1、Designation: D 5922 96 (Reapproved 2004)Standard Guide forAnalysis of Spatial Variation in Geostatistical SiteInvestigations1This standard is issued under the fixed designation D 5922; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision
2、, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.INTRODUCTIONGeostatistics is a framework for data analysis, estimation, and simulation in media whosemeasurable att
3、ributes 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 investigations present such features, and theirsampled
4、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 standard practice to follow in all cases.1. S
5、cope1.1 This guide covers recommendations for analyzing, in-terpreting, and modeling spatial variation of regionalizedvariables in geotechnical and environmental site investigations.1.2 The measures of spatial variation discussed in this guideinclude variograms and correlograms; these are fully desc
6、ribedin Refs. (1-4).21.3 This guide is intended to assist those who are alreadyfamiliar with the geostatistical tools discussed herein and doesnot provide introductory information on the analysis, interpre-tation, and modeling of spatial variation.1.4 This standard does not purport to address all of
7、 thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.1.5 This guide offers an organized collection of informationor a se
8、ries of options and does not recommend a specificcourse of action. This document cannot replace education orexperience and should be used in conjunction with professionaljudgment. Not all aspects of this guide may be applicable in allcircumstances. This ASTM standard is not intended to repre-sent or
9、 replace the standard of care by which the adequacy ofa given professional service must be judged, nor should thisdocument be applied without consideration of a projects manyunique aspects. The word “Standard” in the title of thisdocument means only that the document has been approvedthrough the AST
10、M consensus process.2. Referenced Documents2.1 ASTM Standards:3D 653 Terminology Relating to Soil, Rock, and ContainedFluidsD 5549 Guide for the Contents of Geostatistical Site Inves-tigation Report4D 5923 Guide for Selection of Kriging Methods in Geo-statistical Site InvestigationsD 5924 Guide for
11、Selection of Simulation Approaches inGeostatistical Site Investigations3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 anisotropy, nin geostatistics, a property of thevariogram or covariance stating that different spatial variationstructures are observed in different direction
12、s.3.1.2 correlogram, na measure of spatial variation ex-pressing the coefficient of correlation between two variables asa function of the lag separating their locations.1This guide is under the jurisdiction of ASTM Committee D18 on Soil and Rockand is the direct responsibility of Subcommittee D18.01
13、 on Surface and SubsurfaceCharacterization.Current edition approved July 1, 2004. Published August 2004. Originallyapproved in 1996. Last previous edition approved in 1996 as D 5922 - 96e1.2The boldface numbers in parentheses refer to a list of references at the end ofthe text.3For referenced ASTM s
14、tandards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.4Withdrawn.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West
15、Conshohocken, PA 19428-2959, United States.3.1.3 drift, nin geostatistics, a systematic spatial variationof the local mean of a variable, usually expressed as apolynomial function of location coordinates.3.1.4 estimation, na procedure by which the value of avariable at an unsampled location is predi
16、cted using a weightedaverage of sample values from the neighborhood of thatlocation.3.1.5 experimental variogram, nan experimental measureof spatial variation usually calculated as one half the averagesquared difference between all pairs of data values within thesame lag.3.1.6 geometric anisotropy,
17、na form of anisotropy inwhich the variogram range changes with direction while the sillremains constant.3.1.7 lag, nin geostatistics, the vector separating thelocations of two variables, as used in measures of spatialvariation.3.1.8 nugget effect, nthe component of spatial varianceunresolved by the
18、sample spacing including the variance due tomeasurement error.3.1.9 range, nin geostatistics, the maximum distance overwhich a variable exhibits spatial correlation in a given direc-tion.3.1.10 regionalized variable, na measured quantity or anumerical attribute characterizing a spatially variable ph
19、enom-enon at a location in the field.3.1.11 sill, nin geostatistics, a stable level of spatialvariation observed for lags greater than the range.3.1.12 simulation, nin geostatistics, a Monte-Carlo pro-cedure for generating realizations of fields based on the randomfunction model chosen to represent
20、a regionalized variable. Inaddition to honoring a random function model, the realizationsmay also be constrained to honor data values observed atsampled locations.3.1.13 structure, nin geostatistics, a source of spatialvariability with a characteristic length scale.3.1.14 variogram, na measure of sp
21、atial variation definedas one half the variance of the difference between two variablesand expressed as a function of the lag; it is also sometimesreferred to as the semi-variogram.3.1.15 zonal anisotropy, na form of anisotropy in whichthe variogram sill changes with direction.3.2 For definitions of
22、 other terms used in this guide, refer toTerminology D 653 and Guides D 5549, D 5923, and D 5924.A complete glossary of geostatistical terminology is given inRef (5).4. Summary of Guide4.1 This guide presents advice on three separate but relatedcomponents of the study of spatial variation: the analy
23、ticaltools that are used, the interpretation of the results, and thedevelopment of an appropriate mathematical model.4.2 For the analysis of spatial variation, this guide empha-sizes the use of variograms and correlograms on both trans-formed and untransformed variables since these are the mostcommo
24、n and successful analytical tools in most practicalsituations. Other methods exist and may enhance the develop-ment of an appropriate model of spatial variation.4.3 For the interpretation of spatial variation, this guideemphasizes the importance of site-specific quantitative andqualitative informati
25、on. Quantitative information includes thenumber and configuration of the available data, their precision,and their univariate statistics; qualitative information includesitems such as local geology and geomorphology, site usage,and history. All of these are necessary for a sound interpreta-tion of s
26、patial variation.4.4 For the modeling of spatial variation, this guide recom-mends attention to the short-scale behavior of the mathematicalmodel of spatial variation and to its anisotropy as reflected inthe directional changes in the range.5. Significance and Use5.1 This guide is intended to encour
27、age consistency in theanalysis, interpretation, and modeling of spatial variation.5.2 This guide should be used in conjunction with GuidesD 5549, D 5923, and D 5924.6. Analysis of Spatial Variation6.1 The principal tools for analyzing spatial variation are thevariogram and the correlogram; whenever
28、possible, bothshould be used.NOTE 1Features that appear on both the variogram and correlogramare usually worthy of interpretation and should be reflected in themathematical model for spatial variation. Features that appear on one butnot the other may reflect artifacts of the calculation or peculiari
29、ties of theavailable data and their configuration; such features require furtherinvestigation before a decision can be made on whether they should bereflected in the mathematical model for spatial variation.6.2 If univariate data analysis has revealed that the datahave a skewed distribution or if st
30、udy objectives require thatthe data be transformed, then the analysis of spatial variationshould be performed on an appropriate transform of the data.NOTE 2One of the most important aspects of a mathematical model ofspatial variation is the direction and degree of anisotropy. This is oftenmuch bette
31、r revealed by variograms and correlograms of transformed datavalues, such as logarithms or normal scores. Even if the study ultimatelymakes use of the original data values in estimation or simulation, theanalysis of spatial variation on transformed data values often leads to thedevelopment of a more
32、 appropriate model of spatial variation.6.3 The choice of lag spacing and tolerance should take intoaccount the data configuration, particularly the minimumspacing between the available data and the average spacingbetween the available data. Whenever possible, the choices oflag spacing and tolerance
33、 should ensure that at least 20 paireddata values will be available for each lag.NOTE 3With data configurations that are pseudo-regular, it is com-mon to use the spacing between the columns and rows of the samplinggrid as the lag spacing and to use half of this distance as the lag tolerance.If the d
34、ata configuration is irregular, then the lag spacing and tolerancemay also need to be irregular (see Refs (3), and (6).6.4 Spatial variation should be analyzed in different direc-tions; the choice of directions and directional tolerances shouldreflect the configuration of the available data and shou
35、ld alsotake into account qualitative information about the physicaland chemical characteristics of the regionalized variable beingstudied.D 5922 96 (2004)2NOTE 4Omni-directional variograms or correlograms often are ap-propriate for refining decisions on lag spacing and lag tolerance; they alsoprovid
36、e preliminary insight into the range of correlation and the short-scale variability of the data. However, omni-directional calculations ofspatial variation do not constitute a thorough analysis of spatial variationsince they offer no insight into directional anisotropies that commonlyoccur in geolog
37、ic data. For two-dimensional (2D) problems, contour mapsof the spatial variation for all possible distances and directions can assistwith the identification of directions of maximum and minimum continuity(see Ref (2).6.5 Once the directions of maximum and minimum conti-nuity have been identified, th
38、e experimental variogram valuesand correlogram values should be plotted as a function ofdistance for these two directions. These plots should beaccompanied by tables that provide for each lag the followinginformation:6.5.1 The number of data pairs within the lag,6.5.2 The average separation distance
39、 between the datapairs in the lag,6.5.3 The average squared difference between the paireddata values in the lag, and6.5.4 The coefficient of linear correlation between the paireddata values in the lag.6.6 Supplementary information that often assists with anappropriate interpretation of the pattern o
40、f spatial variationincludes:6.6.1 The average separation direction between the datapairs in the lag,6.6.2 The average difference between the paired data valuesin the lag,6.6.3 The variance of the differences between the paireddata values in the lag,6.6.4 The average of the data values within the lag
41、, and6.6.5 The variance of the data values within the lag.7. Interpretation of Spatial Variation7.1 If there are fewer than 20 pairs of data within a lag, theexperimental variogram and correlogram values for this lagshould not influence the interpretation of spatial variation.NOTE 5For lags that con
42、tain fewer than 20 pairs, the variogram andcorrelogram values should still be tabulated and plotted, but should beannotated or marked in such a way that it is clear that the lag containsinsufficient data to influence any interpretation of spatial variation.7.2 If the variance of the data within each
43、 lag depends onthe average distance of the paired data values within the lag,then the experimental variogram should not influence theinterpretation of spatial continuity.NOTE 6With data sets in which there is intentional clustering ofadditional samples in areas with high data values, the variance of
44、 the mostclosely spaced data pairs is often much higher than that of the overall dataset. In such situations, the fluctuations in the variogram often mirror thechanges in the lag variance and do not directly convey meaningfulinformation about spatial variation. The correlogram is often more easilyin
45、terpreted since it takes into account fluctuations in the lag means and thelag variances.7.3 The nugget effect shown by the experimental variogramand correlogram should be consistent with the precision of thedata values.NOTE 7The nugget effect reflects a combination of the very shortscale variabilit
46、y and variance due to various sampling errors. Even insituations where there is no short-scale variability, the nugget effect of anexperimental variogram must be at least as large as the variance of theerrors that accumulate during sample collection, preparation, and analysis.7.4 Directional anisotr
47、opy in the ranges shown by theexperimental variogram and correlogram should be supportedby information on the physics and chemistry of the regional-ized variable under study or by information on site history andusage.7.5 If the experimental variogram or correlogram does notreach a stable sill, then
48、the report on spatial variation shouldspecifically address the issue of whether the data values showa trend or drift.NOTE 8A drift often causes the sill of an experimental variogram toincrease steadily rather than stabilize. Both estimation and simulationstudies will usually be improved by an explic
49、it attempt to remove anydrift, and to add it back after the residuals have been geostatisticallyanalyzed and modelled.7.6 If the sill of the experimental variogram or correlogramoscillates in a periodic manner, then the report on spatialvariation should specifically address the issue of whetherchemical or physical processes have imparted any cyclicity orperiodicity to the data values.NOTE 9Temporal fluctuations may manifest themselves as periodicfluctuations in vertical profiles through soils and sediments. Such periodicfluctuations often cause the sill of an
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