1、Designation: D8215 18Standard Practice forStatistical Modeling of Uncertainty in Assessment of In-place Coal Resources1This standard is issued under the fixed designation D8215; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the y
2、ear 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.INTRODUCTIONAssessment of coal tonnage in-place is a fundamental factor in evaluating the commercial feasibilityof any depo
3、sit. Equally important is an appraisal of the reliability that can be placed in the drilling dataavailable for an estimation. Traditional methods for quantitatively expressing uncertainty usereliability categories based simply on the distance between drill-hole data within the boundaries of acoal be
4、d. A significant limitation of the distance approach is the inability to express uncertainty interms of how close a resource estimate is to the true value.This practice provides a geostatistical methodology to calculate the uncertainty of an in-place, coalresource estimate, both at the deposit and b
5、lock level. In addition to examining the drilling pattern bothwithin and outside the coal bed, other factors influencing the complexity in the geology are alsoconsidered, resulting in realistic estimates of uncertainty. Most importantly, the uncertainty isexpressed directly in tons of coal. Like oth
6、er coal properties, uncertainty can be used to rank theresources in classes.1. Scope1.1 This practice covers a procedure for quantitativelydetermining in-place tonnage uncertainty in a coal resourceassessment. The practice uses a database on coal occurrenceand applies geostatistical methods to model
7、 the uncertaintyassociated with a tonnage estimated for one or more coalseams. The practice includes instruction for the preparation ofresults in graphical form.1.2 This document does not include a detailed presentationof the basic theory behind the formulation of the standard,which can be found in
8、numerous publications, with a selectionbeing given in the references (1-3).21.3 This practice should be used in conjunction with pro-fessional judgment of the many unique aspects of a coaldeposit.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use
9、. It is theresponsibility of the user of this standard to establish appro-priate safety, health, and environmental practices and deter-mine the applicability of regulatory limitations prior to use.1.5 This international standard was developed in accor-dance with internationally recognized principles
10、 on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:3D621 Test Methods for Deformation of
11、Plastics Under Load(Withdrawn 1994)4D653 Terminology Relating to Soil, Rock, and ContainedFluidsD5549 Guide for The Contents of Geostatistical Site Inves-tigation Report (Withdrawn 2002)4D5922 Guide for Analysis of Spatial Variation in Geostatis-tical Site InvestigationsD5923 Guide for Selection of
12、Kriging Methods in Geostatis-tical Site InvestigationsD5924 Guide for Selection of Simulation Approaches inGeostatistical Site Investigations1This practice is under the jurisdiction of ASTM Committee D05 on Coal andCoke and is the direct responsibility of Subcommittee D05.07 on PhysicalCharacteristi
13、cs of Coal.Current edition approved Nov. 1, 2018. Published December 2018. DOI:10.1520/D8215-18.2The boldface numbers in parentheses refer to the list of references at the end ofthis standard.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at ser
14、viceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.4The last approved version of this historical standard is referenced onwww.astm.org.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken,
15、PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization
16、 Technical Barriers to Trade (TBT) Committee.12.2 ASTM Manuals, Monographs, and Data Series:5MNL11 Manual on Drilling, Sampling, andAnalysis of Coal3. Terminology3.1 Definitions:3.1.1 average, nmean.3.1.2 bin, neach of a set of the adjoining intervals used forseparating numerical values according to
17、 magnitude.3.1.3 cell, nany of the subdivisions of a seam whosecenters are the nodes in a regular grid.3.1.4 confidence interval, na range of values calculatedfrom sample observations and supposed to contain the trueparameter value with certain probability of coverage.3.1.4.1 DiscussionFor example,
18、a 95 % confidence inter-val implies that if the estimation process were repeated manytimes, then 95 % of the calculated intervals would be expectedto contain the true value.3.1.5 cumulative distribution function, na mathematicalexpression providing the probability that the value of a randomvariable
19、is less than any given value.3.1.6 estimation, nthe process of providing a numericalvalue for an unknown quantity based on the informationprovided by a sample.3.1.7 geostatistics, na branch of statistics in which allinferences are done by taking into account data, the style ofspatial fluctuation of
20、the variable(s), and the location of eachobservation.3.1.8 grid, na regular arrangement of crossing lines, suchas the threads in a square mesh. The intersection points are thenodes.3.1.9 histogram, na graphical representation of an empiri-cal probability distribution.3.1.9.1 DiscussionThe values of
21、the random variable aredivided into multiple intervals called bins; all values areallocated to the bins; final relative counts are displayed as barsthat are proportional to the empirical probabilities.3.1.10 kriging, na group of geostatistical estimation meth-ods formulated to minimize estimation er
22、rors in a minimummean square error sense.3.1.11 lower quartile, nin a split of a ranked sample intofour parts of equal size, the divider between the two partitionsbelow the median. It is synonymous with the 25th percentile.3.1.12 mean, na measure of centrality in a sample,population, or probability
23、distribution. For a sample, thesample mean is equal to the sum of all values divided by thesample size:z 51n(i51nzi(1)3.1.13 median, nin a probability distribution or rankedsample or population, the divider evenly splitting the observa-tions into two halves of equal size: a half of lowest values and
24、a half of highest values; it is a measure of centrality and issynonymous with the 50th percentile.3.1.14 normal distribution, nthe family of symmetric,bell-shaped functions that expresses the probability, f(x), thatthe random variable will be between any two values of x:fx! 51=2expF2Sx 2 D2G(2)where
25、 is the mean and is the standard deviation of theprobability density function. See Fig. 1.3.1.15 percentile, nin a probability distribution, sample,or population sorted by increasing observation value, each oneof the 99 dividers that produce exactly 100 subsets with equalnumber of observations.3.1.1
26、5.1 DiscussionThe dividers are sequential ordinalnumbers starting from the one between the two groups with thelowest values. The dividers denote the proportion of valuesbelow them.3.1.16 population, nthe complete set of all specimenscomprising a system of interest and from which data can becollected
27、.3.1.16.1 DiscussionFor the tonnage of a deposit, thepopulation is any exhaustive set of weight measurements thatcould be taken, thus adding to the deposit weight.5For referenced ASTM publications, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org.FIG. 1 Exampl
28、es of Normal DistributionsD8215 1823.1.17 probability, na measure of the likelihood of occur-rence of an event.3.1.17.1 DiscussionIt takes real values between 0 and 1,with 0 denoting absolute impossibility and 1 total certitude.Sometimes probabilities are multiplied by 100 to express themas percenta
29、ges.3.1.18 probability density function, nan analyticalexpression, f(x), describing the relative likelihood of a randomvariable.3.1.18.1 DiscussionFor discrete random variables, f(x)directly provides the likelihood of each random variable value;for a continuous random variable, the area under f(x) b
30、etweenany two values of the variable provides the likelihood of theinterval.3.1.19 probability distribution, nprobability density func-tion.3.1.20 quartile, nin a distribution, ranked sample, orpopulation, any of the three dividers that separate the obser-vations in four parts of equal size.3.1.21 r
31、andom function, na collection of random vari-ables.3.1.22 random variable, nthe collection of all possibleoutcomes in an event or study, and their associated probabilityof occurrence.3.1.23 realization, nan observed or simulated outcome ofa random variable, such as three tails in flipping a coin or
32、amap of a random function.3.1.24 resource, na numerical representation of theamount of a commodity in the ground.3.1.25 sample, n(a) in geology, a specimen taken forinspection, analysis, or display; (b) in statistics, a representa-tive subset of a population comprising several observations.3.1.26 sa
33、mple size, nthe number of specimens in a subsetof a population, which coincides with the number of observa-tions when there is one variable.3.1.27 standard deviation, nthe positive square root of thevariance.3.1.28 stochastic simulation, nmathematical modeling ofa complex system using probabilistic
34、methods involving ran-dom variables.3.1.29 upper quartile, nin a split of a sample into fourparts of equal size, the divider between the two partitionsabove the median; it is equivalent to the 75th percentile.3.1.30 variance, na measure of spread in a sample,population, or probability distribution.
35、For a sample, it is equalto the sum of the square of all observations minus the meandivided by the sample size minus 1:s251n 2 1(i51nzi2 z!2(3)3.2 For definitions of other terms used in this standard, referto Olea (4); Test Methods D621; Terminology D653; andGuides D5549, D5922, D5923, and D5924.4.
36、Summary of Practice4.1 The practice has two phases: data gathering and prepa-ration of a geologic model. These phases assess two forms ofuncertainty associated with in-place coal resource calculations:uncertainty in total coal tonnage and uncertainty in the mod-eling at the cell level.4.2 All availa
37、ble geologic information is used to create themodel of seam thickness and other variables if required by thegeological complexity, so that geologic or technically feasibleboundaries of individual coal seams, or of the entire deposit,can be taken into account in the modeling.4.3 The deposit is subdiv
38、ided into cells. Geostatisticalmodeling, stochastic simulation in particular, is applied to thecoal seam data. The simulations create a series of two-dimensional maps (realizations), each honoring the originaldata and having the same probability of being the correctsolution. Different types of sampl
39、ing and deposits requireapplying different procedures. Annex A1 and Annex A2 are atoolkit for the practical modeling of scenarios with variousdegrees of geologic complexity.4.4 Results from the realizations and tonnage calculationsare summarized in two graphs, one for each form of uncer-tainty: (a)
40、a numerical approximation to the probability distri-bution (histogram) of the total coal resources denoting uncer-tainty in the magnitude of the deposit and (b) a graphdisplaying uncertainty in cell by cell assessment as measuredby a 90 % confidence interval plotted against cumulativetonnage and cel
41、l count. The user can select any desireduncertainty boundaries from this graph to subdivide the depositaccording to the degree of reliability of interest in the analysisof cell tonnage calculations.5. Significance and Use5.1 Traditional methods for expressing geological uncer-tainty consist of prepa
42、ring reliability categories based simplyon the distance between drill hole data points, such as the onedescribed by Wood et al. (5) that uses only the drill holeswithin the coal bed. A major drawback of distance methods istheir weak to null association with estimation errors. Thispractice provides a
43、 methodology for effectively assessing theuncertainty in coal resource estimates utilizing stochasticsimulation. In determining uncertainty for any coal assessment,stochastic simulation enables consideration of other importantfactors and information beyond the geometry of drill holelocations, both i
44、n and out of the coal bed, including: non-depositional channels, depth of weathering, complexity ofseam boundaries, coal seam subcrop projections, and varyingcoal bed geology for different seams due to fluctuating peatdepositional environments.5.2 For multi-seam deposits, uncertainty can be expresse
45、don an individual seam basis as well as an aggregated uncer-tainty for an entire coal deposit.5.3 The uncertainty is expressed directly in tons of coal.Additionally, this practice allows the statistical analysis to bepresented according to widely-accepted conventions, such asD8215 183percentiles and
46、 confidence intervals, say, that there is a 90 %probability that the actual tonnage in place is 346 6 31.7million tons of coal.5.4 The results of an uncertainty determination can provideimportant input into an overall risk analysis assessing thecommercial feasibility of a coal deposit.5.5 A company
47、may rank coal resources per block (cell)based on the degree of uncertainty.6. Software6.1 Mathematical modeling of a deposit requires the use ofcomputer programs for the fast and precise performance ofnumerical calculations.6.2 Use of a geostatistical software package that is capableof generating pr
48、obabilistic geologic mapping in the form ofkriging estimations and stochastic realizations, such as the onesby Remy et al. (6) or Geovariances (7) is required.6.3 Application of the standard also requires a programcapable of performing grid operations, such as convertingthickness maps to tonnage map
49、s, and preparing the summariesdescribed in Sections 9 and 10.7. Sampling and Data Preparation7.1 Prepare a database that ideally is free of institutionaluncertainties, such as insufficient drilling depth, inconsistencyin picking the top and bottom of a seam, or errors coding thedata (MNL11).7.2 Like in the distance methods, if drill hole locations arein some system that is not Cartesian, such as latitude andlongitude, convert the values to Cartesian coordinates, such asUniversal Transverse Mercator (UTM) coordinates or stateplane coor
