1、Designation: D5924 96 (Reapproved 2010)D5924 18Standard Guide forSelection of Simulation Approaches in Geostatistical SiteInvestigations1This standard is issued under the fixed designation D5924; the number immediately following the designation indicates the year oforiginal adoption or, in the case
2、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, and simulation in media whosemeas
3、urable 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 the
4、irsampled 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 acon
5、sensus of views without recommending a standard practice to follow in all cases.1. Scope1.1 This guide covers the conditions that determine the selection of a suitable simulation approach for a site investigationproblem.Alternative simulation approaches considered here are conditional and nonconditi
6、onal, indicator and Gaussian, single andmultiple realization, point, and block.1.2 This guide describes the conditions for which the use of simulation is an appropriate alternative to the use of estimation ingeostatistical site investigations.1.3 This guide does not discuss the basic principles of g
7、eostatistics. Introductions to geostatistics may be found in numeroustexts including Refs (1-3).21.4 This guide is concerned with general simulation approaches only and does not discuss particular simulation algorithmscurrently in use. These are described in Refs (4-6).1.5 This guide offers an organ
8、ized 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 in all circumstances. This ASTM s
9、tandard 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 this document means only that thed
10、ocument 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 Standards, Guides and Recommendations i
11、ssuedby the World Trade Organization Technical Barriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:3D653 Terminology Relating to Soil, Rock, and Contained Fluids1 This guide is under the jurisdiction of ASTM Committee D18 on Soil and Rock and is the direct responsibility of S
12、ubcommittee D18.01 on Surface and SubsurfaceCharacterization.Current edition approved May 1, 2010July 15, 2018. Published September 2010August 2018. Originally approved in 1996. Last previous edition approved in 20042010as D592496(2004).D592496(2010). DOI: 10.1520/D5924-96R10.10.1520/D5924-18.2 The
13、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 Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary p
14、age on the ASTM website.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. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that
15、 users consult prior editions as appropriate. In all cases only the current versionof the 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 States1D5549 Guide for The Cont
16、ents of Geostatistical Site Investigation Report (Withdrawn 2002)4D5922 Guide for Analysis of Spatial Variation in Geostatistical Site InvestigationsD5923 Guide for Selection of Kriging Methods in Geostatistical Site Investigations3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.
17、1 conditional simulation, na simulation approach where realizations of the random function model are constrained byvalues at sampled locations.3.1.2 drift, nin geostatistics, a systematic spatial variation of the local mean of a variable, usually expressed as a polynomialfunction of location coordin
18、ates.3.1.3 field, nin geostatistics, the region of one-, two- or three-dimensional space within which a regionalized variable isdefined.3.1.4 indicator variable, na regionalized variable that can have only two possible values, zero or one.3.1.5 kriging, nan estimation method where sample weights are
19、 obtained using a linear least-squares optimization procedurebased on a mathematical model of spatial variability and where the unknown variable and the available sample values may havea point or block support.3.1.6 nonconditional simulation, na simulation approach where realizations of the random f
20、unction model are unconstrainedby sample data.3.1.7 nugget effect, nthe component of spatial variance unresolved by the sample spacing and the additional variance due tomeasurement error.3.1.8 point, nin geostatistics, the location in the field at which a regionalized variable is defined. It also co
21、mmonly refers tothe support of sample-scale variables.3.1.9 realization, nan outcome of a spatial random function or a random variable.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 simulatio
22、n, nin geostatistics, a numerical procedure for generating realizations of fields based on the random functionmodel chosen to represent a regionalized variable.3.1.12 smoothing effect, nin geostatistics, the reduction in spatial variance of estimated values compared to true values.3.1.13 spatial ave
23、rage, na quantity obtained by averaging a regionalized variable over a finite region of space.3.1.14 support, nin geostatistics, the spatial averaging region over which a regionalized variable is defined, oftenapproximated by a point for sample-scale variables.3.1 Definitions of Other TermsDefinitio
24、ns: For definitions of other terms used in this guide, refer to Terminology D653 andGuides D5549, D5922, and D5923. A complete glossary of geostatistical terminology is given in Ref (7).3.1.1 For definitions of common technical terms used in this standard, refer to Terminology D653.3.2 Definitions o
25、f Terms Specific to This Standard:3.2.1 conditional simulation, na simulation approach where realizations of the random function model are constrained byvalues at sampled locations.3.2.2 drift, nin geostatistics, a systematic spatial variation of the local mean of a variable, usually expressed as a
26、polynomialfunction of location coordinates.3.2.3 field, nin geostatistics, the region of one-, two- or three-dimensional space within which a regionalized variable isdefined.3.2.4 indicator variable, na regionalized variable that can have only two possible values, zero or one.3.2.5 kriging, nan esti
27、mation method where sample weights are obtained using a linear least-squares optimization procedurebased on a mathematical model of spatial variability and where the unknown variable and the available sample values may havea point or block support.3.2.6 nonconditional simulation, na simulation appro
28、ach where realizations of the random function model are unconstrainedby sample data.3.2.7 nugget effect, nthe component of spatial variance unresolved by the sample spacing and the additional variance due tomeasurement error.3.2.8 point, nin geostatistics, the location in the field at which a region
29、alized variable is defined. It also commonly refers tothe support of sample-scale variables.4 The last approved version of this historical standard is referenced on www.astm.org.D5924 1823.2.9 realization, nan outcome of a spatial random function or a random variable.3.2.10 regionalized variable, na
30、 measured quantity or a numerical attribute characterizing a spatially variable phenomenonat a location in the field.3.2.11 simulation, nin geostatistics, a numerical procedure for generating realizations of fields based on the random functionmodel chosen to represent a regionalized variable.3.2.12
31、smoothing effect, nin geostatistics, the reduction in spatial variance of estimated values compared to true values.3.2.13 spatial average, na quantity obtained by averaging a regionalized variable over a finite region of space.3.2.14 support, nin geostatistics, the spatial averaging region over whic
32、h a regionalized variable is defined, oftenapproximated by a point for sample-scale variables.4. Significance and Use4.1 This guide is intended to encourage consistency and thoroughness in the application of geostatistical simulation toenvironmental, geotechnical, and hydrogeological site investigat
33、ions.4.2 This guide may be used to assist those performing a simulation study or as an explanation of procedures for qualifiednonparticipants who may be reviewing or auditing the study.4.3 This guide should be used in conjunction with Guides D5549, D5922, and D5923.4.4 This guide describes condition
34、s for which simulation or particular simulation approaches are recommended. However, theseapproaches are not necessarily inappropriate if the stated conditions are not encountered.5. Selection of Simulation Approaches5.1 Simulation Versus EstimationA common objective of geostatistical site investiga
35、tions is to produce a two- orthree-dimensional spatial representation of a regionalized variable field from a set of measured values at different locations. Suchspatial representations are referred to here as maps. Estimation approaches, including all forms of kriging, yield maps that exhibita smoot
36、hing effect, whereas simulation approaches yield maps that preserve the spatial variability of the regionalized variable.5.1.1 If mapped values of the regionalized variable are required to provide an estimate of actual values at unsampled points,then an estimation approach such as kriging is appropr
37、iate.5.1.2 If mapped values of the regionalized variable are to preserve the spatial variability of values at unsampled points, thensimulation rather than estimation should be used.NOTE 1Preservation of in-situ spatial variability is important if mapped values of the regionalized variable are to be
38、entered in a numerical modelof a dynamic process, and therefore, simulation should generally be used. For example, mapped values of transmissivity to be entered in a numericalmodel of groundwater flow should be generated by simulation (87). However, if the numerical process model is insensitive to s
39、patial variations of theregionalized variable, then an estimation approach may also be used.5.2 Conditional Versus Nonconditional Simulation SimulationGeostatistical simulation methods are able to produce mapsof a regionalized variable that honor values observed at sampled points, a selected univari
40、ate distribution model, and a selectedmodel of spatial variation. The univariate distribution model may be that of the observed sample values or a model that is deemedmore appropriate. The model of spatial variation may be that of observed sample values or a model of spatial variation that isdeemed
41、more appropriate.5.2.1 If the simulated field need honor only a univariate distribution model and a spatial variability model, then a nonconditionalsimulation approach is sufficient.5.2.2 If the simulated field is to honor values of the regionalized variable observed at sampled points in addition to
42、 histogramand spatial variability models, then a conditional simulation approach should be used.5.2.3 If the regionalized variable exhibits a drift or other feature that is not explicitly considered in the geostatistical model, thenconditional simulation may be used to impart some of this feature in
43、 the simulated field.5.2.4 If part of the nugget effect exhibited by the sampled regionalized variable is due to sampling error and the simulation isto reproduce in-situ spatial variability, then a conditional simulation approach may be used if it ensures that the differences betweenobserved and sim
44、ulated values of the regionalized variable at sampled points are consistent with the sampling precision.5.3 Gaussian Versus Indicator SimulationGaussian and indicator geostatistical simulation approaches each have their ownparticular characteristics rendering them more suitable for some applications
45、 than others. Simulation algorithms based on Gaussian(normal) variables produce realizations in which there is a maximum scatter of extreme high and low values. Simulation algorithmsbased on indicator variables, on the other hand, are intended to produce realizations that honor the spatial variabili
46、ty of extremevalues.5.3.1 If the simulated regionalized variable is binary or categorical, then an indicator-based simulation approach should be used.5.3.2 If the simulated regionalized variable is continuous and the spatial variability of extreme values must be reproduced, thenthis variable may be
47、coded into a sequence of indicator variables that should be simulated using an indicator-based approach.5.3.3 If the simulated regionalized variable is continuous and the spatial variability of extreme values is unimportant, then aGaussian-based simulation approach should be used.D5924 1835.3.4 If t
48、he simulated regionalized variable is continuous but may be grouped into two or more distinct populations, then anindicator-based approach may be used to simulate group boundaries and a Gaussian-based approach may be used to simulate theregionalized variable within each group.5.3.5 If available samp
49、le data are limited and a Gaussian model cannot be refuted, then a Gaussian-based simulation approachis the conventional default.5.4 Single Versus Multiple RealizationsRealizations from SimulationGeostatistical simulation approaches may be used togenerate one or more possible maps of a regionalized variable that honor specified probability distribution and spatial variationmodels and, if desired, data values at sampled points.5.4.1 If uncertainty in mapped values of the regionalized variable is the focus of a sensitivity analysis, then multip
