1、Designation: D 5924 96 (Reapproved 2004)Standard Guide forSelection of Simulation Approaches in Geostatistical SiteInvestigations1This standard is issued under the fixed designation D 5924; the number immediately following the designation indicates the year oforiginal adoption or, in the case of rev
2、ision, 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 whosemeasurabl
3、e 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 investigations present such features, and theirsam
4、pled attributes are therefore amenable to geostatistical treatment. Geostatistical simulationapproaches are used to produce maps of an attribute that honor the spatial variability of sampledvalues. This guide reviews criteria for selecting a simulation approach, offering direction based on aconsensu
5、s of views without recommending a standard practice to follow in all cases.1. Scope1.1 This guide covers the conditions that determine theselection of a suitable simulation approach for a site investi-gation problem. Alternative simulation approaches consideredhere are conditional and nonconditional
6、, indicator and Gauss-ian, single and multiple realization, point, and block.1.2 This guide describes the conditions for which the use ofsimulation is an appropriate alternative to the use of estimationin geostatistical site investigations.1.3 This guide does not discuss the basic principles ofgeost
7、atistics. Introductions to geostatistics may be found innumerous texts including Refs (1-3).21.4 This guide is concerned with general simulation ap-proaches only and does not discuss particular simulationalgorithms currently in use. These are described in Refs (4-6).1.5 This guide offers an organize
8、d collection of informationor a series 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 standar
9、d is not intended to repre-sent or 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 documen
10、t has been approvedthrough the ASTM 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 5922 Guide for Analysis of Spatial Variation in Geostatis-tical S
11、ite InvestigationsD 5923 Guide for Selection of Kriging Methods in Geo-statistical Site Investigations3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 conditional simulation, na simulation approachwhere realizations of the random function model are con-strained by values at sam
12、pled locations.3.1.2 drift, nin geostatistics, a systematic spatial variationof the local mean of a variable, usually expressed as apolynomial function of location coordinates.3.1.3 field, nin geostatistics, the region of one-, two- orthree-dimensional space within which a regionalized variableis de
13、fined.3.1.4 indicator variable, na regionalized variable that canhave only two possible values, zero or one.1This guide is under the jurisdiction of ASTM Committee D18 on Soil and Rockand is the direct responsibility of Subcommittee D18.01 on Surface and SubsurfaceCharacterization.Current edition ap
14、proved July 1, 2004. Published August 2004. Originallyapproved in 1996. Last previous edition approved in 1996 as D 5924 - 96e1.2The boldface numbers in parentheses refer to a list of references at the end ofthe text.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact AST
15、M 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 Conshohocken, PA 19428-2959, United States.3.1.5 kriging, nan
16、 estimation method where sampleweights are obtained using a linear least-squares optimizationprocedure based on a mathematical model of spatial variabilityand where the unknown variable and the available samplevalues may have a point or block support.3.1.6 nonconditional simulation, na simulation ap
17、proachwhere realizations of the random function model are uncon-strained by sample data.3.1.7 nugget effect, nthe component of spatial varianceunresolved by the sample spacing and the additional variancedue to measurement error.3.1.8 point, nin geostatistics, the location in the field atwhich a regi
18、onalized variable is defined. It also commonlyrefers to the support of sample-scale variables.3.1.9 realization, nan outcome of a spatial random func-tion or a random variable.3.1.10 regionalized variable, na measured quantity or anumerical attribute characterizing a spatially variable phenom-enon a
19、t a location in the field.3.1.11 simulation, nin geostatistics, a numerical proce-dure for generating realizations of fields based on the randomfunction model chosen to represent a regionalized variable.3.1.12 smoothing effect, nin geostatistics, the reduction inspatial variance of estimated values
20、compared to true values.3.1.13 spatial average, na quantity obtained by averaginga regionalized variable over a finite region of space.3.1.14 support, nin geostatistics, the spatial averagingregion over which a regionalized variable is defined, oftenapproximated by a point for sample-scale variables
21、.3.2 Definitions of Other TermsFor definitions of otherterms used in this guide, refer to Terminology D 653 andGuides D 5549, D 5922, and D 5923. A complete glossary ofgeostatistical terminology is given in Ref (7).4. Significance and Use4.1 This guide is intended to encourage consistency andthoroug
22、hness in the application of geostatistical simulation toenvironmental, geotechnical, and hydrogeological site investi-gations.4.2 This guide may be used to assist those performing asimulation study or as an explanation of procedures forqualified nonparticipants who may be reviewing or auditing thest
23、udy.4.3 This guide should be used in conjunction with GuidesD 5549, D 5922, and D 5923.4.4 This guide describes conditions for which simulation orparticular simulation approaches are recommended. However,these approaches are not necessarily inappropriate if the statedconditions are not encountered.5
24、. Selection of Simulation Approaches5.1 Simulation Versus EstimationA common objective ofgeostatistical site investigations is to produce a two- orthree-dimensional spatial representation of a regionalized vari-able field from a set of measured values at different locations.Such spatial representati
25、ons are referred to here as maps.Estimation approaches, including all forms of kriging, yieldmaps that exhibit a smoothing effect, whereas simulationapproaches yield maps that preserve the spatial variability ofthe regionalized variable.5.1.1 If mapped values of the regionalized variable arerequired
26、 to provide an estimate of actual values at unsampledpoints, then an estimation approach such as kriging is appro-priate.5.1.2 If mapped values of the regionalized variable are topreserve the spatial variability of values at unsampled points,then simulation rather than estimation should be used.NOTE
27、 1Preservation of in-situ spatial variability is important ifmapped values of the regionalized variable are to be entered in anumerical model of a dynamic process, and therefore, simulation shouldgenerally be used. For example, mapped values of transmissivity to beentered in a numerical model of gro
28、und water flow should be generated bysimulation (8). However, if the numerical process model is insensitive tospatial variations of the regionalized variable, then an estimation approachmay also be used.5.2 Conditional Versus Nonconditional SimulationGeostatistical simulation methods are able to pro
29、duce maps ofa regionalized variable that honor values observed at sampledpoints, a selected univariate distribution model, and a selectedmodel of spatial variation. The univariate distribution modelmay be that of the observed sample values or a model that isdeemed more appropriate. The model of spat
30、ial variation maybe that of observed sample values or a model of spatialvariation that is deemed more appropriate.5.2.1 If the simulated field need honor only a univariatedistribution model and a spatial variability model, then anonconditional simulation approach is sufficient.5.2.2 If the simulated
31、 field is to honor values of theregionalized variable observed at sampled points in addition tohistogram and spatial variability models, then a conditionalsimulation approach should be used.5.2.3 If the regionalized variable exhibits a drift or otherfeature that is not explicitly considered in the g
32、eostatisticalmodel, then conditional simulation may be used to impart someof this feature in the simulated field.5.2.4 If part of the nugget effect exhibited by the sampledregionalized variable is due to sampling error and the simula-tion is to reproduce in-situ spatial variability, then a condition
33、alsimulation approach may be used if it ensures that thedifferences between observed and simulated values of theregionalized variable at sampled points are consistent with thesampling precision.5.3 Gaussian Versus Indicator SimulationGaussian andindicator geostatistical simulation approaches each ha
34、ve theirown particular characteristics rendering them more suitable forsome applications than others. Simulation algorithms based onGaussian (normal) variables produce realizations in whichthere is a maximum scatter of extreme high and low values.Simulation algorithms based on indicator variables, o
35、n theother hand, are intended to produce realizations that honor thespatial variability of extreme values.5.3.1 If the simulated regionalized variable is binary orcategorical, then an indicator-based simulation approachshould be used.D 5924 96 (2004)25.3.2 If the simulated regionalized variable is c
36、ontinuousand the spatial variability of extreme values must be repro-duced, then this variable may be coded into a sequence ofindicator variables that should be simulated using an indicator-based approach.5.3.3 If the simulated regionalized variable is continuousand the spatial variability of extrem
37、e values is unimportant,then a Gaussian-based simulation approach should be used.5.3.4 If the simulated regionalized variable is continuousbut may be grouped into two or more distinct populations, thenan indicator-based approach may be used to simulate groupboundaries and a Gaussian-based approach m
38、ay be used tosimulate the regionalized variable within each group.5.3.5 If available sample data are limited and a Gaussianmodel cannot be refuted, then a Gaussian-based simulationapproach is the conventional default.5.4 Single Versus Multiple RealizationsGeostatisticalsimulation approaches may be u
39、sed to generate one or morepossible maps of a regionalized variable that honor specifiedprobability distribution and spatial variation models and, ifdesired, data values at sampled points.5.4.1 If uncertainty in mapped values of the regionalizedvariable is the focus of a sensitivity analysis, then m
40、ultiplerealizations should be simulated.5.4.2 If the simulated field is part of a Monte-Carlo sensi-tivity analysis, then a simulation approach capable of generat-ing equally probable realizations is required.5.5 Point Versus Block SimulationGeostatistical simula-tion approaches may be used to gener
41、ate maps of regionalizedvariables with either point or block support. These simulationapproaches must ensure that the spatial variability of simulatedvalues is consistent with the spatial averaging or change-of-support process.5.5.1 If the simulated regionalized variable has a pointsupport or the sa
42、me support as the sampled variable, then apoint simulation approach should be used.5.5.2 If the simulated regionalized variable has a blocksupport discretized by a finite number of points, then pointsimulation followed by spatial averaging over the discretizedblocks is an approach that can be used p
43、rovided the spatialaveraging process is known.5.5.3 If the simulated regionalized variable has a blocksupport and the spatial averaging process is arithmetic, then adirect block simulation approach may be used.6. Keywords6.1 estimation; geostatistics; kriging; simulationREFERENCES(1) Journel, A. G.,
44、 and Huijbregts, C., Mining Geostatistics, AcademicPress, London, 1978.(2) Isaaks, E. H., and Srivastava, R. M., An Introduction to AppliedGeostatistics, Oxford University Press, New York, 1989.(3) Marsily, G. de, Quantitative Hydrogeology, Academic Press, Orlando,1986.(4) Luster, G. R., “Raw Materi
45、als for Portland Cement: Applications ofConditional Simulation of Coregionalization,” Ph.D. Thesis, Depart-ment of Applied Earth Sciences, Stanford University, Stanford, CA,1985.(5) Deutsch, C. V., and Journel, A. G., GSLIB Geostatistical SoftwareLibrary an Users Guide, Oxford University Press, New
46、York, 1992.(6) Srivastava, R. M., “An Overview of Stochastic Methods for ReservoirCharacterization, in Stochastic Modeling and Geostatistics: Principles,Methods and Case Studies,” J. Yarus and R. Chambers, eds., AAPG,inpress, 1995.(7) Olea, R. A., ed., Geostatistical Glossary and Multilingual Dictio
47、nary,Oxford University Press, New York, 1991.(8) Desbarats, A. J., and Dimitrakopoulos, R., “Geostatistical Modellingof Transmissibility for 2D Reservoir Studies,” SPE Formation Evalu-ation, 5(4), 1990, pp. 437443.ASTM International takes no position respecting the validity of any patent rights asse
48、rted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by
49、 the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This stand
