared difference between all pairs of data values within the same lag.3.2.5 geometric anisotropy, na form of anisotropy in which the variog
29、ram range changes with direction while the sill remainsconstant.3.2.6 lag, nin geostatistics, the vector separating the locations of two variables, as used in measures of spatial variation.3.2.7 nugget effect, nthe component of spatial variance unresolved by the sample spacing including the variance
30、 due tomeasurement error.3.2.8 range, nin geostatistics, the maximum distance over which a variable exhibits spatial correlation in a given direction.3.2.9 regionalized variable, na measured quantity or a numerical attribute characterizing a spatially variable phenomenon ata location in the field.3.
31、2.10 sill, nin geostatistics, a stable level of spatial variation observed for lags greater than the range.D5922 1823.2.11 simulation, nin geostatistics, a Monte-Carlo procedure for generating realizations of fields based on the randomfunction model chosen to represent a regionalized variable. In ad
32、dition to honoring a random function model, the realizations mayalso be constrained to honor data values observed at sampled locations.3.2.12 structure, nin geostatistics, a source of spatial variability with a characteristic length scale.3.2.13 variogram, na measure of spatial variation defined as
33、one half the variance of the difference between two variables andexpressed as a function of the lag; it is also sometimes referred to as the semi-variogram.3.2.14 zonal anisotropy, na form of anisotropy in which the variogram sill changes with direction.4. Summary of Guide4.1 This guide presents adv
34、ice on three separate but related components of the study of spatial variation: the analytical toolsthat 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 co
35、rrelograms on both transformed anduntransformed variables since these are the most common and successful analytical tools in most practical situations. Othermethods exist and may enhance the development of an appropriate model of spatial variation.4.3 For the interpretation of spatial variation, thi
36、s guide emphasizes the importance of site-specific quantitative and qualitativeinformation. Quantitative information includes the number and configuration of the available data, their precision, and theirunivariate statistics; qualitative information includes items such as local geology and geomorph
37、ology, site usage, and history. Allof 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 modelof spatial variation and to its anisotropy as reflected in the dir
38、ectional changes in the range.5. Significance and Use5.1 Whether for the sake of simplicity or because of a lack of information, geotechnical engineers regularly assume that soiland rock properties are the same throughout a particular location, even though they realize that the use of averaged param
39、etervalues 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 beconsidered as it will provide a more accurate estimation of the soi
40、l 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.variationin geostatistical site investigations.5.4 This guide should be used in conjunction with Guides D5549, D5923,
41、and D5924.6. Analysis of Spatial Variation6.1 The principal tools for analyzing spatial variation are the variogram and the correlogram; whenever possible, both shouldbe used.NOTE 1Features that appear on both the variogram and correlogram are usually worthy of interpretation and should be reflected
42、 in the mathematicalmodel for spatial variation. Features that appear on one but not the other may reflect artifacts of the calculation or peculiarities of the available data andtheir configuration; such features require generally warrant further investigation before a decision can be made on whethe
43、r they should be reflected inthe 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 thatthe data be transformed, then the analysis of spatial variation should be performed on an appropria
44、te transform of the data.NOTE 2One of the most important aspects of a mathematical model of spatial variation is the direction and degree of anisotropy. This is often muchbetter revealed by variograms and correlograms of transformed data values, such as logarithms or normal scores. Even if the study
45、 ultimately makes useof the original data values in estimation or simulation, the analysis of spatial variation on transformed data values often leads to the development of amore appropriate model of spatial variation.6.3 The choice of lag spacing and tolerance should take into account the data conf
46、iguration, particularly the minimum spacingbetween the available data and the average spacing between the available data. Whenever possible, the choices of lag spacing andtolerance should ensure be such that at least 20 paired data values will be available for each lag.NOTE 3With data configurations
47、 that are pseudo-regular, it is common to use the spacing between the columns and rows of the sampling grid as thelag spacing and to use half of this distance as the lag tolerance. If the data configuration is irregular, then the lag spacing and tolerance may also needto be irregular (see Refs (3),
48、and (65).6.4 Spatial variation should be analyzed in different directions; the choice of directions and directional tolerances should reflectthe configuration of the available data and should also take into account qualitative information about the physical and chemicalcharacteristics of the regiona
49、lized variable being studied.NOTE 4Omni-directional variograms or correlograms often are appropriate for refining decisions on lag spacing and lag tolerance; they also provideD5922 183preliminary insight into the range of correlation and the short-scale variability of the data. However, omni-directional calculations of spatial variationgenerally do not constituteprovide a thorough analysis of spatial variation since they offer no insight into directional anisotropies that commonly occurin geologic data. For two-dimensional (2D) problems, contou
