Research ArticleUsing EVT for Geological Anomaly Design and Its Application inIdentifying Anomalies in Mining Areas
Feilong Qin1 Bingli Liu12 and Ke Guo1
1Chengdu University of Technology The Key Laboratory of Mathematical Geology in Sichuan Chengdu 610059 China2Institute of Geophysical and Geochemical Exploration Chinese Academy of Geoscience Langfang 065000 China
Correspondence should be addressed to Bingli Liu liubingli-82163com
Received 28 April 2016 Revised 21 July 2016 Accepted 21 August 2016
Academic Editor Cheng-Tang Wu
Copyright copy 2016 Feilong Qin et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
A geological anomaly is the basis ofmineral deposit predictionThrough the study of the knowledge and characteristics of geologicalanomalies the category of extreme value theory (EVT) to which a geological anomaly belongs can be determined Associating theprinciple of the EVT and ensuring the methods of the shape parameter and scale parameter for the generalized Pareto distribution(GPD) the methods to select the threshold of the GPD can be studied This paper designs a new algorithm called the EVT modelof geological anomaly These study data on Cu and Au originate from 26 exploration lines of the Jiguanzui Cu-Au mining area inHubei China The proposed EVTmodel of the geological anomaly is applied to identify anomalies in the Jiguanzui Cu-Au miningarea The results show that the model can effectively identify the geological anomaly region of Cu and Au The anomaly region ofCu and Au is consistent with the range of ore bodies of actual engineering exploration Therefore the EVTmodel of the geologicalanomaly can effectively identify anomalies and it has a high indicating function with respect to ore prospecting
1 Introduction
In mineral deposit prediction searching for mineral depositsrequires identification of a geological anomaly indicating thatthe economic value is high (ldquoas discussed by Darehshiri et al[1]rdquo) A geological anomaly is a geological body or complexof bodies with obvious different compositions structuresor orders of genesis as compared with the surroundingcircumstances (ldquoas discussed by Lu and Zhao [2]rdquo) Withthe evolution of the earth the nature source and intensityof force will not be the same across different times andspace In addition the distribution of material of the earthis not uniform in time and space which results in differentevents and responses such as the tension and compressionof layers deposition and erosion of material subsidenceand uplift of the crust simple and complex structures andintrusion and ejection of magma these differences form thegeological anomaly (ldquoas discussed by Pengda et al [3]rdquo) If anumerical value or numerical interval is used as a thresholdto represent the background field the field that is above orbelow the threshold constitutes a geological anomaly (ldquoas
discussed by Cheng [4]rdquo) The character of the geologicalanomaly and the size and type of mineral resources aredetermined by the geological environment geological agerock type and structural background of the formation ofthe geological anomaly With the evolution of geology thegeological anomaly has an evolution sequence in the timeand space With respect to time evolution has the stage withrespect to space evolution has inheritance and superposition(ldquoas discussed by Freedman and Parsons [5]rdquo)
Not all geological anomalies can form deposits but theconstitution of a geological anomaly is a prerequisite forthe formation of deposits (ldquoas discussed by Shen et al[6]rdquo) Determining which geological anomaly can result ina mineral deposit can allow effective identification of thedeposit Based on the time required for ore formation ageological anomaly can be classified into a front ore-forminganomaly an ore-forming anomaly and a tail ore-forminganomaly (ldquoas discussed by Zhao et al [7]rdquo) Different factorsand combinations of ore-forming geologies have certainspecial properties related to ore formation However variousminerals with different genetic morphological mineral and
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 3436192 11 pageshttpdxdoiorg10115520163436192
2 Mathematical Problems in Engineering
industrial types are needed to select certain geological factorsand combinationsTherefore it is necessary to find the targetanomaly in all of the possible ore-forming geological anoma-lies the area of the target anomaly is known as the feasiblelocation for prospecting According to additional informa-tion on ore formation such as the remote sensing anomalygeophysical anomaly and geochemical anomaly we can findthe location of the required ore deposit these areas are knownas the favorable areas for prospectingWithmore informationon the geological anomaly the area of the prospecting targetwill be gradually reducedmaking it easy to locate the depositTherefore the geological anomaly is the basis of mineraldeposit prediction it is effective in locating deposits byprecisely identifying the geological anomaly Therefore it isimportant to identify more reasonable methods to locate thegeological anomaly To meet this challenge various methodshave been proposed and successfully applied with respectto the geological anomaly such as the Three-ComponentMineral Prediction theory (ldquoas discussed by Zhao et al [8]rdquo)the quantitative prediction theory of geological anomaly (ldquoasdiscussed by Pengda et al [3]rdquo) and singularity theories andmethods for mineral deposit prediction (ldquoas discussed byCheng and Zhao [9]rdquo) However each method pertainingto the geological anomaly needs to meet the conditions ofthe algorithms when they identify the geological anomalyIn fact not every algorithm satisfies the entire geologicalenvironment Consequently more algorithms related to thecharacteristics of the geological anomaly and those basedon the environment are needed which match the extractioncriteria of the geological anomaly
At the International Statistics Congress held in SeoulRepublic of Korea (ldquoas discussed by Chen et al [10]rdquo) PengdaZhao described the geological anomaly as an extreme valuebased on amathematical foundation For the geological back-ground he thought that an abnormal value was the geologicalanomaly which directly infers that knowledge of the mathe-matical foundation of the geological anomaly is of extremevalue The extreme value analysis pertains to research on therandom character in the process of quantification at a verylarge or small level and an estimate of the probability of anextreme event at the existing observational level while theobservation data of the geological anomaly are located in thetail end of the distributionTherefore the geological anomalybelongs to the EVT category The extreme value theorem isa branch of statistics that studies the limiting distribution ofthe minimum and maximum value and evaluates the riskof extreme events (ldquoas discussed by Allen et al [11]rdquo) Inrecent years the EVT has been widely used in the fields offinance insurance floods earthquakes rainfall analysis andso on (ldquoas discussed by Chen and Lv [12]rdquo and ldquoas discussedelsewhere [12ndash14]rdquo) Since the geological anomaly belongs tothe EVT category the EVT has been widely used in manyfields so we can learn from the experience of these typesof applications and design the extreme value model of thegeological anomaly that can effectively identify the geologicalanomaly Does the EVT model of the geological anomalyreally identify anomaliesThis study was performed to verifythe use of the model to identify anomalies in the Jiguanzui
Cu-Au mining area The results show that the model caneffectively identify the geological anomaly region
The rest of this paper is organized as follows Section 2studies the EVT themethod of selecting the threshold EVT isstudied and some parameters of the EVT are also discussedSection 3 designs the EVT model of the geological anomalyand provides a new method to increase the accuracy withwhich the threshold can be selected The feasibility of usingthe EVTmodel to identify the anomaly is discussed Section 4will demonstrate the application of the EVTmodel of the geo-logical anomaly Some conclusions are presented in Section 5
2 The Study of the EVT
21 The Knowledge Related to the EVT In the sample data ifthe parent distribution or the sample size is not fully knownthe parent distribution can be obtained from the asymptoticdistribution of the extreme value of the sample While thesample data are large the largest or smallest value from asample has a degradation problem However the extremaltype theorem can effectively solve this problem (ldquoas discussedby Vanem [15]rdquo) The extremal type theorem is presented asfollows
If 1199091 1199092 119909
119899is a sequence of independent random
variables with a common distribution parent distribution119865(119909) is unknown 119872
119899is the largest value of the sample
interval and 119867(119909) is a nondegenerate distribution functionIf there exists a sequence of constants 119886
119899 gt 0 and 119887
119899 isin 119877
Pr(119872119899minus 119887119899
119886119899
le 119909) 997888rarr 119867(119909) (1)
119867(119909) indicates a generalized extreme value distributionHere 119886
119899is a scaling constant and 119887
119899is a location constant
Then this limiting distribution 119867(119909) after standardization(119872119899minus 119887119899)119886119899must be one of the three following types
119867(119909) =
0 119909 le 119887
expminus(119909 minus 119887119886
)
minus120572
119909 gt 119887
120572 gt 0 (FRECHET)
119867 (119909) =
expminus[minus(119909 minus 119887119886
)
minus120572
] 119909 le 119887
1 119909 gt 119887
120572 lt 0 (WEIBULL)
119867 (119909) = expminus exp [minus(119909 minus 119887119886
)]
119909 isin 119877 (GUMBEL)
(2)
Here 120572 is a shape parameter 119887 is a location parameter and 119886is a scale parameter
22 The GPD Model In the EVT the block maxima method(BMM) is a traditional model (ldquoas discussed by Rivas et al
Mathematical Problems in Engineering 3
0
01
02
03
04
05
06
07
08
09
1
0 1 2 3 4 5 6 7 8
( = 05 = 1)( = 0 = 1)
( = minus05 = 1)
(a)
0
01
02
03
04
05
06
07
08
09
1
0 1 2 3 4 5 6 7 8
( = 05 = 1)( = 0 = 1)
( = minus05 = 1)
(b)
Figure 1 The standard GPD (a) is the distribution function of the GPD and (b) is the density function of the GPD
[16]rdquo) The BMM divides the sample interval into severalnonoverlapping cells in accordance with the time the lengthand so on Then there is an extreme sequence that isformed by selecting all the maximum values of each smallinterval from the extreme sequence the parent distributioncan be obtained by distribution fitting of the extremal typetheorem However the BMMmodel has a problem that somemaximum values of intervals are greater than those of theother intervals thus the validity of the BMM model is notsatisfactory The defects can be solved by generalized Paretodistribution (GPD) (ldquoas discussed by Ashkar and El Adlouni[17]rdquo) The GPD is a fitting of the observed data which isgreater than a certain threshold
Here 1199091 1199092 119909
119899is a sequence of independent random
variables with a common distribution and 120583 is a sufficientlyhigh threshold If there is positive number 120573 the excessdistribution (119909
119894minus 120583 119894 = 1 2 119899) can be expressed as
119866120585120573(119909) =
1 minus (1 + 120585
119909 minus 120583
120573
)
minus1120585
120585 = 0
1 minus 119890minus(119909minus120583)120573
120585 = 0
(3)
where 120585 is a shape parameter and 120573 is a scale parameter If120585 ge 0 119909 ge 120583 and 120585 lt 0 120583 le 119909 le minus120573120585 + 120583 The sequence(119909119894 119894 = 1 2 119899) obeys the GPD The general formula of
the GPD is given by
119866120585120573(119909) =
1 minus (1 +
120585
120573
119909)
minus1120585
120585 = 0
1 minus 119890minus119909120573
120585 = 0
(4)
Here if 120573 = 1 the expression of the GPD is referred to asthe standard form If 120585 = minus05 05 and 0 then the image ofthe standard distribution function and density distributionfunction of the GPD is as presented in Figure 1 From
Figure 1(a) it is seen that the tail of the GPD thickens as theshape parameter increases Figure 1(b) shows that the densityfunction of the GPD decreases monotonically
TheGPD requires estimates of the parameters and thresh-oldThe shape parameter 120585 and scale parameter 120573 of the GPDcan be estimated by the maximum likelihood function (ldquoasdiscussed by Castillo and Serra [18]rdquo) Taking the derivativeof (4) we can obtain the density function of the GPD
119891120585120573(119909) =
1
120573
(1 + 120585
119909
120573
)
minus1120585minus1
(5)
Taking natural logarithms of both sides of (5) we obtainthe log likelihood function
119871 (120585 120573 119909) = minus119899119871119899120573 minus (
1
120585
+ 1)
119899
sum
119894=1
119871119899(1 +
120585
120573
119909119894) (6)
Taking the partial derivative of 120585 and120573 of (6) respectively thelikelihood equation is as follows
119899 minus (1 minus120585)
sum119899
119894=1119909119894
[120573 +
120585 (119909119894)]
= 0
119899
sum
119894=1
ln[1 +120585 (119909119894)
120573
] minus
119899
sum
119894=1
119909119894
[120573 +
120585 (119909119894)]
= 0
(7)
Thus the maximum likelihood estimate value 120585 of theshape parameter 120585 and the maximum likelihood estimatevalue 120573 of the scale parameter 120573 can be obtained from (7)In addition the shape parameter and scale parameter of theGPDcan be estimated by themomentmethod the estimationresults obtained by the moment method are superior to those
4 Mathematical Problems in Engineering
obtained using the likelihood function (ldquoas discussed byErgun and Jun [19]rdquo) The moment method is given by
120585 =
[1 minus (119905120575)
2
]
2
120573 = 119905 (1 minus
120585)
(8)
where 119905119894= 119909119894minus 120583 ge 0 119905 is the mean value of 119905
119894 and 120575 is
the standard deviation of 119905119894 In the GPDmodel the threshold
selection methods mainly concern the mean excess function(MEF) (ldquoas discussed by Gencay and Selcuk [20]rdquo) and Hillplotting (ldquoas discussed by J H T Kim and J Kim [21]rdquo) Ifrandom variable119883 obeys the GPD the MEF 119864(120583) is given by
For the actual sample data 119864(120583) can be calculated by thefollowing
119864 (120583) =
sum119899
119894=1(119909119894minus 120583)+
119873119899
(10)
where 119899 is the total number of sample data and119873119899is the total
number of sample data that exceed threshold120583 If119909119894ge 120583 (119909
119894minus
120583)+= 119909119894minus120583 or 119909
119894lt 120583 (119909
119894minus120583)+= 0 Then we can plot scatter
diagram (120583 119864(120583)) In the scatter diagram there is sufficientlyhigh threshold 120583 when 119909 gt 120583 119864(120583) is an approximate linearfunction
3 Design the EVT Model ofthe Geological Anomaly
For the actual observational data 119883 = 1199091 1199092 119909
119899 of
the geological anomaly the tail distribution of the geologicalobservational data is called the geological anomalyThereforeif the data are higher than sufficiently high threshold 120583 inthe sample data we can model these data using the GPDThe parameters of the GPD can be estimated by the momentmethod or the likelihood function Threshold 120583 can also becalculated using the MEF or Hill plottingThus the designedEVT model of the geological anomaly is as follows
Step 1 (conditional test) Before using the EVT model ofthe geological anomaly the stationary and posttail of thesample data need to be tested The common method of theconditional test is as follows probability plot and quantile-quantile (Q-Q) plot (ldquoas discussed by Feng et al [22]rdquo)augmented Dickey-Fuller (ADF) test (ldquoas discussed by Leeand Chang [23]rdquo) and so on
Step 2 (estimate the parameters of themodel) For the sampledata use the moment method or likelihood function toestimate shape parameter 120585 and scale parameter120573 of theGPD
Step 3 (determine the threshold) Select different thresholds120583 from the sample data Then we can calculate the MEF ofthe sample data through scatter diagram (120583 119864(120583)) there is
The original geological data
Conditional test The common method of conditional test is as follows P-P plot Q-Q plot and ADF
Estimate the parameters of model
Determine the threshold
Determine the distribution of excess threshold
Diagnostic test of model
Get the threshold of geological anomaly
No
Yes
Figure 2 The chart of the algorithm
sufficiently high threshold 120583 when 119909 gt 120583 and 119864(120583) is anapproximate linear function Here the value 120583 is called thethreshold of the geological anomaly
Step 4 (determine the distribution of the excess threshold)After the threshold and parameters are determined we insertthe threshold and parameters into the GPD to obtain thedistribution of the excess threshold this distribution is calledthe abnormal probability distribution
Step 5 After the distribution of excess threshold is deter-mined a diagnostic test can determine whether the thresholdselection is rational The diagnostic test of the model mainlytests the consistency between the theoretical distribution andthe actual distribution especially the fitting degree of theactual data and the model distribution The methods weusually use are the Q-Q plot and probability plot If the testeffect is not satisfactory repeat Step 3 and determine the newreasonable threshold The chart of the EVT model of thegeological anomaly is shown in Figure 2
In this study the determination of threshold 120583 in theEVT model is critical If the selection of the threshold valueis higher the number of samples that exceed the thresholdvalue is lower and the parameters of the GPD are verysensitive to the high values of the observational data whichwill cause errors in the parameter estimation Converselythe selection of a threshold value that is low will increasethe number of observations increasing the accuracy of theestimation of the parameters but the excess data 119909
119894minus 120583 do
not obey the GPD distribution At present there is no clearmethod to select the accuracy threshold The MEF can beused to estimate the threshold with some defects in whichthe selection of the threshold is usually an interval value andnot an accurate constantTherefore this paper provides a newmethod to increase the accuracywithwhich the threshold canbe selected In the GPD when the initial threshold value 120583
0
Mathematical Problems in Engineering 5
Table 1 The basic statistics of Cu and Au
Elements Mean Minimum Maximum Std dev CV Skewness KurtosisCu 64144 5326 1720277 72765 113 738 10696Au 7082 713 187797 025 082 842 15493
is determined the excess data 119909119894minus1205830approximately obey the
GPD distribution Regardless of any threshold 120583 (120583 gt 1205830)
the shape parameter 120585 and scale parameter 120573 of the GPDshould remain unchanged Therefore information can beobtained on the transformation relationship between 120573(120583)and threshold 120583 (120583 gt 120583
0) from (3)
120573 (120583) = 120573 (1205830) + 120585 (120583 minus 120583
0) (11)
Let 120573lowast(120583) = 120573(1205830)+120585(120583minus120583
0) 120573lowast(120583) is called themodified
scale and the values of 120573lowast(120583)will not change when threshold120583 changes Therefore when the interval threshold value isdetermined byMEF the accuracy threshold can be estimatedby 120573lowast(120583) Estimating the threshold using 120573lowast(120583) is detailed inSection 42
In this paper the EVT model of the geological anomalytakes full account of the characteristic of the geologicalanomaly distribution and the practical features of the EVTRelative to the geological background value the anomaly andextreme value can be used to describe the geological anomalyThe observations of the geological anomaly are located in thetail of the samples which are related to the random charactersin the process of quantification at the very large or smalllevel and estimate the probability of the extreme event inthe existing observation levelsmdashthese characteristics are alsothe contents of the EVT The EVT is a branch of statisticsthat studies the limiting distribution of the minimum andmaximum value and evaluates the risk of extreme eventsTherefore the mathematical foundation of the geologicalanomaly is described by the EVT On the one hand the EVTdescribes the characteristic of the geological anomaly distri-bution from the perspective of mathematics the results from(3) show the distribution of the sample data which is provedin (12) On the other hand the EVT provides a quantitativeand digital research method for predicting and evaluatingthe mineral resources which is proved in Figure 10 Besidesthis paper also discusses the methods of estimate parametersand the threshold of the EVT Consequently a mathematicalstatisticalmodel is established for quantitative geological dataand geology information where the data exceed the thresholdof the sample in (12) Therefore the ability of the EVT modelto identify the geological anomaly is feasible
4 The Model Application in Identifyingthe Geological Anomaly of the JiguanzuiCu-Au Mining Area
In order to show the effect of identifying the anomaly usingthe EVT model with geological anomaly recognition themodel was applied to identify the anomaly in an actualmining area The study data with Cu and Au originate from26 exploration lines of the Jiguanzui Cu-Au mining area inHubei China The count of the sample data with Cu and Au
is 14309 The Jiguanzui Cu-Au mining deposit is the blinddeposits at the lower part of the Quaternary overburdenlayer Currently I II III and VII main ore body groups 14main ore bodies and 105 small fragmentary ore bodies havebeen identified in the mining area The main ore bodies ofthe Jiguanzui Cu-Au mining area are distributed in the 013to 034 lines which are 950 meters long the width is 160ndash800 meters the elevation ranges from minus5m to minus1412m deepextension and the level projection area of the ore bodies is058 square kilometers The overall distribution of the orebodies is northeast 30∘ the trend of the ore bodies is northeast15∘ndash72∘ and the local trend of the ore bodies is northwest I IIIII andVII ore bodies are arranged in the form of an echelonin which the tendency is northwest and the local tendency issouthThemain ore bodies occur in the fault basin at the edgeof the northwestern rock body of the Tonglushan near thecontact zone of the dolomitic marble the quartz monzonitediorite porphyry and quartz diorite in the Lower TriassicJialingjiang Formation and near the different lithology andthe echelon fracture of dolomitic marble The pattern of theJiguanzui Cu-Au mining deposit is shown in Figure 3
41 The Condition Test of the Model
411 The Posttail Test of Sample Data Firstly this paperanalyses the basic statistics of the Cu and Au elements andthe results are shown in Table 1 From Table 1 we can see thatthe skewness of the sample data is greater than zero and thesample data are not normally distributed that is distributedto the right By observing the coefficient of variation it is seenthat the coefficient of variation of Au is smaller than that ofCu and the stability of Au is higher than that of Cu Besidesthe kurtosis of Cu and Au is greater than that of the normaldistribution (of which the kurtosis value is 3) which resultsin a leptokurtic distribution for Cu and Au Therefore thedistribution of Cu and Au is shown to be skewed to the rightwith leptokurtic characteristics Secondly in order to indicatethe difference between the actual distribution and normaldistribution Q-Q plot can be used for the observation test(Figure 4) The distribution of Cu and Au is also shown to beskewed to the right with posttail characteristics
412 The Stationary Test of the Sample Data The stationarytestmainly inspects the self-correlation of the geological datathe commonmethods of the stationary test are as follows theaugmented Dickey-Fuller (ADF) and sequence correlationanalysis Through the ADF we can obtain the test resultsof the sample data (Table 2) The 119905-statistics of Cu and Auare minus3393498 and minus1319081 respectively which are smallerthan their own 1 significant level Therefore the sequencesof Cu and Au do not have unit roots they are stationarysequencesThe results of the sequence correlation analysis are
6 Mathematical Problems in Engineering
A
D
C
B
Volcaniclastic rocks of neighboring group
Breccia of Majiashan group
Pelitic siltstone of Puqi group
Dolomitic marble of Lower Triassic Jialingjiang Formation
Quartz monzonite diorite porphyry
Diorite
Fracture
Stratigraphic boundary
Unconformity boundary
Structural breccia
Ore bodies and numbers
The first metallogenic region
The second metallogenic region
The third metallogenic region
The fourth metallogenic region
A
B
C
D
K1l
K1l
I
VIVII
IVIII
IIJ3m
J3m
F3
F1
T2p
T2p
T2p
T1minus2j
T1minus2j
T1minus2j
T1minus2j
T1minus2j
T1minus2j
Q25Q25
Q25
Q25
35
35
Figure 3 The pattern of the Jiguanzui Cu-Au mining deposit
Table 2 The ADF test of Cu and Au
Elements ADT (119905-statistic) Test critical values Probability1 level 5 level 10 level
shown in Figure 5 where we can see that the autocorrelationcoefficients (AC) and the partial autocorrelation coefficient(PAC) are not zero and the significance of 119876-states is highso the uncorrelated hypothesis cannot be rejectedThereforethe sequence of the geological data is a stationary time series
Together the results indicate that the data follow astationary sequence and the distributions of Cu and Au haveposttail characteristics indicating that they are abnormallydistributed Therefore we can use the EVT model of thegeological anomaly to identify the anomaly
Mathematical Problems in Engineering 7
4000
3000
2000
1000
0
0 5000 10000 15000 20000
Normal Q-Q plot of Cu
Expe
cted
nor
mal
val
ue
Observed value
minus1000
minus2000
minus3000minus5000
(a)
Expe
cted
nor
mal
val
ue
300
200
100
0
0 500 1000 1500 2000
Normal Q-Q plot of Au
Observed value
minus100
minus200minus500
(b)
Figure 4 The posttail test of the sample data according to Q-Q plot (a) is Q-Q plot test of Cu and (b) is Q-Q plot test of Au
Autocorrelation Partial correlation AC PAC Prob
12345678910
0958 0958 12885 0000
000000000000000000000000
000000000000
087107780695062805760535049604570420
0254
00010055
00650011
235293201938804443484900153015564705940361886
0072
minus0570
minus0026
minus0115
Q-stat
(a)
Autocorrelation Partial correlation AC PAC Prob
123456789
10
0963 13029 0000
000000000000000000000000
000000000000
08860799071606410574051404610413
240543302740230460055069254341573255972661650
0963
0198
0042
00070005
0029
0370
minus0580
minus0044
minus0033
minus0029
Q-stat
(b)
Figure 5The sequence correlation analysis of the sample data (a) is the sequence correlation analysis of Cu and (b) is the sequence correlationanalysis of Au
42 The Solution of the Model
421 Estimate the Parameters and Threshold Through theEVT model of the geological anomaly we can calculate theMEF of Cu and Au and plot the scatter diagram of the MEF(Figure 6) From Figure 6 it is seen that in the interval[7845406 8413659]with Cu and interval [721178 851918]with Au 119864(120583) for Cu and Au follows an approximately lineardistribution These intervals are selected as the thresholdfor Cu and Au As the result of the threshold selectionis subjective modified scale 120573lowast(120583) is used to estimate theaccuracy threshold Based on 120573lowast(120583) if initial threshold value1205830is determined regardless of any threshold 120583 (120583 gt 120583
0)
the shape parameter 120585 and scale parameter 120573 of GPD willnot change Uniformly selecting 50 threshold values from[7845406 8413659] and [721178 851918] respectively wecan obtain the transformation relations between 120573lowast(120583) 120585and the threshold 120583 (120583 gt 120583
0) for Cu and Au using (3) and
(11) see Figures 7 and 8 In order to ensure the accuracyof the EVT the threshold selection is as large as possiblein the permissible range of threshold estimation where thedata show the stationary characteristic (ldquoas discussed by Cao
and Zhang [24]rdquo) From Figures 7 and 8 it is seen that thethreshold of Cu is 8164006 and that of Au is 754736 Afterthe thresholds are determined the parameters of the EVTmodel of the geological anomaly can be estimated using themoment method which reveals that the shape parameter ofCu is 03162 and that of Au is 03342 the scale parameter ofCu is 4409216 and that of Au is 315699 Then inserting thethresholds and parameters into the GPD the distribution ofthe excess threshold of Cu and Au can be obtained by
119865Cu (119909) = 1 minus (1 +03162
4409216
119909)
minus103162
119865Au (119909) = 1 minus (1 +03342
315699
119909)
minus103342
(12)
The distribution of the excess threshold is called theabnormal probability distribution In themineral deposit pre-diction information on the geological data can be describedand expressed by the distribution of the excess threshold
422 The Diagnostic Test of the Model and Identificationof the Anomaly The diagnostic test shows whether the
8 Mathematical Problems in Engineering
0 4000 8000 12000 160000
500
1000
1500
2000
2500
3000
3500
4000
4500E
()
(a)
0 500 1000 1500 20000
50
100
150
200
250
300
350
400
450
500
E(
)
(b)
Figure 6 The scatter diagram of the MEF (a) is the MEF of Cu and (b) is the MEF of Au
780 790 800 810 820 830 840 850410
420
430
440
450
460
470
480
Mod
ified
(a)
780 790 800 810 820 830 840 850
029
0295
03
0305
031
0315
032
0325
033
Mod
ified
(b)
Figure 7 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Cu
72 74 76 78 80 82 84 8622
24
26
28
30
32
34
36
Mod
ified
(a)
72 74 76 78 80 82 84 86
031
032
033
034
035
036
037
038
039
04
Mod
ified
(b)
Figure 8 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Au
Mathematical Problems in Engineering 9
10
10
08
08
06
06
04
04
02
02
0000
Pareto P-P plot of Cu
Observed cum prob
Expe
cted
cum
pro
b
(a)
100806040200Observed cum prob
10
08
06
04
02
00
Expe
cted
cum
pro
b
Pareto P-P plot of Au
(b)
Figure 9 The GPD fitting of the sample data (a) is the distribution fitting of Cu and (b) is the distribution fitting of Au
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ile13429109378164
class
ifica
tion
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
(a)
1002811755
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ilecla
ssifi
catio
n
(b)
Figure 10 The identified anomaly region of Cu and Au (a) is the anomaly region of Cu and (b) is the anomaly region of Au
selection of the thresholds is reasonable Fitting the excessthreshold of the sample data using the GPD (Figure 9)indicates that the excess threshold of the sample data is inthe vicinity of the line the results show that the theoreticaldistribution and actual distribution of the sample data areconsistent Therefore the threshold selection is reasonableThere are currently seven mining drill holes that is KZK10KZK11 KZK23 KZK28 ZK02618 ZK02619 and ZK02620
and the exploitation ore bodies are mostly VII main orebody in the 26 exploration lines of the Cu-Au mining areaGIS technology is used to show the geological anomalyregion with the selection of the thresholds (Figure 10)From Figure 10 it is seen that the anomaly region of Cuand Au is consistent with the range of ore bodies of theactual engineering exploration which has a high indicatingfunction with respect to ore prospecting The results show
10 Mathematical Problems in Engineering
that the EVT model of the geological anomaly is good atmineral deposit prediction and it has good prospectingsignificance
5 Conclusion
In this study the proposed EVT model of the geologicalanomaly was applied to identify geochemical anomaliesassociated with Cu and Au mineralizationThe results of thisstudy led to the following
(1) The characteristics of the geological anomaly and theprinciple of EVT were studied knowledge of the dis-tribution of the EVT coincides with the distributionof the geological anomaly data The designed EVTmodel of the geological anomaly takes full accountof the characteristic of the geological anomaly andthe practical features of the EVT The thresholdselection and parameter estimates of the model weredetermined
(2) The proposed EVT model of the geological anomalywas successfully applied to identify the geologicalanomaly region in the Jiguanzui Cu-Au mining areaThe results show that the anomaly threshold of Cu is8164006 and that of Au is 754736 the shape param-eter of Cu is 03162 and that of Au is 03342 and thescale parameter of Cu is 4409216 and that of the Auis 315699 The abnormal probability distribution wasalso determined Testing the results of the model byfitting the excess threshold of the sample data showedthat the results of the theoretical distribution andactual distribution of the sample data were consistent
(3) The geological anomalies of Cu and Au predictedby the EVT model are consistent with the rangeof ore bodies of the actual engineering explorationThe EVT model has a high indicating function withrespect to ore prospecting and it is applicable for theexploration of mineral deposits
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This study was supported by the GeophysiochemistryProspecting Institute of the Academy of Geological Scienceof China and the Program for the Core of High Spec-trum of Primary Halo Geochemical Prospecting Project (no12120114002001) and the project of the special funds foruniversities was supported by the central governmentmdashtheconstruction of discipline platform inmanagement engineer-ing theory and quantitative methods (no 80000-14Z019002)The authors are grateful to the First Geological Brigade ofthe Hubei Geological Bureau for providing the data Theywould also like to express their appreciation for the teammembers of the Key Laboratory of Mathematical Geology inSichuan China They are grateful to Professor HongJun Liu
at ChengduUniversity of Technology for providing construc-tive advice for this studyThey also thank LetPub (httpwwwletpubcom) for its linguistic assistance during the prepara-tion of this manuscript
References
[1] A Darehshiri M Panji and A R Mokhtari ldquoIdentifyinggeochemical anomalies associated with Cu mineralization instream sediment samples in Gharachaman area northwest ofIranrdquo Journal of African Earth Sciences vol 110 pp 92ndash99 2015
[2] X Lu and P Zhao ldquoGeologic anomaly analysis for space-timedistribution of mineral deposits in the middle-lower Yangtzearea southeastern Chinardquo Nonrenewable Resources vol 17 no3 pp 187ndash196 1998
[3] Z Pengda C Qiuming and X Qinglin ldquoQuantitative predic-tion for deep mineral explorationrdquo Journal of China Universityof Geosciences vol 19 no 4 pp 309ndash318 2008
[4] Q Cheng ldquoSingularity theory and methods for mapping geo-chemical anomalies caused by buried sources and for predictingundiscovered mineral deposits in covered areasrdquo Journal ofGeochemical Exploration vol 122 pp 55ndash70 2012
[5] A P Freedman and B Parsons ldquoGeoid anomalies over twoSouth Atlantic fracture zonesrdquo Earth and Planetary ScienceLetters vol 100 no 1ndash3 pp 18ndash41 1990
[6] P Shen Y Shen T Liu L Meng H Dai and Y YangldquoGeochemical signature of porphyries in the Baogutu porphyrycopper belt western Junggar NW Chinardquo Gondwana Researchvol 16 no 2 pp 227ndash242 2009
[7] J Zhao S Chen and R Zuo ldquoIdentifying geochemical anoma-lies associated with AundashCu mineralization using multifractaland artificial neural network models in the Ningqiang districtShaanxi Chinardquo Journal of Geochemical Exploration vol 164pp 54ndash64 2016
[8] P Zhao J Chen J Chen S Zhang and Y Chen ldquoThelsquothree-componentrsquo digital prospecting method a new approachfor mineral resource quantitative prediction and assessmentrdquoNatural Resources Research vol 14 no 4 pp 295ndash303 2005
[9] Q Cheng and P Zhao ldquoSingularity theories and methodsfor characterizing mineralization processes and mapping geo-anomalies for mineral deposit predictionrdquoGeoscience Frontiersvol 2 no 1 pp 67ndash79 2011
[10] Y Chen P Zhao J Chen and J Liu ldquoApplication of the geo-anomaly unit concept in quantitative delineation and assess-ment of gold ore targets in western Shandong uplift terraineastern ChinardquoNatural Resources Research vol 10 no 1 pp 35ndash49 2001
[11] D E Allen A K Singh and R J Powell ldquoExtreme marketrisk-an extreme value theory approachrdquo Mathematics andComputers in Simulation vol 94 pp 310ndash328 2011
[12] Q Chen and X Lv ldquoThe extreme-value dependence betweenthe crude oil price and Chinese stock marketsrdquo InternationalReview of Economics and Finance vol 39 pp 121ndash132 2015
[13] KWhan J Zscheischler R Orth et al ldquoImpact of soil moistureon extreme maximum temperatures in Europerdquo Weather andClimate Extremes vol 9 pp 57ndash67 2015
[14] D Faranda J M Freitas P Guiraud and S Vaienti ldquoSamplinglocal properties of attractors via extreme value theoryrdquo ChaosSolitons and Fractals vol 74 pp 55ndash66 2015
[15] E Vanem ldquoNon-stationary extreme value models to accountfor trends and shifts in the extreme wave climate due to climatechangerdquo Applied Ocean Research vol 52 pp 201ndash211 2015
Mathematical Problems in Engineering 11
[16] D Rivas F Caleyo A Valor and J M Hallen ldquoExtreme valueanalysis applied to pitting corrosion experiments in low carbonsteel comparison of block maxima and peak over thresholdapproachesrdquo Corrosion Science vol 50 no 11 pp 3193ndash32042008
[17] F Ashkar and S-E El Adlouni ldquoAdjusting for small-samplenon-normality of design event estimators under a generalizedPareto distributionrdquo Journal of Hydrology vol 530 pp 384ndash3912015
[18] J D Castillo and I Serra ldquoLikelihood inference for generalizedPareto distributionrdquo Computational Statistics amp Data Analysisvol 83 pp 116ndash128 2015
[19] A T Ergun and J Jun ldquoTime-varying higher-order conditionalmoments and forecasting intraday VaR and Expected ShortfallrdquoThe Quarterly Review of Economics and Finance vol 50 no 3pp 264ndash272 2010
[20] R Gencay and F Selcuk ldquoExtreme value theory and value-at-risk relative performance in emerging marketsrdquo InternationalJournal of Forecasting vol 20 pp 287ndash303 2004
[21] J H T Kim and J Kim ldquoA parametric alternative to the Hillestimator for heavy-tailed distributionsrdquo Journal of Banking ampFinance vol 54 pp 60ndash71 2015
[22] Z-H Feng Y-M Wei and K Wang ldquoEstimating risk for thecarbon market via extreme value theory an empirical analysisof the EU ETSrdquo Applied Energy vol 99 pp 97ndash108 2012
[23] C-C Lee and C-P Chang ldquoNew evidence on the convergenceof per capita carbon dioxide emissions from panel seeminglyunrelated regressions augmented Dickey-Fuller testsrdquo Energyvol 33 no 9 pp 1468ndash1475 2008
[24] G Cao and M Zhang ldquoExtreme values in the Chinese andAmerican stock markets based on detrended fluctuation anal-ysisrdquo Physica A Statistical Mechanics and its Applications vol436 pp 25ndash35 2015
industrial types are needed to select certain geological factorsand combinationsTherefore it is necessary to find the targetanomaly in all of the possible ore-forming geological anoma-lies the area of the target anomaly is known as the feasiblelocation for prospecting According to additional informa-tion on ore formation such as the remote sensing anomalygeophysical anomaly and geochemical anomaly we can findthe location of the required ore deposit these areas are knownas the favorable areas for prospectingWithmore informationon the geological anomaly the area of the prospecting targetwill be gradually reducedmaking it easy to locate the depositTherefore the geological anomaly is the basis of mineraldeposit prediction it is effective in locating deposits byprecisely identifying the geological anomaly Therefore it isimportant to identify more reasonable methods to locate thegeological anomaly To meet this challenge various methodshave been proposed and successfully applied with respectto the geological anomaly such as the Three-ComponentMineral Prediction theory (ldquoas discussed by Zhao et al [8]rdquo)the quantitative prediction theory of geological anomaly (ldquoasdiscussed by Pengda et al [3]rdquo) and singularity theories andmethods for mineral deposit prediction (ldquoas discussed byCheng and Zhao [9]rdquo) However each method pertainingto the geological anomaly needs to meet the conditions ofthe algorithms when they identify the geological anomalyIn fact not every algorithm satisfies the entire geologicalenvironment Consequently more algorithms related to thecharacteristics of the geological anomaly and those basedon the environment are needed which match the extractioncriteria of the geological anomaly
At the International Statistics Congress held in SeoulRepublic of Korea (ldquoas discussed by Chen et al [10]rdquo) PengdaZhao described the geological anomaly as an extreme valuebased on amathematical foundation For the geological back-ground he thought that an abnormal value was the geologicalanomaly which directly infers that knowledge of the mathe-matical foundation of the geological anomaly is of extremevalue The extreme value analysis pertains to research on therandom character in the process of quantification at a verylarge or small level and an estimate of the probability of anextreme event at the existing observational level while theobservation data of the geological anomaly are located in thetail end of the distributionTherefore the geological anomalybelongs to the EVT category The extreme value theorem isa branch of statistics that studies the limiting distribution ofthe minimum and maximum value and evaluates the riskof extreme events (ldquoas discussed by Allen et al [11]rdquo) Inrecent years the EVT has been widely used in the fields offinance insurance floods earthquakes rainfall analysis andso on (ldquoas discussed by Chen and Lv [12]rdquo and ldquoas discussedelsewhere [12ndash14]rdquo) Since the geological anomaly belongs tothe EVT category the EVT has been widely used in manyfields so we can learn from the experience of these typesof applications and design the extreme value model of thegeological anomaly that can effectively identify the geologicalanomaly Does the EVT model of the geological anomalyreally identify anomaliesThis study was performed to verifythe use of the model to identify anomalies in the Jiguanzui
Cu-Au mining area The results show that the model caneffectively identify the geological anomaly region
The rest of this paper is organized as follows Section 2studies the EVT themethod of selecting the threshold EVT isstudied and some parameters of the EVT are also discussedSection 3 designs the EVT model of the geological anomalyand provides a new method to increase the accuracy withwhich the threshold can be selected The feasibility of usingthe EVTmodel to identify the anomaly is discussed Section 4will demonstrate the application of the EVTmodel of the geo-logical anomaly Some conclusions are presented in Section 5
2 The Study of the EVT
21 The Knowledge Related to the EVT In the sample data ifthe parent distribution or the sample size is not fully knownthe parent distribution can be obtained from the asymptoticdistribution of the extreme value of the sample While thesample data are large the largest or smallest value from asample has a degradation problem However the extremaltype theorem can effectively solve this problem (ldquoas discussedby Vanem [15]rdquo) The extremal type theorem is presented asfollows
If 1199091 1199092 119909
119899is a sequence of independent random
variables with a common distribution parent distribution119865(119909) is unknown 119872
119899is the largest value of the sample
interval and 119867(119909) is a nondegenerate distribution functionIf there exists a sequence of constants 119886
119899 gt 0 and 119887
119899 isin 119877
Pr(119872119899minus 119887119899
119886119899
le 119909) 997888rarr 119867(119909) (1)
119867(119909) indicates a generalized extreme value distributionHere 119886
119899is a scaling constant and 119887
119899is a location constant
Then this limiting distribution 119867(119909) after standardization(119872119899minus 119887119899)119886119899must be one of the three following types
119867(119909) =
0 119909 le 119887
expminus(119909 minus 119887119886
)
minus120572
119909 gt 119887
120572 gt 0 (FRECHET)
119867 (119909) =
expminus[minus(119909 minus 119887119886
)
minus120572
] 119909 le 119887
1 119909 gt 119887
120572 lt 0 (WEIBULL)
119867 (119909) = expminus exp [minus(119909 minus 119887119886
)]
119909 isin 119877 (GUMBEL)
(2)
Here 120572 is a shape parameter 119887 is a location parameter and 119886is a scale parameter
22 The GPD Model In the EVT the block maxima method(BMM) is a traditional model (ldquoas discussed by Rivas et al
Mathematical Problems in Engineering 3
0
01
02
03
04
05
06
07
08
09
1
0 1 2 3 4 5 6 7 8
( = 05 = 1)( = 0 = 1)
( = minus05 = 1)
(a)
0
01
02
03
04
05
06
07
08
09
1
0 1 2 3 4 5 6 7 8
( = 05 = 1)( = 0 = 1)
( = minus05 = 1)
(b)
Figure 1 The standard GPD (a) is the distribution function of the GPD and (b) is the density function of the GPD
[16]rdquo) The BMM divides the sample interval into severalnonoverlapping cells in accordance with the time the lengthand so on Then there is an extreme sequence that isformed by selecting all the maximum values of each smallinterval from the extreme sequence the parent distributioncan be obtained by distribution fitting of the extremal typetheorem However the BMMmodel has a problem that somemaximum values of intervals are greater than those of theother intervals thus the validity of the BMM model is notsatisfactory The defects can be solved by generalized Paretodistribution (GPD) (ldquoas discussed by Ashkar and El Adlouni[17]rdquo) The GPD is a fitting of the observed data which isgreater than a certain threshold
Here 1199091 1199092 119909
119899is a sequence of independent random
variables with a common distribution and 120583 is a sufficientlyhigh threshold If there is positive number 120573 the excessdistribution (119909
119894minus 120583 119894 = 1 2 119899) can be expressed as
119866120585120573(119909) =
1 minus (1 + 120585
119909 minus 120583
120573
)
minus1120585
120585 = 0
1 minus 119890minus(119909minus120583)120573
120585 = 0
(3)
where 120585 is a shape parameter and 120573 is a scale parameter If120585 ge 0 119909 ge 120583 and 120585 lt 0 120583 le 119909 le minus120573120585 + 120583 The sequence(119909119894 119894 = 1 2 119899) obeys the GPD The general formula of
the GPD is given by
119866120585120573(119909) =
1 minus (1 +
120585
120573
119909)
minus1120585
120585 = 0
1 minus 119890minus119909120573
120585 = 0
(4)
Here if 120573 = 1 the expression of the GPD is referred to asthe standard form If 120585 = minus05 05 and 0 then the image ofthe standard distribution function and density distributionfunction of the GPD is as presented in Figure 1 From
Figure 1(a) it is seen that the tail of the GPD thickens as theshape parameter increases Figure 1(b) shows that the densityfunction of the GPD decreases monotonically
TheGPD requires estimates of the parameters and thresh-oldThe shape parameter 120585 and scale parameter 120573 of the GPDcan be estimated by the maximum likelihood function (ldquoasdiscussed by Castillo and Serra [18]rdquo) Taking the derivativeof (4) we can obtain the density function of the GPD
119891120585120573(119909) =
1
120573
(1 + 120585
119909
120573
)
minus1120585minus1
(5)
Taking natural logarithms of both sides of (5) we obtainthe log likelihood function
119871 (120585 120573 119909) = minus119899119871119899120573 minus (
1
120585
+ 1)
119899
sum
119894=1
119871119899(1 +
120585
120573
119909119894) (6)
Taking the partial derivative of 120585 and120573 of (6) respectively thelikelihood equation is as follows
119899 minus (1 minus120585)
sum119899
119894=1119909119894
[120573 +
120585 (119909119894)]
= 0
119899
sum
119894=1
ln[1 +120585 (119909119894)
120573
] minus
119899
sum
119894=1
119909119894
[120573 +
120585 (119909119894)]
= 0
(7)
Thus the maximum likelihood estimate value 120585 of theshape parameter 120585 and the maximum likelihood estimatevalue 120573 of the scale parameter 120573 can be obtained from (7)In addition the shape parameter and scale parameter of theGPDcan be estimated by themomentmethod the estimationresults obtained by the moment method are superior to those
4 Mathematical Problems in Engineering
obtained using the likelihood function (ldquoas discussed byErgun and Jun [19]rdquo) The moment method is given by
120585 =
[1 minus (119905120575)
2
]
2
120573 = 119905 (1 minus
120585)
(8)
where 119905119894= 119909119894minus 120583 ge 0 119905 is the mean value of 119905
119894 and 120575 is
the standard deviation of 119905119894 In the GPDmodel the threshold
selection methods mainly concern the mean excess function(MEF) (ldquoas discussed by Gencay and Selcuk [20]rdquo) and Hillplotting (ldquoas discussed by J H T Kim and J Kim [21]rdquo) Ifrandom variable119883 obeys the GPD the MEF 119864(120583) is given by
For the actual sample data 119864(120583) can be calculated by thefollowing
119864 (120583) =
sum119899
119894=1(119909119894minus 120583)+
119873119899
(10)
where 119899 is the total number of sample data and119873119899is the total
number of sample data that exceed threshold120583 If119909119894ge 120583 (119909
119894minus
120583)+= 119909119894minus120583 or 119909
119894lt 120583 (119909
119894minus120583)+= 0 Then we can plot scatter
diagram (120583 119864(120583)) In the scatter diagram there is sufficientlyhigh threshold 120583 when 119909 gt 120583 119864(120583) is an approximate linearfunction
3 Design the EVT Model ofthe Geological Anomaly
For the actual observational data 119883 = 1199091 1199092 119909
119899 of
the geological anomaly the tail distribution of the geologicalobservational data is called the geological anomalyThereforeif the data are higher than sufficiently high threshold 120583 inthe sample data we can model these data using the GPDThe parameters of the GPD can be estimated by the momentmethod or the likelihood function Threshold 120583 can also becalculated using the MEF or Hill plottingThus the designedEVT model of the geological anomaly is as follows
Step 1 (conditional test) Before using the EVT model ofthe geological anomaly the stationary and posttail of thesample data need to be tested The common method of theconditional test is as follows probability plot and quantile-quantile (Q-Q) plot (ldquoas discussed by Feng et al [22]rdquo)augmented Dickey-Fuller (ADF) test (ldquoas discussed by Leeand Chang [23]rdquo) and so on
Step 2 (estimate the parameters of themodel) For the sampledata use the moment method or likelihood function toestimate shape parameter 120585 and scale parameter120573 of theGPD
Step 3 (determine the threshold) Select different thresholds120583 from the sample data Then we can calculate the MEF ofthe sample data through scatter diagram (120583 119864(120583)) there is
The original geological data
Conditional test The common method of conditional test is as follows P-P plot Q-Q plot and ADF
Estimate the parameters of model
Determine the threshold
Determine the distribution of excess threshold
Diagnostic test of model
Get the threshold of geological anomaly
No
Yes
Figure 2 The chart of the algorithm
sufficiently high threshold 120583 when 119909 gt 120583 and 119864(120583) is anapproximate linear function Here the value 120583 is called thethreshold of the geological anomaly
Step 4 (determine the distribution of the excess threshold)After the threshold and parameters are determined we insertthe threshold and parameters into the GPD to obtain thedistribution of the excess threshold this distribution is calledthe abnormal probability distribution
Step 5 After the distribution of excess threshold is deter-mined a diagnostic test can determine whether the thresholdselection is rational The diagnostic test of the model mainlytests the consistency between the theoretical distribution andthe actual distribution especially the fitting degree of theactual data and the model distribution The methods weusually use are the Q-Q plot and probability plot If the testeffect is not satisfactory repeat Step 3 and determine the newreasonable threshold The chart of the EVT model of thegeological anomaly is shown in Figure 2
In this study the determination of threshold 120583 in theEVT model is critical If the selection of the threshold valueis higher the number of samples that exceed the thresholdvalue is lower and the parameters of the GPD are verysensitive to the high values of the observational data whichwill cause errors in the parameter estimation Converselythe selection of a threshold value that is low will increasethe number of observations increasing the accuracy of theestimation of the parameters but the excess data 119909
119894minus 120583 do
not obey the GPD distribution At present there is no clearmethod to select the accuracy threshold The MEF can beused to estimate the threshold with some defects in whichthe selection of the threshold is usually an interval value andnot an accurate constantTherefore this paper provides a newmethod to increase the accuracywithwhich the threshold canbe selected In the GPD when the initial threshold value 120583
0
Mathematical Problems in Engineering 5
Table 1 The basic statistics of Cu and Au
Elements Mean Minimum Maximum Std dev CV Skewness KurtosisCu 64144 5326 1720277 72765 113 738 10696Au 7082 713 187797 025 082 842 15493
is determined the excess data 119909119894minus1205830approximately obey the
GPD distribution Regardless of any threshold 120583 (120583 gt 1205830)
the shape parameter 120585 and scale parameter 120573 of the GPDshould remain unchanged Therefore information can beobtained on the transformation relationship between 120573(120583)and threshold 120583 (120583 gt 120583
0) from (3)
120573 (120583) = 120573 (1205830) + 120585 (120583 minus 120583
0) (11)
Let 120573lowast(120583) = 120573(1205830)+120585(120583minus120583
0) 120573lowast(120583) is called themodified
scale and the values of 120573lowast(120583)will not change when threshold120583 changes Therefore when the interval threshold value isdetermined byMEF the accuracy threshold can be estimatedby 120573lowast(120583) Estimating the threshold using 120573lowast(120583) is detailed inSection 42
In this paper the EVT model of the geological anomalytakes full account of the characteristic of the geologicalanomaly distribution and the practical features of the EVTRelative to the geological background value the anomaly andextreme value can be used to describe the geological anomalyThe observations of the geological anomaly are located in thetail of the samples which are related to the random charactersin the process of quantification at the very large or smalllevel and estimate the probability of the extreme event inthe existing observation levelsmdashthese characteristics are alsothe contents of the EVT The EVT is a branch of statisticsthat studies the limiting distribution of the minimum andmaximum value and evaluates the risk of extreme eventsTherefore the mathematical foundation of the geologicalanomaly is described by the EVT On the one hand the EVTdescribes the characteristic of the geological anomaly distri-bution from the perspective of mathematics the results from(3) show the distribution of the sample data which is provedin (12) On the other hand the EVT provides a quantitativeand digital research method for predicting and evaluatingthe mineral resources which is proved in Figure 10 Besidesthis paper also discusses the methods of estimate parametersand the threshold of the EVT Consequently a mathematicalstatisticalmodel is established for quantitative geological dataand geology information where the data exceed the thresholdof the sample in (12) Therefore the ability of the EVT modelto identify the geological anomaly is feasible
4 The Model Application in Identifyingthe Geological Anomaly of the JiguanzuiCu-Au Mining Area
In order to show the effect of identifying the anomaly usingthe EVT model with geological anomaly recognition themodel was applied to identify the anomaly in an actualmining area The study data with Cu and Au originate from26 exploration lines of the Jiguanzui Cu-Au mining area inHubei China The count of the sample data with Cu and Au
is 14309 The Jiguanzui Cu-Au mining deposit is the blinddeposits at the lower part of the Quaternary overburdenlayer Currently I II III and VII main ore body groups 14main ore bodies and 105 small fragmentary ore bodies havebeen identified in the mining area The main ore bodies ofthe Jiguanzui Cu-Au mining area are distributed in the 013to 034 lines which are 950 meters long the width is 160ndash800 meters the elevation ranges from minus5m to minus1412m deepextension and the level projection area of the ore bodies is058 square kilometers The overall distribution of the orebodies is northeast 30∘ the trend of the ore bodies is northeast15∘ndash72∘ and the local trend of the ore bodies is northwest I IIIII andVII ore bodies are arranged in the form of an echelonin which the tendency is northwest and the local tendency issouthThemain ore bodies occur in the fault basin at the edgeof the northwestern rock body of the Tonglushan near thecontact zone of the dolomitic marble the quartz monzonitediorite porphyry and quartz diorite in the Lower TriassicJialingjiang Formation and near the different lithology andthe echelon fracture of dolomitic marble The pattern of theJiguanzui Cu-Au mining deposit is shown in Figure 3
41 The Condition Test of the Model
411 The Posttail Test of Sample Data Firstly this paperanalyses the basic statistics of the Cu and Au elements andthe results are shown in Table 1 From Table 1 we can see thatthe skewness of the sample data is greater than zero and thesample data are not normally distributed that is distributedto the right By observing the coefficient of variation it is seenthat the coefficient of variation of Au is smaller than that ofCu and the stability of Au is higher than that of Cu Besidesthe kurtosis of Cu and Au is greater than that of the normaldistribution (of which the kurtosis value is 3) which resultsin a leptokurtic distribution for Cu and Au Therefore thedistribution of Cu and Au is shown to be skewed to the rightwith leptokurtic characteristics Secondly in order to indicatethe difference between the actual distribution and normaldistribution Q-Q plot can be used for the observation test(Figure 4) The distribution of Cu and Au is also shown to beskewed to the right with posttail characteristics
412 The Stationary Test of the Sample Data The stationarytestmainly inspects the self-correlation of the geological datathe commonmethods of the stationary test are as follows theaugmented Dickey-Fuller (ADF) and sequence correlationanalysis Through the ADF we can obtain the test resultsof the sample data (Table 2) The 119905-statistics of Cu and Auare minus3393498 and minus1319081 respectively which are smallerthan their own 1 significant level Therefore the sequencesof Cu and Au do not have unit roots they are stationarysequencesThe results of the sequence correlation analysis are
6 Mathematical Problems in Engineering
A
D
C
B
Volcaniclastic rocks of neighboring group
Breccia of Majiashan group
Pelitic siltstone of Puqi group
Dolomitic marble of Lower Triassic Jialingjiang Formation
Quartz monzonite diorite porphyry
Diorite
Fracture
Stratigraphic boundary
Unconformity boundary
Structural breccia
Ore bodies and numbers
The first metallogenic region
The second metallogenic region
The third metallogenic region
The fourth metallogenic region
A
B
C
D
K1l
K1l
I
VIVII
IVIII
IIJ3m
J3m
F3
F1
T2p
T2p
T2p
T1minus2j
T1minus2j
T1minus2j
T1minus2j
T1minus2j
T1minus2j
Q25Q25
Q25
Q25
35
35
Figure 3 The pattern of the Jiguanzui Cu-Au mining deposit
Table 2 The ADF test of Cu and Au
Elements ADT (119905-statistic) Test critical values Probability1 level 5 level 10 level
shown in Figure 5 where we can see that the autocorrelationcoefficients (AC) and the partial autocorrelation coefficient(PAC) are not zero and the significance of 119876-states is highso the uncorrelated hypothesis cannot be rejectedThereforethe sequence of the geological data is a stationary time series
Together the results indicate that the data follow astationary sequence and the distributions of Cu and Au haveposttail characteristics indicating that they are abnormallydistributed Therefore we can use the EVT model of thegeological anomaly to identify the anomaly
Mathematical Problems in Engineering 7
4000
3000
2000
1000
0
0 5000 10000 15000 20000
Normal Q-Q plot of Cu
Expe
cted
nor
mal
val
ue
Observed value
minus1000
minus2000
minus3000minus5000
(a)
Expe
cted
nor
mal
val
ue
300
200
100
0
0 500 1000 1500 2000
Normal Q-Q plot of Au
Observed value
minus100
minus200minus500
(b)
Figure 4 The posttail test of the sample data according to Q-Q plot (a) is Q-Q plot test of Cu and (b) is Q-Q plot test of Au
Autocorrelation Partial correlation AC PAC Prob
12345678910
0958 0958 12885 0000
000000000000000000000000
000000000000
087107780695062805760535049604570420
0254
00010055
00650011
235293201938804443484900153015564705940361886
0072
minus0570
minus0026
minus0115
Q-stat
(a)
Autocorrelation Partial correlation AC PAC Prob
123456789
10
0963 13029 0000
000000000000000000000000
000000000000
08860799071606410574051404610413
240543302740230460055069254341573255972661650
0963
0198
0042
00070005
0029
0370
minus0580
minus0044
minus0033
minus0029
Q-stat
(b)
Figure 5The sequence correlation analysis of the sample data (a) is the sequence correlation analysis of Cu and (b) is the sequence correlationanalysis of Au
42 The Solution of the Model
421 Estimate the Parameters and Threshold Through theEVT model of the geological anomaly we can calculate theMEF of Cu and Au and plot the scatter diagram of the MEF(Figure 6) From Figure 6 it is seen that in the interval[7845406 8413659]with Cu and interval [721178 851918]with Au 119864(120583) for Cu and Au follows an approximately lineardistribution These intervals are selected as the thresholdfor Cu and Au As the result of the threshold selectionis subjective modified scale 120573lowast(120583) is used to estimate theaccuracy threshold Based on 120573lowast(120583) if initial threshold value1205830is determined regardless of any threshold 120583 (120583 gt 120583
0)
the shape parameter 120585 and scale parameter 120573 of GPD willnot change Uniformly selecting 50 threshold values from[7845406 8413659] and [721178 851918] respectively wecan obtain the transformation relations between 120573lowast(120583) 120585and the threshold 120583 (120583 gt 120583
0) for Cu and Au using (3) and
(11) see Figures 7 and 8 In order to ensure the accuracyof the EVT the threshold selection is as large as possiblein the permissible range of threshold estimation where thedata show the stationary characteristic (ldquoas discussed by Cao
and Zhang [24]rdquo) From Figures 7 and 8 it is seen that thethreshold of Cu is 8164006 and that of Au is 754736 Afterthe thresholds are determined the parameters of the EVTmodel of the geological anomaly can be estimated using themoment method which reveals that the shape parameter ofCu is 03162 and that of Au is 03342 the scale parameter ofCu is 4409216 and that of Au is 315699 Then inserting thethresholds and parameters into the GPD the distribution ofthe excess threshold of Cu and Au can be obtained by
119865Cu (119909) = 1 minus (1 +03162
4409216
119909)
minus103162
119865Au (119909) = 1 minus (1 +03342
315699
119909)
minus103342
(12)
The distribution of the excess threshold is called theabnormal probability distribution In themineral deposit pre-diction information on the geological data can be describedand expressed by the distribution of the excess threshold
422 The Diagnostic Test of the Model and Identificationof the Anomaly The diagnostic test shows whether the
8 Mathematical Problems in Engineering
0 4000 8000 12000 160000
500
1000
1500
2000
2500
3000
3500
4000
4500E
()
(a)
0 500 1000 1500 20000
50
100
150
200
250
300
350
400
450
500
E(
)
(b)
Figure 6 The scatter diagram of the MEF (a) is the MEF of Cu and (b) is the MEF of Au
780 790 800 810 820 830 840 850410
420
430
440
450
460
470
480
Mod
ified
(a)
780 790 800 810 820 830 840 850
029
0295
03
0305
031
0315
032
0325
033
Mod
ified
(b)
Figure 7 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Cu
72 74 76 78 80 82 84 8622
24
26
28
30
32
34
36
Mod
ified
(a)
72 74 76 78 80 82 84 86
031
032
033
034
035
036
037
038
039
04
Mod
ified
(b)
Figure 8 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Au
Mathematical Problems in Engineering 9
10
10
08
08
06
06
04
04
02
02
0000
Pareto P-P plot of Cu
Observed cum prob
Expe
cted
cum
pro
b
(a)
100806040200Observed cum prob
10
08
06
04
02
00
Expe
cted
cum
pro
b
Pareto P-P plot of Au
(b)
Figure 9 The GPD fitting of the sample data (a) is the distribution fitting of Cu and (b) is the distribution fitting of Au
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ile13429109378164
class
ifica
tion
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
(a)
1002811755
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ilecla
ssifi
catio
n
(b)
Figure 10 The identified anomaly region of Cu and Au (a) is the anomaly region of Cu and (b) is the anomaly region of Au
selection of the thresholds is reasonable Fitting the excessthreshold of the sample data using the GPD (Figure 9)indicates that the excess threshold of the sample data is inthe vicinity of the line the results show that the theoreticaldistribution and actual distribution of the sample data areconsistent Therefore the threshold selection is reasonableThere are currently seven mining drill holes that is KZK10KZK11 KZK23 KZK28 ZK02618 ZK02619 and ZK02620
and the exploitation ore bodies are mostly VII main orebody in the 26 exploration lines of the Cu-Au mining areaGIS technology is used to show the geological anomalyregion with the selection of the thresholds (Figure 10)From Figure 10 it is seen that the anomaly region of Cuand Au is consistent with the range of ore bodies of theactual engineering exploration which has a high indicatingfunction with respect to ore prospecting The results show
10 Mathematical Problems in Engineering
that the EVT model of the geological anomaly is good atmineral deposit prediction and it has good prospectingsignificance
5 Conclusion
In this study the proposed EVT model of the geologicalanomaly was applied to identify geochemical anomaliesassociated with Cu and Au mineralizationThe results of thisstudy led to the following
(1) The characteristics of the geological anomaly and theprinciple of EVT were studied knowledge of the dis-tribution of the EVT coincides with the distributionof the geological anomaly data The designed EVTmodel of the geological anomaly takes full accountof the characteristic of the geological anomaly andthe practical features of the EVT The thresholdselection and parameter estimates of the model weredetermined
(2) The proposed EVT model of the geological anomalywas successfully applied to identify the geologicalanomaly region in the Jiguanzui Cu-Au mining areaThe results show that the anomaly threshold of Cu is8164006 and that of Au is 754736 the shape param-eter of Cu is 03162 and that of Au is 03342 and thescale parameter of Cu is 4409216 and that of the Auis 315699 The abnormal probability distribution wasalso determined Testing the results of the model byfitting the excess threshold of the sample data showedthat the results of the theoretical distribution andactual distribution of the sample data were consistent
(3) The geological anomalies of Cu and Au predictedby the EVT model are consistent with the rangeof ore bodies of the actual engineering explorationThe EVT model has a high indicating function withrespect to ore prospecting and it is applicable for theexploration of mineral deposits
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This study was supported by the GeophysiochemistryProspecting Institute of the Academy of Geological Scienceof China and the Program for the Core of High Spec-trum of Primary Halo Geochemical Prospecting Project (no12120114002001) and the project of the special funds foruniversities was supported by the central governmentmdashtheconstruction of discipline platform inmanagement engineer-ing theory and quantitative methods (no 80000-14Z019002)The authors are grateful to the First Geological Brigade ofthe Hubei Geological Bureau for providing the data Theywould also like to express their appreciation for the teammembers of the Key Laboratory of Mathematical Geology inSichuan China They are grateful to Professor HongJun Liu
at ChengduUniversity of Technology for providing construc-tive advice for this studyThey also thank LetPub (httpwwwletpubcom) for its linguistic assistance during the prepara-tion of this manuscript
References
[1] A Darehshiri M Panji and A R Mokhtari ldquoIdentifyinggeochemical anomalies associated with Cu mineralization instream sediment samples in Gharachaman area northwest ofIranrdquo Journal of African Earth Sciences vol 110 pp 92ndash99 2015
[2] X Lu and P Zhao ldquoGeologic anomaly analysis for space-timedistribution of mineral deposits in the middle-lower Yangtzearea southeastern Chinardquo Nonrenewable Resources vol 17 no3 pp 187ndash196 1998
[3] Z Pengda C Qiuming and X Qinglin ldquoQuantitative predic-tion for deep mineral explorationrdquo Journal of China Universityof Geosciences vol 19 no 4 pp 309ndash318 2008
[4] Q Cheng ldquoSingularity theory and methods for mapping geo-chemical anomalies caused by buried sources and for predictingundiscovered mineral deposits in covered areasrdquo Journal ofGeochemical Exploration vol 122 pp 55ndash70 2012
[5] A P Freedman and B Parsons ldquoGeoid anomalies over twoSouth Atlantic fracture zonesrdquo Earth and Planetary ScienceLetters vol 100 no 1ndash3 pp 18ndash41 1990
[6] P Shen Y Shen T Liu L Meng H Dai and Y YangldquoGeochemical signature of porphyries in the Baogutu porphyrycopper belt western Junggar NW Chinardquo Gondwana Researchvol 16 no 2 pp 227ndash242 2009
[7] J Zhao S Chen and R Zuo ldquoIdentifying geochemical anoma-lies associated with AundashCu mineralization using multifractaland artificial neural network models in the Ningqiang districtShaanxi Chinardquo Journal of Geochemical Exploration vol 164pp 54ndash64 2016
[8] P Zhao J Chen J Chen S Zhang and Y Chen ldquoThelsquothree-componentrsquo digital prospecting method a new approachfor mineral resource quantitative prediction and assessmentrdquoNatural Resources Research vol 14 no 4 pp 295ndash303 2005
[9] Q Cheng and P Zhao ldquoSingularity theories and methodsfor characterizing mineralization processes and mapping geo-anomalies for mineral deposit predictionrdquoGeoscience Frontiersvol 2 no 1 pp 67ndash79 2011
[10] Y Chen P Zhao J Chen and J Liu ldquoApplication of the geo-anomaly unit concept in quantitative delineation and assess-ment of gold ore targets in western Shandong uplift terraineastern ChinardquoNatural Resources Research vol 10 no 1 pp 35ndash49 2001
[11] D E Allen A K Singh and R J Powell ldquoExtreme marketrisk-an extreme value theory approachrdquo Mathematics andComputers in Simulation vol 94 pp 310ndash328 2011
[12] Q Chen and X Lv ldquoThe extreme-value dependence betweenthe crude oil price and Chinese stock marketsrdquo InternationalReview of Economics and Finance vol 39 pp 121ndash132 2015
[13] KWhan J Zscheischler R Orth et al ldquoImpact of soil moistureon extreme maximum temperatures in Europerdquo Weather andClimate Extremes vol 9 pp 57ndash67 2015
[14] D Faranda J M Freitas P Guiraud and S Vaienti ldquoSamplinglocal properties of attractors via extreme value theoryrdquo ChaosSolitons and Fractals vol 74 pp 55ndash66 2015
[15] E Vanem ldquoNon-stationary extreme value models to accountfor trends and shifts in the extreme wave climate due to climatechangerdquo Applied Ocean Research vol 52 pp 201ndash211 2015
Mathematical Problems in Engineering 11
[16] D Rivas F Caleyo A Valor and J M Hallen ldquoExtreme valueanalysis applied to pitting corrosion experiments in low carbonsteel comparison of block maxima and peak over thresholdapproachesrdquo Corrosion Science vol 50 no 11 pp 3193ndash32042008
[17] F Ashkar and S-E El Adlouni ldquoAdjusting for small-samplenon-normality of design event estimators under a generalizedPareto distributionrdquo Journal of Hydrology vol 530 pp 384ndash3912015
[18] J D Castillo and I Serra ldquoLikelihood inference for generalizedPareto distributionrdquo Computational Statistics amp Data Analysisvol 83 pp 116ndash128 2015
[19] A T Ergun and J Jun ldquoTime-varying higher-order conditionalmoments and forecasting intraday VaR and Expected ShortfallrdquoThe Quarterly Review of Economics and Finance vol 50 no 3pp 264ndash272 2010
[20] R Gencay and F Selcuk ldquoExtreme value theory and value-at-risk relative performance in emerging marketsrdquo InternationalJournal of Forecasting vol 20 pp 287ndash303 2004
[21] J H T Kim and J Kim ldquoA parametric alternative to the Hillestimator for heavy-tailed distributionsrdquo Journal of Banking ampFinance vol 54 pp 60ndash71 2015
[22] Z-H Feng Y-M Wei and K Wang ldquoEstimating risk for thecarbon market via extreme value theory an empirical analysisof the EU ETSrdquo Applied Energy vol 99 pp 97ndash108 2012
[23] C-C Lee and C-P Chang ldquoNew evidence on the convergenceof per capita carbon dioxide emissions from panel seeminglyunrelated regressions augmented Dickey-Fuller testsrdquo Energyvol 33 no 9 pp 1468ndash1475 2008
[24] G Cao and M Zhang ldquoExtreme values in the Chinese andAmerican stock markets based on detrended fluctuation anal-ysisrdquo Physica A Statistical Mechanics and its Applications vol436 pp 25ndash35 2015
Figure 1 The standard GPD (a) is the distribution function of the GPD and (b) is the density function of the GPD
[16]rdquo) The BMM divides the sample interval into severalnonoverlapping cells in accordance with the time the lengthand so on Then there is an extreme sequence that isformed by selecting all the maximum values of each smallinterval from the extreme sequence the parent distributioncan be obtained by distribution fitting of the extremal typetheorem However the BMMmodel has a problem that somemaximum values of intervals are greater than those of theother intervals thus the validity of the BMM model is notsatisfactory The defects can be solved by generalized Paretodistribution (GPD) (ldquoas discussed by Ashkar and El Adlouni[17]rdquo) The GPD is a fitting of the observed data which isgreater than a certain threshold
Here 1199091 1199092 119909
119899is a sequence of independent random
variables with a common distribution and 120583 is a sufficientlyhigh threshold If there is positive number 120573 the excessdistribution (119909
119894minus 120583 119894 = 1 2 119899) can be expressed as
119866120585120573(119909) =
1 minus (1 + 120585
119909 minus 120583
120573
)
minus1120585
120585 = 0
1 minus 119890minus(119909minus120583)120573
120585 = 0
(3)
where 120585 is a shape parameter and 120573 is a scale parameter If120585 ge 0 119909 ge 120583 and 120585 lt 0 120583 le 119909 le minus120573120585 + 120583 The sequence(119909119894 119894 = 1 2 119899) obeys the GPD The general formula of
the GPD is given by
119866120585120573(119909) =
1 minus (1 +
120585
120573
119909)
minus1120585
120585 = 0
1 minus 119890minus119909120573
120585 = 0
(4)
Here if 120573 = 1 the expression of the GPD is referred to asthe standard form If 120585 = minus05 05 and 0 then the image ofthe standard distribution function and density distributionfunction of the GPD is as presented in Figure 1 From
Figure 1(a) it is seen that the tail of the GPD thickens as theshape parameter increases Figure 1(b) shows that the densityfunction of the GPD decreases monotonically
TheGPD requires estimates of the parameters and thresh-oldThe shape parameter 120585 and scale parameter 120573 of the GPDcan be estimated by the maximum likelihood function (ldquoasdiscussed by Castillo and Serra [18]rdquo) Taking the derivativeof (4) we can obtain the density function of the GPD
119891120585120573(119909) =
1
120573
(1 + 120585
119909
120573
)
minus1120585minus1
(5)
Taking natural logarithms of both sides of (5) we obtainthe log likelihood function
119871 (120585 120573 119909) = minus119899119871119899120573 minus (
1
120585
+ 1)
119899
sum
119894=1
119871119899(1 +
120585
120573
119909119894) (6)
Taking the partial derivative of 120585 and120573 of (6) respectively thelikelihood equation is as follows
119899 minus (1 minus120585)
sum119899
119894=1119909119894
[120573 +
120585 (119909119894)]
= 0
119899
sum
119894=1
ln[1 +120585 (119909119894)
120573
] minus
119899
sum
119894=1
119909119894
[120573 +
120585 (119909119894)]
= 0
(7)
Thus the maximum likelihood estimate value 120585 of theshape parameter 120585 and the maximum likelihood estimatevalue 120573 of the scale parameter 120573 can be obtained from (7)In addition the shape parameter and scale parameter of theGPDcan be estimated by themomentmethod the estimationresults obtained by the moment method are superior to those
4 Mathematical Problems in Engineering
obtained using the likelihood function (ldquoas discussed byErgun and Jun [19]rdquo) The moment method is given by
120585 =
[1 minus (119905120575)
2
]
2
120573 = 119905 (1 minus
120585)
(8)
where 119905119894= 119909119894minus 120583 ge 0 119905 is the mean value of 119905
119894 and 120575 is
the standard deviation of 119905119894 In the GPDmodel the threshold
selection methods mainly concern the mean excess function(MEF) (ldquoas discussed by Gencay and Selcuk [20]rdquo) and Hillplotting (ldquoas discussed by J H T Kim and J Kim [21]rdquo) Ifrandom variable119883 obeys the GPD the MEF 119864(120583) is given by
For the actual sample data 119864(120583) can be calculated by thefollowing
119864 (120583) =
sum119899
119894=1(119909119894minus 120583)+
119873119899
(10)
where 119899 is the total number of sample data and119873119899is the total
number of sample data that exceed threshold120583 If119909119894ge 120583 (119909
119894minus
120583)+= 119909119894minus120583 or 119909
119894lt 120583 (119909
119894minus120583)+= 0 Then we can plot scatter
diagram (120583 119864(120583)) In the scatter diagram there is sufficientlyhigh threshold 120583 when 119909 gt 120583 119864(120583) is an approximate linearfunction
3 Design the EVT Model ofthe Geological Anomaly
For the actual observational data 119883 = 1199091 1199092 119909
119899 of
the geological anomaly the tail distribution of the geologicalobservational data is called the geological anomalyThereforeif the data are higher than sufficiently high threshold 120583 inthe sample data we can model these data using the GPDThe parameters of the GPD can be estimated by the momentmethod or the likelihood function Threshold 120583 can also becalculated using the MEF or Hill plottingThus the designedEVT model of the geological anomaly is as follows
Step 1 (conditional test) Before using the EVT model ofthe geological anomaly the stationary and posttail of thesample data need to be tested The common method of theconditional test is as follows probability plot and quantile-quantile (Q-Q) plot (ldquoas discussed by Feng et al [22]rdquo)augmented Dickey-Fuller (ADF) test (ldquoas discussed by Leeand Chang [23]rdquo) and so on
Step 2 (estimate the parameters of themodel) For the sampledata use the moment method or likelihood function toestimate shape parameter 120585 and scale parameter120573 of theGPD
Step 3 (determine the threshold) Select different thresholds120583 from the sample data Then we can calculate the MEF ofthe sample data through scatter diagram (120583 119864(120583)) there is
The original geological data
Conditional test The common method of conditional test is as follows P-P plot Q-Q plot and ADF
Estimate the parameters of model
Determine the threshold
Determine the distribution of excess threshold
Diagnostic test of model
Get the threshold of geological anomaly
No
Yes
Figure 2 The chart of the algorithm
sufficiently high threshold 120583 when 119909 gt 120583 and 119864(120583) is anapproximate linear function Here the value 120583 is called thethreshold of the geological anomaly
Step 4 (determine the distribution of the excess threshold)After the threshold and parameters are determined we insertthe threshold and parameters into the GPD to obtain thedistribution of the excess threshold this distribution is calledthe abnormal probability distribution
Step 5 After the distribution of excess threshold is deter-mined a diagnostic test can determine whether the thresholdselection is rational The diagnostic test of the model mainlytests the consistency between the theoretical distribution andthe actual distribution especially the fitting degree of theactual data and the model distribution The methods weusually use are the Q-Q plot and probability plot If the testeffect is not satisfactory repeat Step 3 and determine the newreasonable threshold The chart of the EVT model of thegeological anomaly is shown in Figure 2
In this study the determination of threshold 120583 in theEVT model is critical If the selection of the threshold valueis higher the number of samples that exceed the thresholdvalue is lower and the parameters of the GPD are verysensitive to the high values of the observational data whichwill cause errors in the parameter estimation Converselythe selection of a threshold value that is low will increasethe number of observations increasing the accuracy of theestimation of the parameters but the excess data 119909
119894minus 120583 do
not obey the GPD distribution At present there is no clearmethod to select the accuracy threshold The MEF can beused to estimate the threshold with some defects in whichthe selection of the threshold is usually an interval value andnot an accurate constantTherefore this paper provides a newmethod to increase the accuracywithwhich the threshold canbe selected In the GPD when the initial threshold value 120583
0
Mathematical Problems in Engineering 5
Table 1 The basic statistics of Cu and Au
Elements Mean Minimum Maximum Std dev CV Skewness KurtosisCu 64144 5326 1720277 72765 113 738 10696Au 7082 713 187797 025 082 842 15493
is determined the excess data 119909119894minus1205830approximately obey the
GPD distribution Regardless of any threshold 120583 (120583 gt 1205830)
the shape parameter 120585 and scale parameter 120573 of the GPDshould remain unchanged Therefore information can beobtained on the transformation relationship between 120573(120583)and threshold 120583 (120583 gt 120583
0) from (3)
120573 (120583) = 120573 (1205830) + 120585 (120583 minus 120583
0) (11)
Let 120573lowast(120583) = 120573(1205830)+120585(120583minus120583
0) 120573lowast(120583) is called themodified
scale and the values of 120573lowast(120583)will not change when threshold120583 changes Therefore when the interval threshold value isdetermined byMEF the accuracy threshold can be estimatedby 120573lowast(120583) Estimating the threshold using 120573lowast(120583) is detailed inSection 42
In this paper the EVT model of the geological anomalytakes full account of the characteristic of the geologicalanomaly distribution and the practical features of the EVTRelative to the geological background value the anomaly andextreme value can be used to describe the geological anomalyThe observations of the geological anomaly are located in thetail of the samples which are related to the random charactersin the process of quantification at the very large or smalllevel and estimate the probability of the extreme event inthe existing observation levelsmdashthese characteristics are alsothe contents of the EVT The EVT is a branch of statisticsthat studies the limiting distribution of the minimum andmaximum value and evaluates the risk of extreme eventsTherefore the mathematical foundation of the geologicalanomaly is described by the EVT On the one hand the EVTdescribes the characteristic of the geological anomaly distri-bution from the perspective of mathematics the results from(3) show the distribution of the sample data which is provedin (12) On the other hand the EVT provides a quantitativeand digital research method for predicting and evaluatingthe mineral resources which is proved in Figure 10 Besidesthis paper also discusses the methods of estimate parametersand the threshold of the EVT Consequently a mathematicalstatisticalmodel is established for quantitative geological dataand geology information where the data exceed the thresholdof the sample in (12) Therefore the ability of the EVT modelto identify the geological anomaly is feasible
4 The Model Application in Identifyingthe Geological Anomaly of the JiguanzuiCu-Au Mining Area
In order to show the effect of identifying the anomaly usingthe EVT model with geological anomaly recognition themodel was applied to identify the anomaly in an actualmining area The study data with Cu and Au originate from26 exploration lines of the Jiguanzui Cu-Au mining area inHubei China The count of the sample data with Cu and Au
is 14309 The Jiguanzui Cu-Au mining deposit is the blinddeposits at the lower part of the Quaternary overburdenlayer Currently I II III and VII main ore body groups 14main ore bodies and 105 small fragmentary ore bodies havebeen identified in the mining area The main ore bodies ofthe Jiguanzui Cu-Au mining area are distributed in the 013to 034 lines which are 950 meters long the width is 160ndash800 meters the elevation ranges from minus5m to minus1412m deepextension and the level projection area of the ore bodies is058 square kilometers The overall distribution of the orebodies is northeast 30∘ the trend of the ore bodies is northeast15∘ndash72∘ and the local trend of the ore bodies is northwest I IIIII andVII ore bodies are arranged in the form of an echelonin which the tendency is northwest and the local tendency issouthThemain ore bodies occur in the fault basin at the edgeof the northwestern rock body of the Tonglushan near thecontact zone of the dolomitic marble the quartz monzonitediorite porphyry and quartz diorite in the Lower TriassicJialingjiang Formation and near the different lithology andthe echelon fracture of dolomitic marble The pattern of theJiguanzui Cu-Au mining deposit is shown in Figure 3
41 The Condition Test of the Model
411 The Posttail Test of Sample Data Firstly this paperanalyses the basic statistics of the Cu and Au elements andthe results are shown in Table 1 From Table 1 we can see thatthe skewness of the sample data is greater than zero and thesample data are not normally distributed that is distributedto the right By observing the coefficient of variation it is seenthat the coefficient of variation of Au is smaller than that ofCu and the stability of Au is higher than that of Cu Besidesthe kurtosis of Cu and Au is greater than that of the normaldistribution (of which the kurtosis value is 3) which resultsin a leptokurtic distribution for Cu and Au Therefore thedistribution of Cu and Au is shown to be skewed to the rightwith leptokurtic characteristics Secondly in order to indicatethe difference between the actual distribution and normaldistribution Q-Q plot can be used for the observation test(Figure 4) The distribution of Cu and Au is also shown to beskewed to the right with posttail characteristics
412 The Stationary Test of the Sample Data The stationarytestmainly inspects the self-correlation of the geological datathe commonmethods of the stationary test are as follows theaugmented Dickey-Fuller (ADF) and sequence correlationanalysis Through the ADF we can obtain the test resultsof the sample data (Table 2) The 119905-statistics of Cu and Auare minus3393498 and minus1319081 respectively which are smallerthan their own 1 significant level Therefore the sequencesof Cu and Au do not have unit roots they are stationarysequencesThe results of the sequence correlation analysis are
6 Mathematical Problems in Engineering
A
D
C
B
Volcaniclastic rocks of neighboring group
Breccia of Majiashan group
Pelitic siltstone of Puqi group
Dolomitic marble of Lower Triassic Jialingjiang Formation
Quartz monzonite diorite porphyry
Diorite
Fracture
Stratigraphic boundary
Unconformity boundary
Structural breccia
Ore bodies and numbers
The first metallogenic region
The second metallogenic region
The third metallogenic region
The fourth metallogenic region
A
B
C
D
K1l
K1l
I
VIVII
IVIII
IIJ3m
J3m
F3
F1
T2p
T2p
T2p
T1minus2j
T1minus2j
T1minus2j
T1minus2j
T1minus2j
T1minus2j
Q25Q25
Q25
Q25
35
35
Figure 3 The pattern of the Jiguanzui Cu-Au mining deposit
Table 2 The ADF test of Cu and Au
Elements ADT (119905-statistic) Test critical values Probability1 level 5 level 10 level
shown in Figure 5 where we can see that the autocorrelationcoefficients (AC) and the partial autocorrelation coefficient(PAC) are not zero and the significance of 119876-states is highso the uncorrelated hypothesis cannot be rejectedThereforethe sequence of the geological data is a stationary time series
Together the results indicate that the data follow astationary sequence and the distributions of Cu and Au haveposttail characteristics indicating that they are abnormallydistributed Therefore we can use the EVT model of thegeological anomaly to identify the anomaly
Mathematical Problems in Engineering 7
4000
3000
2000
1000
0
0 5000 10000 15000 20000
Normal Q-Q plot of Cu
Expe
cted
nor
mal
val
ue
Observed value
minus1000
minus2000
minus3000minus5000
(a)
Expe
cted
nor
mal
val
ue
300
200
100
0
0 500 1000 1500 2000
Normal Q-Q plot of Au
Observed value
minus100
minus200minus500
(b)
Figure 4 The posttail test of the sample data according to Q-Q plot (a) is Q-Q plot test of Cu and (b) is Q-Q plot test of Au
Autocorrelation Partial correlation AC PAC Prob
12345678910
0958 0958 12885 0000
000000000000000000000000
000000000000
087107780695062805760535049604570420
0254
00010055
00650011
235293201938804443484900153015564705940361886
0072
minus0570
minus0026
minus0115
Q-stat
(a)
Autocorrelation Partial correlation AC PAC Prob
123456789
10
0963 13029 0000
000000000000000000000000
000000000000
08860799071606410574051404610413
240543302740230460055069254341573255972661650
0963
0198
0042
00070005
0029
0370
minus0580
minus0044
minus0033
minus0029
Q-stat
(b)
Figure 5The sequence correlation analysis of the sample data (a) is the sequence correlation analysis of Cu and (b) is the sequence correlationanalysis of Au
42 The Solution of the Model
421 Estimate the Parameters and Threshold Through theEVT model of the geological anomaly we can calculate theMEF of Cu and Au and plot the scatter diagram of the MEF(Figure 6) From Figure 6 it is seen that in the interval[7845406 8413659]with Cu and interval [721178 851918]with Au 119864(120583) for Cu and Au follows an approximately lineardistribution These intervals are selected as the thresholdfor Cu and Au As the result of the threshold selectionis subjective modified scale 120573lowast(120583) is used to estimate theaccuracy threshold Based on 120573lowast(120583) if initial threshold value1205830is determined regardless of any threshold 120583 (120583 gt 120583
0)
the shape parameter 120585 and scale parameter 120573 of GPD willnot change Uniformly selecting 50 threshold values from[7845406 8413659] and [721178 851918] respectively wecan obtain the transformation relations between 120573lowast(120583) 120585and the threshold 120583 (120583 gt 120583
0) for Cu and Au using (3) and
(11) see Figures 7 and 8 In order to ensure the accuracyof the EVT the threshold selection is as large as possiblein the permissible range of threshold estimation where thedata show the stationary characteristic (ldquoas discussed by Cao
and Zhang [24]rdquo) From Figures 7 and 8 it is seen that thethreshold of Cu is 8164006 and that of Au is 754736 Afterthe thresholds are determined the parameters of the EVTmodel of the geological anomaly can be estimated using themoment method which reveals that the shape parameter ofCu is 03162 and that of Au is 03342 the scale parameter ofCu is 4409216 and that of Au is 315699 Then inserting thethresholds and parameters into the GPD the distribution ofthe excess threshold of Cu and Au can be obtained by
119865Cu (119909) = 1 minus (1 +03162
4409216
119909)
minus103162
119865Au (119909) = 1 minus (1 +03342
315699
119909)
minus103342
(12)
The distribution of the excess threshold is called theabnormal probability distribution In themineral deposit pre-diction information on the geological data can be describedand expressed by the distribution of the excess threshold
422 The Diagnostic Test of the Model and Identificationof the Anomaly The diagnostic test shows whether the
8 Mathematical Problems in Engineering
0 4000 8000 12000 160000
500
1000
1500
2000
2500
3000
3500
4000
4500E
()
(a)
0 500 1000 1500 20000
50
100
150
200
250
300
350
400
450
500
E(
)
(b)
Figure 6 The scatter diagram of the MEF (a) is the MEF of Cu and (b) is the MEF of Au
780 790 800 810 820 830 840 850410
420
430
440
450
460
470
480
Mod
ified
(a)
780 790 800 810 820 830 840 850
029
0295
03
0305
031
0315
032
0325
033
Mod
ified
(b)
Figure 7 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Cu
72 74 76 78 80 82 84 8622
24
26
28
30
32
34
36
Mod
ified
(a)
72 74 76 78 80 82 84 86
031
032
033
034
035
036
037
038
039
04
Mod
ified
(b)
Figure 8 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Au
Mathematical Problems in Engineering 9
10
10
08
08
06
06
04
04
02
02
0000
Pareto P-P plot of Cu
Observed cum prob
Expe
cted
cum
pro
b
(a)
100806040200Observed cum prob
10
08
06
04
02
00
Expe
cted
cum
pro
b
Pareto P-P plot of Au
(b)
Figure 9 The GPD fitting of the sample data (a) is the distribution fitting of Cu and (b) is the distribution fitting of Au
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ile13429109378164
class
ifica
tion
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
(a)
1002811755
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ilecla
ssifi
catio
n
(b)
Figure 10 The identified anomaly region of Cu and Au (a) is the anomaly region of Cu and (b) is the anomaly region of Au
selection of the thresholds is reasonable Fitting the excessthreshold of the sample data using the GPD (Figure 9)indicates that the excess threshold of the sample data is inthe vicinity of the line the results show that the theoreticaldistribution and actual distribution of the sample data areconsistent Therefore the threshold selection is reasonableThere are currently seven mining drill holes that is KZK10KZK11 KZK23 KZK28 ZK02618 ZK02619 and ZK02620
and the exploitation ore bodies are mostly VII main orebody in the 26 exploration lines of the Cu-Au mining areaGIS technology is used to show the geological anomalyregion with the selection of the thresholds (Figure 10)From Figure 10 it is seen that the anomaly region of Cuand Au is consistent with the range of ore bodies of theactual engineering exploration which has a high indicatingfunction with respect to ore prospecting The results show
10 Mathematical Problems in Engineering
that the EVT model of the geological anomaly is good atmineral deposit prediction and it has good prospectingsignificance
5 Conclusion
In this study the proposed EVT model of the geologicalanomaly was applied to identify geochemical anomaliesassociated with Cu and Au mineralizationThe results of thisstudy led to the following
(1) The characteristics of the geological anomaly and theprinciple of EVT were studied knowledge of the dis-tribution of the EVT coincides with the distributionof the geological anomaly data The designed EVTmodel of the geological anomaly takes full accountof the characteristic of the geological anomaly andthe practical features of the EVT The thresholdselection and parameter estimates of the model weredetermined
(2) The proposed EVT model of the geological anomalywas successfully applied to identify the geologicalanomaly region in the Jiguanzui Cu-Au mining areaThe results show that the anomaly threshold of Cu is8164006 and that of Au is 754736 the shape param-eter of Cu is 03162 and that of Au is 03342 and thescale parameter of Cu is 4409216 and that of the Auis 315699 The abnormal probability distribution wasalso determined Testing the results of the model byfitting the excess threshold of the sample data showedthat the results of the theoretical distribution andactual distribution of the sample data were consistent
(3) The geological anomalies of Cu and Au predictedby the EVT model are consistent with the rangeof ore bodies of the actual engineering explorationThe EVT model has a high indicating function withrespect to ore prospecting and it is applicable for theexploration of mineral deposits
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This study was supported by the GeophysiochemistryProspecting Institute of the Academy of Geological Scienceof China and the Program for the Core of High Spec-trum of Primary Halo Geochemical Prospecting Project (no12120114002001) and the project of the special funds foruniversities was supported by the central governmentmdashtheconstruction of discipline platform inmanagement engineer-ing theory and quantitative methods (no 80000-14Z019002)The authors are grateful to the First Geological Brigade ofthe Hubei Geological Bureau for providing the data Theywould also like to express their appreciation for the teammembers of the Key Laboratory of Mathematical Geology inSichuan China They are grateful to Professor HongJun Liu
at ChengduUniversity of Technology for providing construc-tive advice for this studyThey also thank LetPub (httpwwwletpubcom) for its linguistic assistance during the prepara-tion of this manuscript
References
[1] A Darehshiri M Panji and A R Mokhtari ldquoIdentifyinggeochemical anomalies associated with Cu mineralization instream sediment samples in Gharachaman area northwest ofIranrdquo Journal of African Earth Sciences vol 110 pp 92ndash99 2015
[2] X Lu and P Zhao ldquoGeologic anomaly analysis for space-timedistribution of mineral deposits in the middle-lower Yangtzearea southeastern Chinardquo Nonrenewable Resources vol 17 no3 pp 187ndash196 1998
[3] Z Pengda C Qiuming and X Qinglin ldquoQuantitative predic-tion for deep mineral explorationrdquo Journal of China Universityof Geosciences vol 19 no 4 pp 309ndash318 2008
[4] Q Cheng ldquoSingularity theory and methods for mapping geo-chemical anomalies caused by buried sources and for predictingundiscovered mineral deposits in covered areasrdquo Journal ofGeochemical Exploration vol 122 pp 55ndash70 2012
[5] A P Freedman and B Parsons ldquoGeoid anomalies over twoSouth Atlantic fracture zonesrdquo Earth and Planetary ScienceLetters vol 100 no 1ndash3 pp 18ndash41 1990
[6] P Shen Y Shen T Liu L Meng H Dai and Y YangldquoGeochemical signature of porphyries in the Baogutu porphyrycopper belt western Junggar NW Chinardquo Gondwana Researchvol 16 no 2 pp 227ndash242 2009
[7] J Zhao S Chen and R Zuo ldquoIdentifying geochemical anoma-lies associated with AundashCu mineralization using multifractaland artificial neural network models in the Ningqiang districtShaanxi Chinardquo Journal of Geochemical Exploration vol 164pp 54ndash64 2016
[8] P Zhao J Chen J Chen S Zhang and Y Chen ldquoThelsquothree-componentrsquo digital prospecting method a new approachfor mineral resource quantitative prediction and assessmentrdquoNatural Resources Research vol 14 no 4 pp 295ndash303 2005
[9] Q Cheng and P Zhao ldquoSingularity theories and methodsfor characterizing mineralization processes and mapping geo-anomalies for mineral deposit predictionrdquoGeoscience Frontiersvol 2 no 1 pp 67ndash79 2011
[10] Y Chen P Zhao J Chen and J Liu ldquoApplication of the geo-anomaly unit concept in quantitative delineation and assess-ment of gold ore targets in western Shandong uplift terraineastern ChinardquoNatural Resources Research vol 10 no 1 pp 35ndash49 2001
[11] D E Allen A K Singh and R J Powell ldquoExtreme marketrisk-an extreme value theory approachrdquo Mathematics andComputers in Simulation vol 94 pp 310ndash328 2011
[12] Q Chen and X Lv ldquoThe extreme-value dependence betweenthe crude oil price and Chinese stock marketsrdquo InternationalReview of Economics and Finance vol 39 pp 121ndash132 2015
[13] KWhan J Zscheischler R Orth et al ldquoImpact of soil moistureon extreme maximum temperatures in Europerdquo Weather andClimate Extremes vol 9 pp 57ndash67 2015
[14] D Faranda J M Freitas P Guiraud and S Vaienti ldquoSamplinglocal properties of attractors via extreme value theoryrdquo ChaosSolitons and Fractals vol 74 pp 55ndash66 2015
[15] E Vanem ldquoNon-stationary extreme value models to accountfor trends and shifts in the extreme wave climate due to climatechangerdquo Applied Ocean Research vol 52 pp 201ndash211 2015
Mathematical Problems in Engineering 11
[16] D Rivas F Caleyo A Valor and J M Hallen ldquoExtreme valueanalysis applied to pitting corrosion experiments in low carbonsteel comparison of block maxima and peak over thresholdapproachesrdquo Corrosion Science vol 50 no 11 pp 3193ndash32042008
[17] F Ashkar and S-E El Adlouni ldquoAdjusting for small-samplenon-normality of design event estimators under a generalizedPareto distributionrdquo Journal of Hydrology vol 530 pp 384ndash3912015
[18] J D Castillo and I Serra ldquoLikelihood inference for generalizedPareto distributionrdquo Computational Statistics amp Data Analysisvol 83 pp 116ndash128 2015
[19] A T Ergun and J Jun ldquoTime-varying higher-order conditionalmoments and forecasting intraday VaR and Expected ShortfallrdquoThe Quarterly Review of Economics and Finance vol 50 no 3pp 264ndash272 2010
[20] R Gencay and F Selcuk ldquoExtreme value theory and value-at-risk relative performance in emerging marketsrdquo InternationalJournal of Forecasting vol 20 pp 287ndash303 2004
[21] J H T Kim and J Kim ldquoA parametric alternative to the Hillestimator for heavy-tailed distributionsrdquo Journal of Banking ampFinance vol 54 pp 60ndash71 2015
[22] Z-H Feng Y-M Wei and K Wang ldquoEstimating risk for thecarbon market via extreme value theory an empirical analysisof the EU ETSrdquo Applied Energy vol 99 pp 97ndash108 2012
[23] C-C Lee and C-P Chang ldquoNew evidence on the convergenceof per capita carbon dioxide emissions from panel seeminglyunrelated regressions augmented Dickey-Fuller testsrdquo Energyvol 33 no 9 pp 1468ndash1475 2008
[24] G Cao and M Zhang ldquoExtreme values in the Chinese andAmerican stock markets based on detrended fluctuation anal-ysisrdquo Physica A Statistical Mechanics and its Applications vol436 pp 25ndash35 2015
obtained using the likelihood function (ldquoas discussed byErgun and Jun [19]rdquo) The moment method is given by
120585 =
[1 minus (119905120575)
2
]
2
120573 = 119905 (1 minus
120585)
(8)
where 119905119894= 119909119894minus 120583 ge 0 119905 is the mean value of 119905
119894 and 120575 is
the standard deviation of 119905119894 In the GPDmodel the threshold
selection methods mainly concern the mean excess function(MEF) (ldquoas discussed by Gencay and Selcuk [20]rdquo) and Hillplotting (ldquoas discussed by J H T Kim and J Kim [21]rdquo) Ifrandom variable119883 obeys the GPD the MEF 119864(120583) is given by
For the actual sample data 119864(120583) can be calculated by thefollowing
119864 (120583) =
sum119899
119894=1(119909119894minus 120583)+
119873119899
(10)
where 119899 is the total number of sample data and119873119899is the total
number of sample data that exceed threshold120583 If119909119894ge 120583 (119909
119894minus
120583)+= 119909119894minus120583 or 119909
119894lt 120583 (119909
119894minus120583)+= 0 Then we can plot scatter
diagram (120583 119864(120583)) In the scatter diagram there is sufficientlyhigh threshold 120583 when 119909 gt 120583 119864(120583) is an approximate linearfunction
3 Design the EVT Model ofthe Geological Anomaly
For the actual observational data 119883 = 1199091 1199092 119909
119899 of
the geological anomaly the tail distribution of the geologicalobservational data is called the geological anomalyThereforeif the data are higher than sufficiently high threshold 120583 inthe sample data we can model these data using the GPDThe parameters of the GPD can be estimated by the momentmethod or the likelihood function Threshold 120583 can also becalculated using the MEF or Hill plottingThus the designedEVT model of the geological anomaly is as follows
Step 1 (conditional test) Before using the EVT model ofthe geological anomaly the stationary and posttail of thesample data need to be tested The common method of theconditional test is as follows probability plot and quantile-quantile (Q-Q) plot (ldquoas discussed by Feng et al [22]rdquo)augmented Dickey-Fuller (ADF) test (ldquoas discussed by Leeand Chang [23]rdquo) and so on
Step 2 (estimate the parameters of themodel) For the sampledata use the moment method or likelihood function toestimate shape parameter 120585 and scale parameter120573 of theGPD
Step 3 (determine the threshold) Select different thresholds120583 from the sample data Then we can calculate the MEF ofthe sample data through scatter diagram (120583 119864(120583)) there is
The original geological data
Conditional test The common method of conditional test is as follows P-P plot Q-Q plot and ADF
Estimate the parameters of model
Determine the threshold
Determine the distribution of excess threshold
Diagnostic test of model
Get the threshold of geological anomaly
No
Yes
Figure 2 The chart of the algorithm
sufficiently high threshold 120583 when 119909 gt 120583 and 119864(120583) is anapproximate linear function Here the value 120583 is called thethreshold of the geological anomaly
Step 4 (determine the distribution of the excess threshold)After the threshold and parameters are determined we insertthe threshold and parameters into the GPD to obtain thedistribution of the excess threshold this distribution is calledthe abnormal probability distribution
Step 5 After the distribution of excess threshold is deter-mined a diagnostic test can determine whether the thresholdselection is rational The diagnostic test of the model mainlytests the consistency between the theoretical distribution andthe actual distribution especially the fitting degree of theactual data and the model distribution The methods weusually use are the Q-Q plot and probability plot If the testeffect is not satisfactory repeat Step 3 and determine the newreasonable threshold The chart of the EVT model of thegeological anomaly is shown in Figure 2
In this study the determination of threshold 120583 in theEVT model is critical If the selection of the threshold valueis higher the number of samples that exceed the thresholdvalue is lower and the parameters of the GPD are verysensitive to the high values of the observational data whichwill cause errors in the parameter estimation Converselythe selection of a threshold value that is low will increasethe number of observations increasing the accuracy of theestimation of the parameters but the excess data 119909
119894minus 120583 do
not obey the GPD distribution At present there is no clearmethod to select the accuracy threshold The MEF can beused to estimate the threshold with some defects in whichthe selection of the threshold is usually an interval value andnot an accurate constantTherefore this paper provides a newmethod to increase the accuracywithwhich the threshold canbe selected In the GPD when the initial threshold value 120583
0
Mathematical Problems in Engineering 5
Table 1 The basic statistics of Cu and Au
Elements Mean Minimum Maximum Std dev CV Skewness KurtosisCu 64144 5326 1720277 72765 113 738 10696Au 7082 713 187797 025 082 842 15493
is determined the excess data 119909119894minus1205830approximately obey the
GPD distribution Regardless of any threshold 120583 (120583 gt 1205830)
the shape parameter 120585 and scale parameter 120573 of the GPDshould remain unchanged Therefore information can beobtained on the transformation relationship between 120573(120583)and threshold 120583 (120583 gt 120583
0) from (3)
120573 (120583) = 120573 (1205830) + 120585 (120583 minus 120583
0) (11)
Let 120573lowast(120583) = 120573(1205830)+120585(120583minus120583
0) 120573lowast(120583) is called themodified
scale and the values of 120573lowast(120583)will not change when threshold120583 changes Therefore when the interval threshold value isdetermined byMEF the accuracy threshold can be estimatedby 120573lowast(120583) Estimating the threshold using 120573lowast(120583) is detailed inSection 42
In this paper the EVT model of the geological anomalytakes full account of the characteristic of the geologicalanomaly distribution and the practical features of the EVTRelative to the geological background value the anomaly andextreme value can be used to describe the geological anomalyThe observations of the geological anomaly are located in thetail of the samples which are related to the random charactersin the process of quantification at the very large or smalllevel and estimate the probability of the extreme event inthe existing observation levelsmdashthese characteristics are alsothe contents of the EVT The EVT is a branch of statisticsthat studies the limiting distribution of the minimum andmaximum value and evaluates the risk of extreme eventsTherefore the mathematical foundation of the geologicalanomaly is described by the EVT On the one hand the EVTdescribes the characteristic of the geological anomaly distri-bution from the perspective of mathematics the results from(3) show the distribution of the sample data which is provedin (12) On the other hand the EVT provides a quantitativeand digital research method for predicting and evaluatingthe mineral resources which is proved in Figure 10 Besidesthis paper also discusses the methods of estimate parametersand the threshold of the EVT Consequently a mathematicalstatisticalmodel is established for quantitative geological dataand geology information where the data exceed the thresholdof the sample in (12) Therefore the ability of the EVT modelto identify the geological anomaly is feasible
4 The Model Application in Identifyingthe Geological Anomaly of the JiguanzuiCu-Au Mining Area
In order to show the effect of identifying the anomaly usingthe EVT model with geological anomaly recognition themodel was applied to identify the anomaly in an actualmining area The study data with Cu and Au originate from26 exploration lines of the Jiguanzui Cu-Au mining area inHubei China The count of the sample data with Cu and Au
is 14309 The Jiguanzui Cu-Au mining deposit is the blinddeposits at the lower part of the Quaternary overburdenlayer Currently I II III and VII main ore body groups 14main ore bodies and 105 small fragmentary ore bodies havebeen identified in the mining area The main ore bodies ofthe Jiguanzui Cu-Au mining area are distributed in the 013to 034 lines which are 950 meters long the width is 160ndash800 meters the elevation ranges from minus5m to minus1412m deepextension and the level projection area of the ore bodies is058 square kilometers The overall distribution of the orebodies is northeast 30∘ the trend of the ore bodies is northeast15∘ndash72∘ and the local trend of the ore bodies is northwest I IIIII andVII ore bodies are arranged in the form of an echelonin which the tendency is northwest and the local tendency issouthThemain ore bodies occur in the fault basin at the edgeof the northwestern rock body of the Tonglushan near thecontact zone of the dolomitic marble the quartz monzonitediorite porphyry and quartz diorite in the Lower TriassicJialingjiang Formation and near the different lithology andthe echelon fracture of dolomitic marble The pattern of theJiguanzui Cu-Au mining deposit is shown in Figure 3
41 The Condition Test of the Model
411 The Posttail Test of Sample Data Firstly this paperanalyses the basic statistics of the Cu and Au elements andthe results are shown in Table 1 From Table 1 we can see thatthe skewness of the sample data is greater than zero and thesample data are not normally distributed that is distributedto the right By observing the coefficient of variation it is seenthat the coefficient of variation of Au is smaller than that ofCu and the stability of Au is higher than that of Cu Besidesthe kurtosis of Cu and Au is greater than that of the normaldistribution (of which the kurtosis value is 3) which resultsin a leptokurtic distribution for Cu and Au Therefore thedistribution of Cu and Au is shown to be skewed to the rightwith leptokurtic characteristics Secondly in order to indicatethe difference between the actual distribution and normaldistribution Q-Q plot can be used for the observation test(Figure 4) The distribution of Cu and Au is also shown to beskewed to the right with posttail characteristics
412 The Stationary Test of the Sample Data The stationarytestmainly inspects the self-correlation of the geological datathe commonmethods of the stationary test are as follows theaugmented Dickey-Fuller (ADF) and sequence correlationanalysis Through the ADF we can obtain the test resultsof the sample data (Table 2) The 119905-statistics of Cu and Auare minus3393498 and minus1319081 respectively which are smallerthan their own 1 significant level Therefore the sequencesof Cu and Au do not have unit roots they are stationarysequencesThe results of the sequence correlation analysis are
6 Mathematical Problems in Engineering
A
D
C
B
Volcaniclastic rocks of neighboring group
Breccia of Majiashan group
Pelitic siltstone of Puqi group
Dolomitic marble of Lower Triassic Jialingjiang Formation
Quartz monzonite diorite porphyry
Diorite
Fracture
Stratigraphic boundary
Unconformity boundary
Structural breccia
Ore bodies and numbers
The first metallogenic region
The second metallogenic region
The third metallogenic region
The fourth metallogenic region
A
B
C
D
K1l
K1l
I
VIVII
IVIII
IIJ3m
J3m
F3
F1
T2p
T2p
T2p
T1minus2j
T1minus2j
T1minus2j
T1minus2j
T1minus2j
T1minus2j
Q25Q25
Q25
Q25
35
35
Figure 3 The pattern of the Jiguanzui Cu-Au mining deposit
Table 2 The ADF test of Cu and Au
Elements ADT (119905-statistic) Test critical values Probability1 level 5 level 10 level
shown in Figure 5 where we can see that the autocorrelationcoefficients (AC) and the partial autocorrelation coefficient(PAC) are not zero and the significance of 119876-states is highso the uncorrelated hypothesis cannot be rejectedThereforethe sequence of the geological data is a stationary time series
Together the results indicate that the data follow astationary sequence and the distributions of Cu and Au haveposttail characteristics indicating that they are abnormallydistributed Therefore we can use the EVT model of thegeological anomaly to identify the anomaly
Mathematical Problems in Engineering 7
4000
3000
2000
1000
0
0 5000 10000 15000 20000
Normal Q-Q plot of Cu
Expe
cted
nor
mal
val
ue
Observed value
minus1000
minus2000
minus3000minus5000
(a)
Expe
cted
nor
mal
val
ue
300
200
100
0
0 500 1000 1500 2000
Normal Q-Q plot of Au
Observed value
minus100
minus200minus500
(b)
Figure 4 The posttail test of the sample data according to Q-Q plot (a) is Q-Q plot test of Cu and (b) is Q-Q plot test of Au
Autocorrelation Partial correlation AC PAC Prob
12345678910
0958 0958 12885 0000
000000000000000000000000
000000000000
087107780695062805760535049604570420
0254
00010055
00650011
235293201938804443484900153015564705940361886
0072
minus0570
minus0026
minus0115
Q-stat
(a)
Autocorrelation Partial correlation AC PAC Prob
123456789
10
0963 13029 0000
000000000000000000000000
000000000000
08860799071606410574051404610413
240543302740230460055069254341573255972661650
0963
0198
0042
00070005
0029
0370
minus0580
minus0044
minus0033
minus0029
Q-stat
(b)
Figure 5The sequence correlation analysis of the sample data (a) is the sequence correlation analysis of Cu and (b) is the sequence correlationanalysis of Au
42 The Solution of the Model
421 Estimate the Parameters and Threshold Through theEVT model of the geological anomaly we can calculate theMEF of Cu and Au and plot the scatter diagram of the MEF(Figure 6) From Figure 6 it is seen that in the interval[7845406 8413659]with Cu and interval [721178 851918]with Au 119864(120583) for Cu and Au follows an approximately lineardistribution These intervals are selected as the thresholdfor Cu and Au As the result of the threshold selectionis subjective modified scale 120573lowast(120583) is used to estimate theaccuracy threshold Based on 120573lowast(120583) if initial threshold value1205830is determined regardless of any threshold 120583 (120583 gt 120583
0)
the shape parameter 120585 and scale parameter 120573 of GPD willnot change Uniformly selecting 50 threshold values from[7845406 8413659] and [721178 851918] respectively wecan obtain the transformation relations between 120573lowast(120583) 120585and the threshold 120583 (120583 gt 120583
0) for Cu and Au using (3) and
(11) see Figures 7 and 8 In order to ensure the accuracyof the EVT the threshold selection is as large as possiblein the permissible range of threshold estimation where thedata show the stationary characteristic (ldquoas discussed by Cao
and Zhang [24]rdquo) From Figures 7 and 8 it is seen that thethreshold of Cu is 8164006 and that of Au is 754736 Afterthe thresholds are determined the parameters of the EVTmodel of the geological anomaly can be estimated using themoment method which reveals that the shape parameter ofCu is 03162 and that of Au is 03342 the scale parameter ofCu is 4409216 and that of Au is 315699 Then inserting thethresholds and parameters into the GPD the distribution ofthe excess threshold of Cu and Au can be obtained by
119865Cu (119909) = 1 minus (1 +03162
4409216
119909)
minus103162
119865Au (119909) = 1 minus (1 +03342
315699
119909)
minus103342
(12)
The distribution of the excess threshold is called theabnormal probability distribution In themineral deposit pre-diction information on the geological data can be describedand expressed by the distribution of the excess threshold
422 The Diagnostic Test of the Model and Identificationof the Anomaly The diagnostic test shows whether the
8 Mathematical Problems in Engineering
0 4000 8000 12000 160000
500
1000
1500
2000
2500
3000
3500
4000
4500E
()
(a)
0 500 1000 1500 20000
50
100
150
200
250
300
350
400
450
500
E(
)
(b)
Figure 6 The scatter diagram of the MEF (a) is the MEF of Cu and (b) is the MEF of Au
780 790 800 810 820 830 840 850410
420
430
440
450
460
470
480
Mod
ified
(a)
780 790 800 810 820 830 840 850
029
0295
03
0305
031
0315
032
0325
033
Mod
ified
(b)
Figure 7 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Cu
72 74 76 78 80 82 84 8622
24
26
28
30
32
34
36
Mod
ified
(a)
72 74 76 78 80 82 84 86
031
032
033
034
035
036
037
038
039
04
Mod
ified
(b)
Figure 8 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Au
Mathematical Problems in Engineering 9
10
10
08
08
06
06
04
04
02
02
0000
Pareto P-P plot of Cu
Observed cum prob
Expe
cted
cum
pro
b
(a)
100806040200Observed cum prob
10
08
06
04
02
00
Expe
cted
cum
pro
b
Pareto P-P plot of Au
(b)
Figure 9 The GPD fitting of the sample data (a) is the distribution fitting of Cu and (b) is the distribution fitting of Au
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ile13429109378164
class
ifica
tion
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
(a)
1002811755
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ilecla
ssifi
catio
n
(b)
Figure 10 The identified anomaly region of Cu and Au (a) is the anomaly region of Cu and (b) is the anomaly region of Au
selection of the thresholds is reasonable Fitting the excessthreshold of the sample data using the GPD (Figure 9)indicates that the excess threshold of the sample data is inthe vicinity of the line the results show that the theoreticaldistribution and actual distribution of the sample data areconsistent Therefore the threshold selection is reasonableThere are currently seven mining drill holes that is KZK10KZK11 KZK23 KZK28 ZK02618 ZK02619 and ZK02620
and the exploitation ore bodies are mostly VII main orebody in the 26 exploration lines of the Cu-Au mining areaGIS technology is used to show the geological anomalyregion with the selection of the thresholds (Figure 10)From Figure 10 it is seen that the anomaly region of Cuand Au is consistent with the range of ore bodies of theactual engineering exploration which has a high indicatingfunction with respect to ore prospecting The results show
10 Mathematical Problems in Engineering
that the EVT model of the geological anomaly is good atmineral deposit prediction and it has good prospectingsignificance
5 Conclusion
In this study the proposed EVT model of the geologicalanomaly was applied to identify geochemical anomaliesassociated with Cu and Au mineralizationThe results of thisstudy led to the following
(1) The characteristics of the geological anomaly and theprinciple of EVT were studied knowledge of the dis-tribution of the EVT coincides with the distributionof the geological anomaly data The designed EVTmodel of the geological anomaly takes full accountof the characteristic of the geological anomaly andthe practical features of the EVT The thresholdselection and parameter estimates of the model weredetermined
(2) The proposed EVT model of the geological anomalywas successfully applied to identify the geologicalanomaly region in the Jiguanzui Cu-Au mining areaThe results show that the anomaly threshold of Cu is8164006 and that of Au is 754736 the shape param-eter of Cu is 03162 and that of Au is 03342 and thescale parameter of Cu is 4409216 and that of the Auis 315699 The abnormal probability distribution wasalso determined Testing the results of the model byfitting the excess threshold of the sample data showedthat the results of the theoretical distribution andactual distribution of the sample data were consistent
(3) The geological anomalies of Cu and Au predictedby the EVT model are consistent with the rangeof ore bodies of the actual engineering explorationThe EVT model has a high indicating function withrespect to ore prospecting and it is applicable for theexploration of mineral deposits
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This study was supported by the GeophysiochemistryProspecting Institute of the Academy of Geological Scienceof China and the Program for the Core of High Spec-trum of Primary Halo Geochemical Prospecting Project (no12120114002001) and the project of the special funds foruniversities was supported by the central governmentmdashtheconstruction of discipline platform inmanagement engineer-ing theory and quantitative methods (no 80000-14Z019002)The authors are grateful to the First Geological Brigade ofthe Hubei Geological Bureau for providing the data Theywould also like to express their appreciation for the teammembers of the Key Laboratory of Mathematical Geology inSichuan China They are grateful to Professor HongJun Liu
at ChengduUniversity of Technology for providing construc-tive advice for this studyThey also thank LetPub (httpwwwletpubcom) for its linguistic assistance during the prepara-tion of this manuscript
References
[1] A Darehshiri M Panji and A R Mokhtari ldquoIdentifyinggeochemical anomalies associated with Cu mineralization instream sediment samples in Gharachaman area northwest ofIranrdquo Journal of African Earth Sciences vol 110 pp 92ndash99 2015
[2] X Lu and P Zhao ldquoGeologic anomaly analysis for space-timedistribution of mineral deposits in the middle-lower Yangtzearea southeastern Chinardquo Nonrenewable Resources vol 17 no3 pp 187ndash196 1998
[3] Z Pengda C Qiuming and X Qinglin ldquoQuantitative predic-tion for deep mineral explorationrdquo Journal of China Universityof Geosciences vol 19 no 4 pp 309ndash318 2008
[4] Q Cheng ldquoSingularity theory and methods for mapping geo-chemical anomalies caused by buried sources and for predictingundiscovered mineral deposits in covered areasrdquo Journal ofGeochemical Exploration vol 122 pp 55ndash70 2012
[5] A P Freedman and B Parsons ldquoGeoid anomalies over twoSouth Atlantic fracture zonesrdquo Earth and Planetary ScienceLetters vol 100 no 1ndash3 pp 18ndash41 1990
[6] P Shen Y Shen T Liu L Meng H Dai and Y YangldquoGeochemical signature of porphyries in the Baogutu porphyrycopper belt western Junggar NW Chinardquo Gondwana Researchvol 16 no 2 pp 227ndash242 2009
[7] J Zhao S Chen and R Zuo ldquoIdentifying geochemical anoma-lies associated with AundashCu mineralization using multifractaland artificial neural network models in the Ningqiang districtShaanxi Chinardquo Journal of Geochemical Exploration vol 164pp 54ndash64 2016
[8] P Zhao J Chen J Chen S Zhang and Y Chen ldquoThelsquothree-componentrsquo digital prospecting method a new approachfor mineral resource quantitative prediction and assessmentrdquoNatural Resources Research vol 14 no 4 pp 295ndash303 2005
[9] Q Cheng and P Zhao ldquoSingularity theories and methodsfor characterizing mineralization processes and mapping geo-anomalies for mineral deposit predictionrdquoGeoscience Frontiersvol 2 no 1 pp 67ndash79 2011
[10] Y Chen P Zhao J Chen and J Liu ldquoApplication of the geo-anomaly unit concept in quantitative delineation and assess-ment of gold ore targets in western Shandong uplift terraineastern ChinardquoNatural Resources Research vol 10 no 1 pp 35ndash49 2001
[11] D E Allen A K Singh and R J Powell ldquoExtreme marketrisk-an extreme value theory approachrdquo Mathematics andComputers in Simulation vol 94 pp 310ndash328 2011
[12] Q Chen and X Lv ldquoThe extreme-value dependence betweenthe crude oil price and Chinese stock marketsrdquo InternationalReview of Economics and Finance vol 39 pp 121ndash132 2015
[13] KWhan J Zscheischler R Orth et al ldquoImpact of soil moistureon extreme maximum temperatures in Europerdquo Weather andClimate Extremes vol 9 pp 57ndash67 2015
[14] D Faranda J M Freitas P Guiraud and S Vaienti ldquoSamplinglocal properties of attractors via extreme value theoryrdquo ChaosSolitons and Fractals vol 74 pp 55ndash66 2015
[15] E Vanem ldquoNon-stationary extreme value models to accountfor trends and shifts in the extreme wave climate due to climatechangerdquo Applied Ocean Research vol 52 pp 201ndash211 2015
Mathematical Problems in Engineering 11
[16] D Rivas F Caleyo A Valor and J M Hallen ldquoExtreme valueanalysis applied to pitting corrosion experiments in low carbonsteel comparison of block maxima and peak over thresholdapproachesrdquo Corrosion Science vol 50 no 11 pp 3193ndash32042008
[17] F Ashkar and S-E El Adlouni ldquoAdjusting for small-samplenon-normality of design event estimators under a generalizedPareto distributionrdquo Journal of Hydrology vol 530 pp 384ndash3912015
[18] J D Castillo and I Serra ldquoLikelihood inference for generalizedPareto distributionrdquo Computational Statistics amp Data Analysisvol 83 pp 116ndash128 2015
[19] A T Ergun and J Jun ldquoTime-varying higher-order conditionalmoments and forecasting intraday VaR and Expected ShortfallrdquoThe Quarterly Review of Economics and Finance vol 50 no 3pp 264ndash272 2010
[20] R Gencay and F Selcuk ldquoExtreme value theory and value-at-risk relative performance in emerging marketsrdquo InternationalJournal of Forecasting vol 20 pp 287ndash303 2004
[21] J H T Kim and J Kim ldquoA parametric alternative to the Hillestimator for heavy-tailed distributionsrdquo Journal of Banking ampFinance vol 54 pp 60ndash71 2015
[22] Z-H Feng Y-M Wei and K Wang ldquoEstimating risk for thecarbon market via extreme value theory an empirical analysisof the EU ETSrdquo Applied Energy vol 99 pp 97ndash108 2012
[23] C-C Lee and C-P Chang ldquoNew evidence on the convergenceof per capita carbon dioxide emissions from panel seeminglyunrelated regressions augmented Dickey-Fuller testsrdquo Energyvol 33 no 9 pp 1468ndash1475 2008
[24] G Cao and M Zhang ldquoExtreme values in the Chinese andAmerican stock markets based on detrended fluctuation anal-ysisrdquo Physica A Statistical Mechanics and its Applications vol436 pp 25ndash35 2015
Elements Mean Minimum Maximum Std dev CV Skewness KurtosisCu 64144 5326 1720277 72765 113 738 10696Au 7082 713 187797 025 082 842 15493
is determined the excess data 119909119894minus1205830approximately obey the
GPD distribution Regardless of any threshold 120583 (120583 gt 1205830)
the shape parameter 120585 and scale parameter 120573 of the GPDshould remain unchanged Therefore information can beobtained on the transformation relationship between 120573(120583)and threshold 120583 (120583 gt 120583
0) from (3)
120573 (120583) = 120573 (1205830) + 120585 (120583 minus 120583
0) (11)
Let 120573lowast(120583) = 120573(1205830)+120585(120583minus120583
0) 120573lowast(120583) is called themodified
scale and the values of 120573lowast(120583)will not change when threshold120583 changes Therefore when the interval threshold value isdetermined byMEF the accuracy threshold can be estimatedby 120573lowast(120583) Estimating the threshold using 120573lowast(120583) is detailed inSection 42
In this paper the EVT model of the geological anomalytakes full account of the characteristic of the geologicalanomaly distribution and the practical features of the EVTRelative to the geological background value the anomaly andextreme value can be used to describe the geological anomalyThe observations of the geological anomaly are located in thetail of the samples which are related to the random charactersin the process of quantification at the very large or smalllevel and estimate the probability of the extreme event inthe existing observation levelsmdashthese characteristics are alsothe contents of the EVT The EVT is a branch of statisticsthat studies the limiting distribution of the minimum andmaximum value and evaluates the risk of extreme eventsTherefore the mathematical foundation of the geologicalanomaly is described by the EVT On the one hand the EVTdescribes the characteristic of the geological anomaly distri-bution from the perspective of mathematics the results from(3) show the distribution of the sample data which is provedin (12) On the other hand the EVT provides a quantitativeand digital research method for predicting and evaluatingthe mineral resources which is proved in Figure 10 Besidesthis paper also discusses the methods of estimate parametersand the threshold of the EVT Consequently a mathematicalstatisticalmodel is established for quantitative geological dataand geology information where the data exceed the thresholdof the sample in (12) Therefore the ability of the EVT modelto identify the geological anomaly is feasible
4 The Model Application in Identifyingthe Geological Anomaly of the JiguanzuiCu-Au Mining Area
In order to show the effect of identifying the anomaly usingthe EVT model with geological anomaly recognition themodel was applied to identify the anomaly in an actualmining area The study data with Cu and Au originate from26 exploration lines of the Jiguanzui Cu-Au mining area inHubei China The count of the sample data with Cu and Au
is 14309 The Jiguanzui Cu-Au mining deposit is the blinddeposits at the lower part of the Quaternary overburdenlayer Currently I II III and VII main ore body groups 14main ore bodies and 105 small fragmentary ore bodies havebeen identified in the mining area The main ore bodies ofthe Jiguanzui Cu-Au mining area are distributed in the 013to 034 lines which are 950 meters long the width is 160ndash800 meters the elevation ranges from minus5m to minus1412m deepextension and the level projection area of the ore bodies is058 square kilometers The overall distribution of the orebodies is northeast 30∘ the trend of the ore bodies is northeast15∘ndash72∘ and the local trend of the ore bodies is northwest I IIIII andVII ore bodies are arranged in the form of an echelonin which the tendency is northwest and the local tendency issouthThemain ore bodies occur in the fault basin at the edgeof the northwestern rock body of the Tonglushan near thecontact zone of the dolomitic marble the quartz monzonitediorite porphyry and quartz diorite in the Lower TriassicJialingjiang Formation and near the different lithology andthe echelon fracture of dolomitic marble The pattern of theJiguanzui Cu-Au mining deposit is shown in Figure 3
41 The Condition Test of the Model
411 The Posttail Test of Sample Data Firstly this paperanalyses the basic statistics of the Cu and Au elements andthe results are shown in Table 1 From Table 1 we can see thatthe skewness of the sample data is greater than zero and thesample data are not normally distributed that is distributedto the right By observing the coefficient of variation it is seenthat the coefficient of variation of Au is smaller than that ofCu and the stability of Au is higher than that of Cu Besidesthe kurtosis of Cu and Au is greater than that of the normaldistribution (of which the kurtosis value is 3) which resultsin a leptokurtic distribution for Cu and Au Therefore thedistribution of Cu and Au is shown to be skewed to the rightwith leptokurtic characteristics Secondly in order to indicatethe difference between the actual distribution and normaldistribution Q-Q plot can be used for the observation test(Figure 4) The distribution of Cu and Au is also shown to beskewed to the right with posttail characteristics
412 The Stationary Test of the Sample Data The stationarytestmainly inspects the self-correlation of the geological datathe commonmethods of the stationary test are as follows theaugmented Dickey-Fuller (ADF) and sequence correlationanalysis Through the ADF we can obtain the test resultsof the sample data (Table 2) The 119905-statistics of Cu and Auare minus3393498 and minus1319081 respectively which are smallerthan their own 1 significant level Therefore the sequencesof Cu and Au do not have unit roots they are stationarysequencesThe results of the sequence correlation analysis are
6 Mathematical Problems in Engineering
A
D
C
B
Volcaniclastic rocks of neighboring group
Breccia of Majiashan group
Pelitic siltstone of Puqi group
Dolomitic marble of Lower Triassic Jialingjiang Formation
Quartz monzonite diorite porphyry
Diorite
Fracture
Stratigraphic boundary
Unconformity boundary
Structural breccia
Ore bodies and numbers
The first metallogenic region
The second metallogenic region
The third metallogenic region
The fourth metallogenic region
A
B
C
D
K1l
K1l
I
VIVII
IVIII
IIJ3m
J3m
F3
F1
T2p
T2p
T2p
T1minus2j
T1minus2j
T1minus2j
T1minus2j
T1minus2j
T1minus2j
Q25Q25
Q25
Q25
35
35
Figure 3 The pattern of the Jiguanzui Cu-Au mining deposit
Table 2 The ADF test of Cu and Au
Elements ADT (119905-statistic) Test critical values Probability1 level 5 level 10 level
shown in Figure 5 where we can see that the autocorrelationcoefficients (AC) and the partial autocorrelation coefficient(PAC) are not zero and the significance of 119876-states is highso the uncorrelated hypothesis cannot be rejectedThereforethe sequence of the geological data is a stationary time series
Together the results indicate that the data follow astationary sequence and the distributions of Cu and Au haveposttail characteristics indicating that they are abnormallydistributed Therefore we can use the EVT model of thegeological anomaly to identify the anomaly
Mathematical Problems in Engineering 7
4000
3000
2000
1000
0
0 5000 10000 15000 20000
Normal Q-Q plot of Cu
Expe
cted
nor
mal
val
ue
Observed value
minus1000
minus2000
minus3000minus5000
(a)
Expe
cted
nor
mal
val
ue
300
200
100
0
0 500 1000 1500 2000
Normal Q-Q plot of Au
Observed value
minus100
minus200minus500
(b)
Figure 4 The posttail test of the sample data according to Q-Q plot (a) is Q-Q plot test of Cu and (b) is Q-Q plot test of Au
Autocorrelation Partial correlation AC PAC Prob
12345678910
0958 0958 12885 0000
000000000000000000000000
000000000000
087107780695062805760535049604570420
0254
00010055
00650011
235293201938804443484900153015564705940361886
0072
minus0570
minus0026
minus0115
Q-stat
(a)
Autocorrelation Partial correlation AC PAC Prob
123456789
10
0963 13029 0000
000000000000000000000000
000000000000
08860799071606410574051404610413
240543302740230460055069254341573255972661650
0963
0198
0042
00070005
0029
0370
minus0580
minus0044
minus0033
minus0029
Q-stat
(b)
Figure 5The sequence correlation analysis of the sample data (a) is the sequence correlation analysis of Cu and (b) is the sequence correlationanalysis of Au
42 The Solution of the Model
421 Estimate the Parameters and Threshold Through theEVT model of the geological anomaly we can calculate theMEF of Cu and Au and plot the scatter diagram of the MEF(Figure 6) From Figure 6 it is seen that in the interval[7845406 8413659]with Cu and interval [721178 851918]with Au 119864(120583) for Cu and Au follows an approximately lineardistribution These intervals are selected as the thresholdfor Cu and Au As the result of the threshold selectionis subjective modified scale 120573lowast(120583) is used to estimate theaccuracy threshold Based on 120573lowast(120583) if initial threshold value1205830is determined regardless of any threshold 120583 (120583 gt 120583
0)
the shape parameter 120585 and scale parameter 120573 of GPD willnot change Uniformly selecting 50 threshold values from[7845406 8413659] and [721178 851918] respectively wecan obtain the transformation relations between 120573lowast(120583) 120585and the threshold 120583 (120583 gt 120583
0) for Cu and Au using (3) and
(11) see Figures 7 and 8 In order to ensure the accuracyof the EVT the threshold selection is as large as possiblein the permissible range of threshold estimation where thedata show the stationary characteristic (ldquoas discussed by Cao
and Zhang [24]rdquo) From Figures 7 and 8 it is seen that thethreshold of Cu is 8164006 and that of Au is 754736 Afterthe thresholds are determined the parameters of the EVTmodel of the geological anomaly can be estimated using themoment method which reveals that the shape parameter ofCu is 03162 and that of Au is 03342 the scale parameter ofCu is 4409216 and that of Au is 315699 Then inserting thethresholds and parameters into the GPD the distribution ofthe excess threshold of Cu and Au can be obtained by
119865Cu (119909) = 1 minus (1 +03162
4409216
119909)
minus103162
119865Au (119909) = 1 minus (1 +03342
315699
119909)
minus103342
(12)
The distribution of the excess threshold is called theabnormal probability distribution In themineral deposit pre-diction information on the geological data can be describedand expressed by the distribution of the excess threshold
422 The Diagnostic Test of the Model and Identificationof the Anomaly The diagnostic test shows whether the
8 Mathematical Problems in Engineering
0 4000 8000 12000 160000
500
1000
1500
2000
2500
3000
3500
4000
4500E
()
(a)
0 500 1000 1500 20000
50
100
150
200
250
300
350
400
450
500
E(
)
(b)
Figure 6 The scatter diagram of the MEF (a) is the MEF of Cu and (b) is the MEF of Au
780 790 800 810 820 830 840 850410
420
430
440
450
460
470
480
Mod
ified
(a)
780 790 800 810 820 830 840 850
029
0295
03
0305
031
0315
032
0325
033
Mod
ified
(b)
Figure 7 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Cu
72 74 76 78 80 82 84 8622
24
26
28
30
32
34
36
Mod
ified
(a)
72 74 76 78 80 82 84 86
031
032
033
034
035
036
037
038
039
04
Mod
ified
(b)
Figure 8 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Au
Mathematical Problems in Engineering 9
10
10
08
08
06
06
04
04
02
02
0000
Pareto P-P plot of Cu
Observed cum prob
Expe
cted
cum
pro
b
(a)
100806040200Observed cum prob
10
08
06
04
02
00
Expe
cted
cum
pro
b
Pareto P-P plot of Au
(b)
Figure 9 The GPD fitting of the sample data (a) is the distribution fitting of Cu and (b) is the distribution fitting of Au
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ile13429109378164
class
ifica
tion
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
(a)
1002811755
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ilecla
ssifi
catio
n
(b)
Figure 10 The identified anomaly region of Cu and Au (a) is the anomaly region of Cu and (b) is the anomaly region of Au
selection of the thresholds is reasonable Fitting the excessthreshold of the sample data using the GPD (Figure 9)indicates that the excess threshold of the sample data is inthe vicinity of the line the results show that the theoreticaldistribution and actual distribution of the sample data areconsistent Therefore the threshold selection is reasonableThere are currently seven mining drill holes that is KZK10KZK11 KZK23 KZK28 ZK02618 ZK02619 and ZK02620
and the exploitation ore bodies are mostly VII main orebody in the 26 exploration lines of the Cu-Au mining areaGIS technology is used to show the geological anomalyregion with the selection of the thresholds (Figure 10)From Figure 10 it is seen that the anomaly region of Cuand Au is consistent with the range of ore bodies of theactual engineering exploration which has a high indicatingfunction with respect to ore prospecting The results show
10 Mathematical Problems in Engineering
that the EVT model of the geological anomaly is good atmineral deposit prediction and it has good prospectingsignificance
5 Conclusion
In this study the proposed EVT model of the geologicalanomaly was applied to identify geochemical anomaliesassociated with Cu and Au mineralizationThe results of thisstudy led to the following
(1) The characteristics of the geological anomaly and theprinciple of EVT were studied knowledge of the dis-tribution of the EVT coincides with the distributionof the geological anomaly data The designed EVTmodel of the geological anomaly takes full accountof the characteristic of the geological anomaly andthe practical features of the EVT The thresholdselection and parameter estimates of the model weredetermined
(2) The proposed EVT model of the geological anomalywas successfully applied to identify the geologicalanomaly region in the Jiguanzui Cu-Au mining areaThe results show that the anomaly threshold of Cu is8164006 and that of Au is 754736 the shape param-eter of Cu is 03162 and that of Au is 03342 and thescale parameter of Cu is 4409216 and that of the Auis 315699 The abnormal probability distribution wasalso determined Testing the results of the model byfitting the excess threshold of the sample data showedthat the results of the theoretical distribution andactual distribution of the sample data were consistent
(3) The geological anomalies of Cu and Au predictedby the EVT model are consistent with the rangeof ore bodies of the actual engineering explorationThe EVT model has a high indicating function withrespect to ore prospecting and it is applicable for theexploration of mineral deposits
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This study was supported by the GeophysiochemistryProspecting Institute of the Academy of Geological Scienceof China and the Program for the Core of High Spec-trum of Primary Halo Geochemical Prospecting Project (no12120114002001) and the project of the special funds foruniversities was supported by the central governmentmdashtheconstruction of discipline platform inmanagement engineer-ing theory and quantitative methods (no 80000-14Z019002)The authors are grateful to the First Geological Brigade ofthe Hubei Geological Bureau for providing the data Theywould also like to express their appreciation for the teammembers of the Key Laboratory of Mathematical Geology inSichuan China They are grateful to Professor HongJun Liu
at ChengduUniversity of Technology for providing construc-tive advice for this studyThey also thank LetPub (httpwwwletpubcom) for its linguistic assistance during the prepara-tion of this manuscript
References
[1] A Darehshiri M Panji and A R Mokhtari ldquoIdentifyinggeochemical anomalies associated with Cu mineralization instream sediment samples in Gharachaman area northwest ofIranrdquo Journal of African Earth Sciences vol 110 pp 92ndash99 2015
[2] X Lu and P Zhao ldquoGeologic anomaly analysis for space-timedistribution of mineral deposits in the middle-lower Yangtzearea southeastern Chinardquo Nonrenewable Resources vol 17 no3 pp 187ndash196 1998
[3] Z Pengda C Qiuming and X Qinglin ldquoQuantitative predic-tion for deep mineral explorationrdquo Journal of China Universityof Geosciences vol 19 no 4 pp 309ndash318 2008
[4] Q Cheng ldquoSingularity theory and methods for mapping geo-chemical anomalies caused by buried sources and for predictingundiscovered mineral deposits in covered areasrdquo Journal ofGeochemical Exploration vol 122 pp 55ndash70 2012
[5] A P Freedman and B Parsons ldquoGeoid anomalies over twoSouth Atlantic fracture zonesrdquo Earth and Planetary ScienceLetters vol 100 no 1ndash3 pp 18ndash41 1990
[6] P Shen Y Shen T Liu L Meng H Dai and Y YangldquoGeochemical signature of porphyries in the Baogutu porphyrycopper belt western Junggar NW Chinardquo Gondwana Researchvol 16 no 2 pp 227ndash242 2009
[7] J Zhao S Chen and R Zuo ldquoIdentifying geochemical anoma-lies associated with AundashCu mineralization using multifractaland artificial neural network models in the Ningqiang districtShaanxi Chinardquo Journal of Geochemical Exploration vol 164pp 54ndash64 2016
[8] P Zhao J Chen J Chen S Zhang and Y Chen ldquoThelsquothree-componentrsquo digital prospecting method a new approachfor mineral resource quantitative prediction and assessmentrdquoNatural Resources Research vol 14 no 4 pp 295ndash303 2005
[9] Q Cheng and P Zhao ldquoSingularity theories and methodsfor characterizing mineralization processes and mapping geo-anomalies for mineral deposit predictionrdquoGeoscience Frontiersvol 2 no 1 pp 67ndash79 2011
[10] Y Chen P Zhao J Chen and J Liu ldquoApplication of the geo-anomaly unit concept in quantitative delineation and assess-ment of gold ore targets in western Shandong uplift terraineastern ChinardquoNatural Resources Research vol 10 no 1 pp 35ndash49 2001
[11] D E Allen A K Singh and R J Powell ldquoExtreme marketrisk-an extreme value theory approachrdquo Mathematics andComputers in Simulation vol 94 pp 310ndash328 2011
[12] Q Chen and X Lv ldquoThe extreme-value dependence betweenthe crude oil price and Chinese stock marketsrdquo InternationalReview of Economics and Finance vol 39 pp 121ndash132 2015
[13] KWhan J Zscheischler R Orth et al ldquoImpact of soil moistureon extreme maximum temperatures in Europerdquo Weather andClimate Extremes vol 9 pp 57ndash67 2015
[14] D Faranda J M Freitas P Guiraud and S Vaienti ldquoSamplinglocal properties of attractors via extreme value theoryrdquo ChaosSolitons and Fractals vol 74 pp 55ndash66 2015
[15] E Vanem ldquoNon-stationary extreme value models to accountfor trends and shifts in the extreme wave climate due to climatechangerdquo Applied Ocean Research vol 52 pp 201ndash211 2015
Mathematical Problems in Engineering 11
[16] D Rivas F Caleyo A Valor and J M Hallen ldquoExtreme valueanalysis applied to pitting corrosion experiments in low carbonsteel comparison of block maxima and peak over thresholdapproachesrdquo Corrosion Science vol 50 no 11 pp 3193ndash32042008
[17] F Ashkar and S-E El Adlouni ldquoAdjusting for small-samplenon-normality of design event estimators under a generalizedPareto distributionrdquo Journal of Hydrology vol 530 pp 384ndash3912015
[18] J D Castillo and I Serra ldquoLikelihood inference for generalizedPareto distributionrdquo Computational Statistics amp Data Analysisvol 83 pp 116ndash128 2015
[19] A T Ergun and J Jun ldquoTime-varying higher-order conditionalmoments and forecasting intraday VaR and Expected ShortfallrdquoThe Quarterly Review of Economics and Finance vol 50 no 3pp 264ndash272 2010
[20] R Gencay and F Selcuk ldquoExtreme value theory and value-at-risk relative performance in emerging marketsrdquo InternationalJournal of Forecasting vol 20 pp 287ndash303 2004
[21] J H T Kim and J Kim ldquoA parametric alternative to the Hillestimator for heavy-tailed distributionsrdquo Journal of Banking ampFinance vol 54 pp 60ndash71 2015
[22] Z-H Feng Y-M Wei and K Wang ldquoEstimating risk for thecarbon market via extreme value theory an empirical analysisof the EU ETSrdquo Applied Energy vol 99 pp 97ndash108 2012
[23] C-C Lee and C-P Chang ldquoNew evidence on the convergenceof per capita carbon dioxide emissions from panel seeminglyunrelated regressions augmented Dickey-Fuller testsrdquo Energyvol 33 no 9 pp 1468ndash1475 2008
[24] G Cao and M Zhang ldquoExtreme values in the Chinese andAmerican stock markets based on detrended fluctuation anal-ysisrdquo Physica A Statistical Mechanics and its Applications vol436 pp 25ndash35 2015
shown in Figure 5 where we can see that the autocorrelationcoefficients (AC) and the partial autocorrelation coefficient(PAC) are not zero and the significance of 119876-states is highso the uncorrelated hypothesis cannot be rejectedThereforethe sequence of the geological data is a stationary time series
Together the results indicate that the data follow astationary sequence and the distributions of Cu and Au haveposttail characteristics indicating that they are abnormallydistributed Therefore we can use the EVT model of thegeological anomaly to identify the anomaly
Mathematical Problems in Engineering 7
4000
3000
2000
1000
0
0 5000 10000 15000 20000
Normal Q-Q plot of Cu
Expe
cted
nor
mal
val
ue
Observed value
minus1000
minus2000
minus3000minus5000
(a)
Expe
cted
nor
mal
val
ue
300
200
100
0
0 500 1000 1500 2000
Normal Q-Q plot of Au
Observed value
minus100
minus200minus500
(b)
Figure 4 The posttail test of the sample data according to Q-Q plot (a) is Q-Q plot test of Cu and (b) is Q-Q plot test of Au
Autocorrelation Partial correlation AC PAC Prob
12345678910
0958 0958 12885 0000
000000000000000000000000
000000000000
087107780695062805760535049604570420
0254
00010055
00650011
235293201938804443484900153015564705940361886
0072
minus0570
minus0026
minus0115
Q-stat
(a)
Autocorrelation Partial correlation AC PAC Prob
123456789
10
0963 13029 0000
000000000000000000000000
000000000000
08860799071606410574051404610413
240543302740230460055069254341573255972661650
0963
0198
0042
00070005
0029
0370
minus0580
minus0044
minus0033
minus0029
Q-stat
(b)
Figure 5The sequence correlation analysis of the sample data (a) is the sequence correlation analysis of Cu and (b) is the sequence correlationanalysis of Au
42 The Solution of the Model
421 Estimate the Parameters and Threshold Through theEVT model of the geological anomaly we can calculate theMEF of Cu and Au and plot the scatter diagram of the MEF(Figure 6) From Figure 6 it is seen that in the interval[7845406 8413659]with Cu and interval [721178 851918]with Au 119864(120583) for Cu and Au follows an approximately lineardistribution These intervals are selected as the thresholdfor Cu and Au As the result of the threshold selectionis subjective modified scale 120573lowast(120583) is used to estimate theaccuracy threshold Based on 120573lowast(120583) if initial threshold value1205830is determined regardless of any threshold 120583 (120583 gt 120583
0)
the shape parameter 120585 and scale parameter 120573 of GPD willnot change Uniformly selecting 50 threshold values from[7845406 8413659] and [721178 851918] respectively wecan obtain the transformation relations between 120573lowast(120583) 120585and the threshold 120583 (120583 gt 120583
0) for Cu and Au using (3) and
(11) see Figures 7 and 8 In order to ensure the accuracyof the EVT the threshold selection is as large as possiblein the permissible range of threshold estimation where thedata show the stationary characteristic (ldquoas discussed by Cao
and Zhang [24]rdquo) From Figures 7 and 8 it is seen that thethreshold of Cu is 8164006 and that of Au is 754736 Afterthe thresholds are determined the parameters of the EVTmodel of the geological anomaly can be estimated using themoment method which reveals that the shape parameter ofCu is 03162 and that of Au is 03342 the scale parameter ofCu is 4409216 and that of Au is 315699 Then inserting thethresholds and parameters into the GPD the distribution ofthe excess threshold of Cu and Au can be obtained by
119865Cu (119909) = 1 minus (1 +03162
4409216
119909)
minus103162
119865Au (119909) = 1 minus (1 +03342
315699
119909)
minus103342
(12)
The distribution of the excess threshold is called theabnormal probability distribution In themineral deposit pre-diction information on the geological data can be describedand expressed by the distribution of the excess threshold
422 The Diagnostic Test of the Model and Identificationof the Anomaly The diagnostic test shows whether the
8 Mathematical Problems in Engineering
0 4000 8000 12000 160000
500
1000
1500
2000
2500
3000
3500
4000
4500E
()
(a)
0 500 1000 1500 20000
50
100
150
200
250
300
350
400
450
500
E(
)
(b)
Figure 6 The scatter diagram of the MEF (a) is the MEF of Cu and (b) is the MEF of Au
780 790 800 810 820 830 840 850410
420
430
440
450
460
470
480
Mod
ified
(a)
780 790 800 810 820 830 840 850
029
0295
03
0305
031
0315
032
0325
033
Mod
ified
(b)
Figure 7 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Cu
72 74 76 78 80 82 84 8622
24
26
28
30
32
34
36
Mod
ified
(a)
72 74 76 78 80 82 84 86
031
032
033
034
035
036
037
038
039
04
Mod
ified
(b)
Figure 8 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Au
Mathematical Problems in Engineering 9
10
10
08
08
06
06
04
04
02
02
0000
Pareto P-P plot of Cu
Observed cum prob
Expe
cted
cum
pro
b
(a)
100806040200Observed cum prob
10
08
06
04
02
00
Expe
cted
cum
pro
b
Pareto P-P plot of Au
(b)
Figure 9 The GPD fitting of the sample data (a) is the distribution fitting of Cu and (b) is the distribution fitting of Au
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ile13429109378164
class
ifica
tion
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
(a)
1002811755
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ilecla
ssifi
catio
n
(b)
Figure 10 The identified anomaly region of Cu and Au (a) is the anomaly region of Cu and (b) is the anomaly region of Au
selection of the thresholds is reasonable Fitting the excessthreshold of the sample data using the GPD (Figure 9)indicates that the excess threshold of the sample data is inthe vicinity of the line the results show that the theoreticaldistribution and actual distribution of the sample data areconsistent Therefore the threshold selection is reasonableThere are currently seven mining drill holes that is KZK10KZK11 KZK23 KZK28 ZK02618 ZK02619 and ZK02620
and the exploitation ore bodies are mostly VII main orebody in the 26 exploration lines of the Cu-Au mining areaGIS technology is used to show the geological anomalyregion with the selection of the thresholds (Figure 10)From Figure 10 it is seen that the anomaly region of Cuand Au is consistent with the range of ore bodies of theactual engineering exploration which has a high indicatingfunction with respect to ore prospecting The results show
10 Mathematical Problems in Engineering
that the EVT model of the geological anomaly is good atmineral deposit prediction and it has good prospectingsignificance
5 Conclusion
In this study the proposed EVT model of the geologicalanomaly was applied to identify geochemical anomaliesassociated with Cu and Au mineralizationThe results of thisstudy led to the following
(1) The characteristics of the geological anomaly and theprinciple of EVT were studied knowledge of the dis-tribution of the EVT coincides with the distributionof the geological anomaly data The designed EVTmodel of the geological anomaly takes full accountof the characteristic of the geological anomaly andthe practical features of the EVT The thresholdselection and parameter estimates of the model weredetermined
(2) The proposed EVT model of the geological anomalywas successfully applied to identify the geologicalanomaly region in the Jiguanzui Cu-Au mining areaThe results show that the anomaly threshold of Cu is8164006 and that of Au is 754736 the shape param-eter of Cu is 03162 and that of Au is 03342 and thescale parameter of Cu is 4409216 and that of the Auis 315699 The abnormal probability distribution wasalso determined Testing the results of the model byfitting the excess threshold of the sample data showedthat the results of the theoretical distribution andactual distribution of the sample data were consistent
(3) The geological anomalies of Cu and Au predictedby the EVT model are consistent with the rangeof ore bodies of the actual engineering explorationThe EVT model has a high indicating function withrespect to ore prospecting and it is applicable for theexploration of mineral deposits
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This study was supported by the GeophysiochemistryProspecting Institute of the Academy of Geological Scienceof China and the Program for the Core of High Spec-trum of Primary Halo Geochemical Prospecting Project (no12120114002001) and the project of the special funds foruniversities was supported by the central governmentmdashtheconstruction of discipline platform inmanagement engineer-ing theory and quantitative methods (no 80000-14Z019002)The authors are grateful to the First Geological Brigade ofthe Hubei Geological Bureau for providing the data Theywould also like to express their appreciation for the teammembers of the Key Laboratory of Mathematical Geology inSichuan China They are grateful to Professor HongJun Liu
at ChengduUniversity of Technology for providing construc-tive advice for this studyThey also thank LetPub (httpwwwletpubcom) for its linguistic assistance during the prepara-tion of this manuscript
References
[1] A Darehshiri M Panji and A R Mokhtari ldquoIdentifyinggeochemical anomalies associated with Cu mineralization instream sediment samples in Gharachaman area northwest ofIranrdquo Journal of African Earth Sciences vol 110 pp 92ndash99 2015
[2] X Lu and P Zhao ldquoGeologic anomaly analysis for space-timedistribution of mineral deposits in the middle-lower Yangtzearea southeastern Chinardquo Nonrenewable Resources vol 17 no3 pp 187ndash196 1998
[3] Z Pengda C Qiuming and X Qinglin ldquoQuantitative predic-tion for deep mineral explorationrdquo Journal of China Universityof Geosciences vol 19 no 4 pp 309ndash318 2008
[4] Q Cheng ldquoSingularity theory and methods for mapping geo-chemical anomalies caused by buried sources and for predictingundiscovered mineral deposits in covered areasrdquo Journal ofGeochemical Exploration vol 122 pp 55ndash70 2012
[5] A P Freedman and B Parsons ldquoGeoid anomalies over twoSouth Atlantic fracture zonesrdquo Earth and Planetary ScienceLetters vol 100 no 1ndash3 pp 18ndash41 1990
[6] P Shen Y Shen T Liu L Meng H Dai and Y YangldquoGeochemical signature of porphyries in the Baogutu porphyrycopper belt western Junggar NW Chinardquo Gondwana Researchvol 16 no 2 pp 227ndash242 2009
[7] J Zhao S Chen and R Zuo ldquoIdentifying geochemical anoma-lies associated with AundashCu mineralization using multifractaland artificial neural network models in the Ningqiang districtShaanxi Chinardquo Journal of Geochemical Exploration vol 164pp 54ndash64 2016
[8] P Zhao J Chen J Chen S Zhang and Y Chen ldquoThelsquothree-componentrsquo digital prospecting method a new approachfor mineral resource quantitative prediction and assessmentrdquoNatural Resources Research vol 14 no 4 pp 295ndash303 2005
[9] Q Cheng and P Zhao ldquoSingularity theories and methodsfor characterizing mineralization processes and mapping geo-anomalies for mineral deposit predictionrdquoGeoscience Frontiersvol 2 no 1 pp 67ndash79 2011
[10] Y Chen P Zhao J Chen and J Liu ldquoApplication of the geo-anomaly unit concept in quantitative delineation and assess-ment of gold ore targets in western Shandong uplift terraineastern ChinardquoNatural Resources Research vol 10 no 1 pp 35ndash49 2001
[11] D E Allen A K Singh and R J Powell ldquoExtreme marketrisk-an extreme value theory approachrdquo Mathematics andComputers in Simulation vol 94 pp 310ndash328 2011
[12] Q Chen and X Lv ldquoThe extreme-value dependence betweenthe crude oil price and Chinese stock marketsrdquo InternationalReview of Economics and Finance vol 39 pp 121ndash132 2015
[13] KWhan J Zscheischler R Orth et al ldquoImpact of soil moistureon extreme maximum temperatures in Europerdquo Weather andClimate Extremes vol 9 pp 57ndash67 2015
[14] D Faranda J M Freitas P Guiraud and S Vaienti ldquoSamplinglocal properties of attractors via extreme value theoryrdquo ChaosSolitons and Fractals vol 74 pp 55ndash66 2015
[15] E Vanem ldquoNon-stationary extreme value models to accountfor trends and shifts in the extreme wave climate due to climatechangerdquo Applied Ocean Research vol 52 pp 201ndash211 2015
Mathematical Problems in Engineering 11
[16] D Rivas F Caleyo A Valor and J M Hallen ldquoExtreme valueanalysis applied to pitting corrosion experiments in low carbonsteel comparison of block maxima and peak over thresholdapproachesrdquo Corrosion Science vol 50 no 11 pp 3193ndash32042008
[17] F Ashkar and S-E El Adlouni ldquoAdjusting for small-samplenon-normality of design event estimators under a generalizedPareto distributionrdquo Journal of Hydrology vol 530 pp 384ndash3912015
[18] J D Castillo and I Serra ldquoLikelihood inference for generalizedPareto distributionrdquo Computational Statistics amp Data Analysisvol 83 pp 116ndash128 2015
[19] A T Ergun and J Jun ldquoTime-varying higher-order conditionalmoments and forecasting intraday VaR and Expected ShortfallrdquoThe Quarterly Review of Economics and Finance vol 50 no 3pp 264ndash272 2010
[20] R Gencay and F Selcuk ldquoExtreme value theory and value-at-risk relative performance in emerging marketsrdquo InternationalJournal of Forecasting vol 20 pp 287ndash303 2004
[21] J H T Kim and J Kim ldquoA parametric alternative to the Hillestimator for heavy-tailed distributionsrdquo Journal of Banking ampFinance vol 54 pp 60ndash71 2015
[22] Z-H Feng Y-M Wei and K Wang ldquoEstimating risk for thecarbon market via extreme value theory an empirical analysisof the EU ETSrdquo Applied Energy vol 99 pp 97ndash108 2012
[23] C-C Lee and C-P Chang ldquoNew evidence on the convergenceof per capita carbon dioxide emissions from panel seeminglyunrelated regressions augmented Dickey-Fuller testsrdquo Energyvol 33 no 9 pp 1468ndash1475 2008
[24] G Cao and M Zhang ldquoExtreme values in the Chinese andAmerican stock markets based on detrended fluctuation anal-ysisrdquo Physica A Statistical Mechanics and its Applications vol436 pp 25ndash35 2015
Figure 4 The posttail test of the sample data according to Q-Q plot (a) is Q-Q plot test of Cu and (b) is Q-Q plot test of Au
Autocorrelation Partial correlation AC PAC Prob
12345678910
0958 0958 12885 0000
000000000000000000000000
000000000000
087107780695062805760535049604570420
0254
00010055
00650011
235293201938804443484900153015564705940361886
0072
minus0570
minus0026
minus0115
Q-stat
(a)
Autocorrelation Partial correlation AC PAC Prob
123456789
10
0963 13029 0000
000000000000000000000000
000000000000
08860799071606410574051404610413
240543302740230460055069254341573255972661650
0963
0198
0042
00070005
0029
0370
minus0580
minus0044
minus0033
minus0029
Q-stat
(b)
Figure 5The sequence correlation analysis of the sample data (a) is the sequence correlation analysis of Cu and (b) is the sequence correlationanalysis of Au
42 The Solution of the Model
421 Estimate the Parameters and Threshold Through theEVT model of the geological anomaly we can calculate theMEF of Cu and Au and plot the scatter diagram of the MEF(Figure 6) From Figure 6 it is seen that in the interval[7845406 8413659]with Cu and interval [721178 851918]with Au 119864(120583) for Cu and Au follows an approximately lineardistribution These intervals are selected as the thresholdfor Cu and Au As the result of the threshold selectionis subjective modified scale 120573lowast(120583) is used to estimate theaccuracy threshold Based on 120573lowast(120583) if initial threshold value1205830is determined regardless of any threshold 120583 (120583 gt 120583
0)
the shape parameter 120585 and scale parameter 120573 of GPD willnot change Uniformly selecting 50 threshold values from[7845406 8413659] and [721178 851918] respectively wecan obtain the transformation relations between 120573lowast(120583) 120585and the threshold 120583 (120583 gt 120583
0) for Cu and Au using (3) and
(11) see Figures 7 and 8 In order to ensure the accuracyof the EVT the threshold selection is as large as possiblein the permissible range of threshold estimation where thedata show the stationary characteristic (ldquoas discussed by Cao
and Zhang [24]rdquo) From Figures 7 and 8 it is seen that thethreshold of Cu is 8164006 and that of Au is 754736 Afterthe thresholds are determined the parameters of the EVTmodel of the geological anomaly can be estimated using themoment method which reveals that the shape parameter ofCu is 03162 and that of Au is 03342 the scale parameter ofCu is 4409216 and that of Au is 315699 Then inserting thethresholds and parameters into the GPD the distribution ofthe excess threshold of Cu and Au can be obtained by
119865Cu (119909) = 1 minus (1 +03162
4409216
119909)
minus103162
119865Au (119909) = 1 minus (1 +03342
315699
119909)
minus103342
(12)
The distribution of the excess threshold is called theabnormal probability distribution In themineral deposit pre-diction information on the geological data can be describedand expressed by the distribution of the excess threshold
422 The Diagnostic Test of the Model and Identificationof the Anomaly The diagnostic test shows whether the
8 Mathematical Problems in Engineering
0 4000 8000 12000 160000
500
1000
1500
2000
2500
3000
3500
4000
4500E
()
(a)
0 500 1000 1500 20000
50
100
150
200
250
300
350
400
450
500
E(
)
(b)
Figure 6 The scatter diagram of the MEF (a) is the MEF of Cu and (b) is the MEF of Au
780 790 800 810 820 830 840 850410
420
430
440
450
460
470
480
Mod
ified
(a)
780 790 800 810 820 830 840 850
029
0295
03
0305
031
0315
032
0325
033
Mod
ified
(b)
Figure 7 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Cu
72 74 76 78 80 82 84 8622
24
26
28
30
32
34
36
Mod
ified
(a)
72 74 76 78 80 82 84 86
031
032
033
034
035
036
037
038
039
04
Mod
ified
(b)
Figure 8 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Au
Mathematical Problems in Engineering 9
10
10
08
08
06
06
04
04
02
02
0000
Pareto P-P plot of Cu
Observed cum prob
Expe
cted
cum
pro
b
(a)
100806040200Observed cum prob
10
08
06
04
02
00
Expe
cted
cum
pro
b
Pareto P-P plot of Au
(b)
Figure 9 The GPD fitting of the sample data (a) is the distribution fitting of Cu and (b) is the distribution fitting of Au
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ile13429109378164
class
ifica
tion
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
(a)
1002811755
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ilecla
ssifi
catio
n
(b)
Figure 10 The identified anomaly region of Cu and Au (a) is the anomaly region of Cu and (b) is the anomaly region of Au
selection of the thresholds is reasonable Fitting the excessthreshold of the sample data using the GPD (Figure 9)indicates that the excess threshold of the sample data is inthe vicinity of the line the results show that the theoreticaldistribution and actual distribution of the sample data areconsistent Therefore the threshold selection is reasonableThere are currently seven mining drill holes that is KZK10KZK11 KZK23 KZK28 ZK02618 ZK02619 and ZK02620
and the exploitation ore bodies are mostly VII main orebody in the 26 exploration lines of the Cu-Au mining areaGIS technology is used to show the geological anomalyregion with the selection of the thresholds (Figure 10)From Figure 10 it is seen that the anomaly region of Cuand Au is consistent with the range of ore bodies of theactual engineering exploration which has a high indicatingfunction with respect to ore prospecting The results show
10 Mathematical Problems in Engineering
that the EVT model of the geological anomaly is good atmineral deposit prediction and it has good prospectingsignificance
5 Conclusion
In this study the proposed EVT model of the geologicalanomaly was applied to identify geochemical anomaliesassociated with Cu and Au mineralizationThe results of thisstudy led to the following
(1) The characteristics of the geological anomaly and theprinciple of EVT were studied knowledge of the dis-tribution of the EVT coincides with the distributionof the geological anomaly data The designed EVTmodel of the geological anomaly takes full accountof the characteristic of the geological anomaly andthe practical features of the EVT The thresholdselection and parameter estimates of the model weredetermined
(2) The proposed EVT model of the geological anomalywas successfully applied to identify the geologicalanomaly region in the Jiguanzui Cu-Au mining areaThe results show that the anomaly threshold of Cu is8164006 and that of Au is 754736 the shape param-eter of Cu is 03162 and that of Au is 03342 and thescale parameter of Cu is 4409216 and that of the Auis 315699 The abnormal probability distribution wasalso determined Testing the results of the model byfitting the excess threshold of the sample data showedthat the results of the theoretical distribution andactual distribution of the sample data were consistent
(3) The geological anomalies of Cu and Au predictedby the EVT model are consistent with the rangeof ore bodies of the actual engineering explorationThe EVT model has a high indicating function withrespect to ore prospecting and it is applicable for theexploration of mineral deposits
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This study was supported by the GeophysiochemistryProspecting Institute of the Academy of Geological Scienceof China and the Program for the Core of High Spec-trum of Primary Halo Geochemical Prospecting Project (no12120114002001) and the project of the special funds foruniversities was supported by the central governmentmdashtheconstruction of discipline platform inmanagement engineer-ing theory and quantitative methods (no 80000-14Z019002)The authors are grateful to the First Geological Brigade ofthe Hubei Geological Bureau for providing the data Theywould also like to express their appreciation for the teammembers of the Key Laboratory of Mathematical Geology inSichuan China They are grateful to Professor HongJun Liu
at ChengduUniversity of Technology for providing construc-tive advice for this studyThey also thank LetPub (httpwwwletpubcom) for its linguistic assistance during the prepara-tion of this manuscript
References
[1] A Darehshiri M Panji and A R Mokhtari ldquoIdentifyinggeochemical anomalies associated with Cu mineralization instream sediment samples in Gharachaman area northwest ofIranrdquo Journal of African Earth Sciences vol 110 pp 92ndash99 2015
[2] X Lu and P Zhao ldquoGeologic anomaly analysis for space-timedistribution of mineral deposits in the middle-lower Yangtzearea southeastern Chinardquo Nonrenewable Resources vol 17 no3 pp 187ndash196 1998
[3] Z Pengda C Qiuming and X Qinglin ldquoQuantitative predic-tion for deep mineral explorationrdquo Journal of China Universityof Geosciences vol 19 no 4 pp 309ndash318 2008
[4] Q Cheng ldquoSingularity theory and methods for mapping geo-chemical anomalies caused by buried sources and for predictingundiscovered mineral deposits in covered areasrdquo Journal ofGeochemical Exploration vol 122 pp 55ndash70 2012
[5] A P Freedman and B Parsons ldquoGeoid anomalies over twoSouth Atlantic fracture zonesrdquo Earth and Planetary ScienceLetters vol 100 no 1ndash3 pp 18ndash41 1990
[6] P Shen Y Shen T Liu L Meng H Dai and Y YangldquoGeochemical signature of porphyries in the Baogutu porphyrycopper belt western Junggar NW Chinardquo Gondwana Researchvol 16 no 2 pp 227ndash242 2009
[7] J Zhao S Chen and R Zuo ldquoIdentifying geochemical anoma-lies associated with AundashCu mineralization using multifractaland artificial neural network models in the Ningqiang districtShaanxi Chinardquo Journal of Geochemical Exploration vol 164pp 54ndash64 2016
[8] P Zhao J Chen J Chen S Zhang and Y Chen ldquoThelsquothree-componentrsquo digital prospecting method a new approachfor mineral resource quantitative prediction and assessmentrdquoNatural Resources Research vol 14 no 4 pp 295ndash303 2005
[9] Q Cheng and P Zhao ldquoSingularity theories and methodsfor characterizing mineralization processes and mapping geo-anomalies for mineral deposit predictionrdquoGeoscience Frontiersvol 2 no 1 pp 67ndash79 2011
[10] Y Chen P Zhao J Chen and J Liu ldquoApplication of the geo-anomaly unit concept in quantitative delineation and assess-ment of gold ore targets in western Shandong uplift terraineastern ChinardquoNatural Resources Research vol 10 no 1 pp 35ndash49 2001
[11] D E Allen A K Singh and R J Powell ldquoExtreme marketrisk-an extreme value theory approachrdquo Mathematics andComputers in Simulation vol 94 pp 310ndash328 2011
[12] Q Chen and X Lv ldquoThe extreme-value dependence betweenthe crude oil price and Chinese stock marketsrdquo InternationalReview of Economics and Finance vol 39 pp 121ndash132 2015
[13] KWhan J Zscheischler R Orth et al ldquoImpact of soil moistureon extreme maximum temperatures in Europerdquo Weather andClimate Extremes vol 9 pp 57ndash67 2015
[14] D Faranda J M Freitas P Guiraud and S Vaienti ldquoSamplinglocal properties of attractors via extreme value theoryrdquo ChaosSolitons and Fractals vol 74 pp 55ndash66 2015
[15] E Vanem ldquoNon-stationary extreme value models to accountfor trends and shifts in the extreme wave climate due to climatechangerdquo Applied Ocean Research vol 52 pp 201ndash211 2015
Mathematical Problems in Engineering 11
[16] D Rivas F Caleyo A Valor and J M Hallen ldquoExtreme valueanalysis applied to pitting corrosion experiments in low carbonsteel comparison of block maxima and peak over thresholdapproachesrdquo Corrosion Science vol 50 no 11 pp 3193ndash32042008
[17] F Ashkar and S-E El Adlouni ldquoAdjusting for small-samplenon-normality of design event estimators under a generalizedPareto distributionrdquo Journal of Hydrology vol 530 pp 384ndash3912015
[18] J D Castillo and I Serra ldquoLikelihood inference for generalizedPareto distributionrdquo Computational Statistics amp Data Analysisvol 83 pp 116ndash128 2015
[19] A T Ergun and J Jun ldquoTime-varying higher-order conditionalmoments and forecasting intraday VaR and Expected ShortfallrdquoThe Quarterly Review of Economics and Finance vol 50 no 3pp 264ndash272 2010
[20] R Gencay and F Selcuk ldquoExtreme value theory and value-at-risk relative performance in emerging marketsrdquo InternationalJournal of Forecasting vol 20 pp 287ndash303 2004
[21] J H T Kim and J Kim ldquoA parametric alternative to the Hillestimator for heavy-tailed distributionsrdquo Journal of Banking ampFinance vol 54 pp 60ndash71 2015
[22] Z-H Feng Y-M Wei and K Wang ldquoEstimating risk for thecarbon market via extreme value theory an empirical analysisof the EU ETSrdquo Applied Energy vol 99 pp 97ndash108 2012
[23] C-C Lee and C-P Chang ldquoNew evidence on the convergenceof per capita carbon dioxide emissions from panel seeminglyunrelated regressions augmented Dickey-Fuller testsrdquo Energyvol 33 no 9 pp 1468ndash1475 2008
[24] G Cao and M Zhang ldquoExtreme values in the Chinese andAmerican stock markets based on detrended fluctuation anal-ysisrdquo Physica A Statistical Mechanics and its Applications vol436 pp 25ndash35 2015
Figure 6 The scatter diagram of the MEF (a) is the MEF of Cu and (b) is the MEF of Au
780 790 800 810 820 830 840 850410
420
430
440
450
460
470
480
Mod
ified
(a)
780 790 800 810 820 830 840 850
029
0295
03
0305
031
0315
032
0325
033
Mod
ified
(b)
Figure 7 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Cu
72 74 76 78 80 82 84 8622
24
26
28
30
32
34
36
Mod
ified
(a)
72 74 76 78 80 82 84 86
031
032
033
034
035
036
037
038
039
04
Mod
ified
(b)
Figure 8 (a) and (b) show the relations between 120573lowast(120583) 120585 and thresholds 120583 of Au
Mathematical Problems in Engineering 9
10
10
08
08
06
06
04
04
02
02
0000
Pareto P-P plot of Cu
Observed cum prob
Expe
cted
cum
pro
b
(a)
100806040200Observed cum prob
10
08
06
04
02
00
Expe
cted
cum
pro
b
Pareto P-P plot of Au
(b)
Figure 9 The GPD fitting of the sample data (a) is the distribution fitting of Cu and (b) is the distribution fitting of Au
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ile13429109378164
class
ifica
tion
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
(a)
1002811755
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ilecla
ssifi
catio
n
(b)
Figure 10 The identified anomaly region of Cu and Au (a) is the anomaly region of Cu and (b) is the anomaly region of Au
selection of the thresholds is reasonable Fitting the excessthreshold of the sample data using the GPD (Figure 9)indicates that the excess threshold of the sample data is inthe vicinity of the line the results show that the theoreticaldistribution and actual distribution of the sample data areconsistent Therefore the threshold selection is reasonableThere are currently seven mining drill holes that is KZK10KZK11 KZK23 KZK28 ZK02618 ZK02619 and ZK02620
and the exploitation ore bodies are mostly VII main orebody in the 26 exploration lines of the Cu-Au mining areaGIS technology is used to show the geological anomalyregion with the selection of the thresholds (Figure 10)From Figure 10 it is seen that the anomaly region of Cuand Au is consistent with the range of ore bodies of theactual engineering exploration which has a high indicatingfunction with respect to ore prospecting The results show
10 Mathematical Problems in Engineering
that the EVT model of the geological anomaly is good atmineral deposit prediction and it has good prospectingsignificance
5 Conclusion
In this study the proposed EVT model of the geologicalanomaly was applied to identify geochemical anomaliesassociated with Cu and Au mineralizationThe results of thisstudy led to the following
(1) The characteristics of the geological anomaly and theprinciple of EVT were studied knowledge of the dis-tribution of the EVT coincides with the distributionof the geological anomaly data The designed EVTmodel of the geological anomaly takes full accountof the characteristic of the geological anomaly andthe practical features of the EVT The thresholdselection and parameter estimates of the model weredetermined
(2) The proposed EVT model of the geological anomalywas successfully applied to identify the geologicalanomaly region in the Jiguanzui Cu-Au mining areaThe results show that the anomaly threshold of Cu is8164006 and that of Au is 754736 the shape param-eter of Cu is 03162 and that of Au is 03342 and thescale parameter of Cu is 4409216 and that of the Auis 315699 The abnormal probability distribution wasalso determined Testing the results of the model byfitting the excess threshold of the sample data showedthat the results of the theoretical distribution andactual distribution of the sample data were consistent
(3) The geological anomalies of Cu and Au predictedby the EVT model are consistent with the rangeof ore bodies of the actual engineering explorationThe EVT model has a high indicating function withrespect to ore prospecting and it is applicable for theexploration of mineral deposits
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This study was supported by the GeophysiochemistryProspecting Institute of the Academy of Geological Scienceof China and the Program for the Core of High Spec-trum of Primary Halo Geochemical Prospecting Project (no12120114002001) and the project of the special funds foruniversities was supported by the central governmentmdashtheconstruction of discipline platform inmanagement engineer-ing theory and quantitative methods (no 80000-14Z019002)The authors are grateful to the First Geological Brigade ofthe Hubei Geological Bureau for providing the data Theywould also like to express their appreciation for the teammembers of the Key Laboratory of Mathematical Geology inSichuan China They are grateful to Professor HongJun Liu
at ChengduUniversity of Technology for providing construc-tive advice for this studyThey also thank LetPub (httpwwwletpubcom) for its linguistic assistance during the prepara-tion of this manuscript
References
[1] A Darehshiri M Panji and A R Mokhtari ldquoIdentifyinggeochemical anomalies associated with Cu mineralization instream sediment samples in Gharachaman area northwest ofIranrdquo Journal of African Earth Sciences vol 110 pp 92ndash99 2015
[2] X Lu and P Zhao ldquoGeologic anomaly analysis for space-timedistribution of mineral deposits in the middle-lower Yangtzearea southeastern Chinardquo Nonrenewable Resources vol 17 no3 pp 187ndash196 1998
[3] Z Pengda C Qiuming and X Qinglin ldquoQuantitative predic-tion for deep mineral explorationrdquo Journal of China Universityof Geosciences vol 19 no 4 pp 309ndash318 2008
[4] Q Cheng ldquoSingularity theory and methods for mapping geo-chemical anomalies caused by buried sources and for predictingundiscovered mineral deposits in covered areasrdquo Journal ofGeochemical Exploration vol 122 pp 55ndash70 2012
[5] A P Freedman and B Parsons ldquoGeoid anomalies over twoSouth Atlantic fracture zonesrdquo Earth and Planetary ScienceLetters vol 100 no 1ndash3 pp 18ndash41 1990
[6] P Shen Y Shen T Liu L Meng H Dai and Y YangldquoGeochemical signature of porphyries in the Baogutu porphyrycopper belt western Junggar NW Chinardquo Gondwana Researchvol 16 no 2 pp 227ndash242 2009
[7] J Zhao S Chen and R Zuo ldquoIdentifying geochemical anoma-lies associated with AundashCu mineralization using multifractaland artificial neural network models in the Ningqiang districtShaanxi Chinardquo Journal of Geochemical Exploration vol 164pp 54ndash64 2016
[8] P Zhao J Chen J Chen S Zhang and Y Chen ldquoThelsquothree-componentrsquo digital prospecting method a new approachfor mineral resource quantitative prediction and assessmentrdquoNatural Resources Research vol 14 no 4 pp 295ndash303 2005
[9] Q Cheng and P Zhao ldquoSingularity theories and methodsfor characterizing mineralization processes and mapping geo-anomalies for mineral deposit predictionrdquoGeoscience Frontiersvol 2 no 1 pp 67ndash79 2011
[10] Y Chen P Zhao J Chen and J Liu ldquoApplication of the geo-anomaly unit concept in quantitative delineation and assess-ment of gold ore targets in western Shandong uplift terraineastern ChinardquoNatural Resources Research vol 10 no 1 pp 35ndash49 2001
[11] D E Allen A K Singh and R J Powell ldquoExtreme marketrisk-an extreme value theory approachrdquo Mathematics andComputers in Simulation vol 94 pp 310ndash328 2011
[12] Q Chen and X Lv ldquoThe extreme-value dependence betweenthe crude oil price and Chinese stock marketsrdquo InternationalReview of Economics and Finance vol 39 pp 121ndash132 2015
[13] KWhan J Zscheischler R Orth et al ldquoImpact of soil moistureon extreme maximum temperatures in Europerdquo Weather andClimate Extremes vol 9 pp 57ndash67 2015
[14] D Faranda J M Freitas P Guiraud and S Vaienti ldquoSamplinglocal properties of attractors via extreme value theoryrdquo ChaosSolitons and Fractals vol 74 pp 55ndash66 2015
[15] E Vanem ldquoNon-stationary extreme value models to accountfor trends and shifts in the extreme wave climate due to climatechangerdquo Applied Ocean Research vol 52 pp 201ndash211 2015
Mathematical Problems in Engineering 11
[16] D Rivas F Caleyo A Valor and J M Hallen ldquoExtreme valueanalysis applied to pitting corrosion experiments in low carbonsteel comparison of block maxima and peak over thresholdapproachesrdquo Corrosion Science vol 50 no 11 pp 3193ndash32042008
[17] F Ashkar and S-E El Adlouni ldquoAdjusting for small-samplenon-normality of design event estimators under a generalizedPareto distributionrdquo Journal of Hydrology vol 530 pp 384ndash3912015
[18] J D Castillo and I Serra ldquoLikelihood inference for generalizedPareto distributionrdquo Computational Statistics amp Data Analysisvol 83 pp 116ndash128 2015
[19] A T Ergun and J Jun ldquoTime-varying higher-order conditionalmoments and forecasting intraday VaR and Expected ShortfallrdquoThe Quarterly Review of Economics and Finance vol 50 no 3pp 264ndash272 2010
[20] R Gencay and F Selcuk ldquoExtreme value theory and value-at-risk relative performance in emerging marketsrdquo InternationalJournal of Forecasting vol 20 pp 287ndash303 2004
[21] J H T Kim and J Kim ldquoA parametric alternative to the Hillestimator for heavy-tailed distributionsrdquo Journal of Banking ampFinance vol 54 pp 60ndash71 2015
[22] Z-H Feng Y-M Wei and K Wang ldquoEstimating risk for thecarbon market via extreme value theory an empirical analysisof the EU ETSrdquo Applied Energy vol 99 pp 97ndash108 2012
[23] C-C Lee and C-P Chang ldquoNew evidence on the convergenceof per capita carbon dioxide emissions from panel seeminglyunrelated regressions augmented Dickey-Fuller testsrdquo Energyvol 33 no 9 pp 1468ndash1475 2008
[24] G Cao and M Zhang ldquoExtreme values in the Chinese andAmerican stock markets based on detrended fluctuation anal-ysisrdquo Physica A Statistical Mechanics and its Applications vol436 pp 25ndash35 2015
Figure 9 The GPD fitting of the sample data (a) is the distribution fitting of Cu and (b) is the distribution fitting of Au
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ile13429109378164
class
ifica
tion
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
(a)
1002811755
0 1724 3448 5172 6896 8620 10344
0 1724 3448 5172 6896 8620 10344352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
352
minus2027
minus4405
minus6783
minus9162
minus11540
minus13918
Drill holeStratigraphic boundaryOre bodiesAnomaly region Q
uant
ilecla
ssifi
catio
n
(b)
Figure 10 The identified anomaly region of Cu and Au (a) is the anomaly region of Cu and (b) is the anomaly region of Au
selection of the thresholds is reasonable Fitting the excessthreshold of the sample data using the GPD (Figure 9)indicates that the excess threshold of the sample data is inthe vicinity of the line the results show that the theoreticaldistribution and actual distribution of the sample data areconsistent Therefore the threshold selection is reasonableThere are currently seven mining drill holes that is KZK10KZK11 KZK23 KZK28 ZK02618 ZK02619 and ZK02620
and the exploitation ore bodies are mostly VII main orebody in the 26 exploration lines of the Cu-Au mining areaGIS technology is used to show the geological anomalyregion with the selection of the thresholds (Figure 10)From Figure 10 it is seen that the anomaly region of Cuand Au is consistent with the range of ore bodies of theactual engineering exploration which has a high indicatingfunction with respect to ore prospecting The results show
10 Mathematical Problems in Engineering
that the EVT model of the geological anomaly is good atmineral deposit prediction and it has good prospectingsignificance
5 Conclusion
In this study the proposed EVT model of the geologicalanomaly was applied to identify geochemical anomaliesassociated with Cu and Au mineralizationThe results of thisstudy led to the following
(1) The characteristics of the geological anomaly and theprinciple of EVT were studied knowledge of the dis-tribution of the EVT coincides with the distributionof the geological anomaly data The designed EVTmodel of the geological anomaly takes full accountof the characteristic of the geological anomaly andthe practical features of the EVT The thresholdselection and parameter estimates of the model weredetermined
(2) The proposed EVT model of the geological anomalywas successfully applied to identify the geologicalanomaly region in the Jiguanzui Cu-Au mining areaThe results show that the anomaly threshold of Cu is8164006 and that of Au is 754736 the shape param-eter of Cu is 03162 and that of Au is 03342 and thescale parameter of Cu is 4409216 and that of the Auis 315699 The abnormal probability distribution wasalso determined Testing the results of the model byfitting the excess threshold of the sample data showedthat the results of the theoretical distribution andactual distribution of the sample data were consistent
(3) The geological anomalies of Cu and Au predictedby the EVT model are consistent with the rangeof ore bodies of the actual engineering explorationThe EVT model has a high indicating function withrespect to ore prospecting and it is applicable for theexploration of mineral deposits
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This study was supported by the GeophysiochemistryProspecting Institute of the Academy of Geological Scienceof China and the Program for the Core of High Spec-trum of Primary Halo Geochemical Prospecting Project (no12120114002001) and the project of the special funds foruniversities was supported by the central governmentmdashtheconstruction of discipline platform inmanagement engineer-ing theory and quantitative methods (no 80000-14Z019002)The authors are grateful to the First Geological Brigade ofthe Hubei Geological Bureau for providing the data Theywould also like to express their appreciation for the teammembers of the Key Laboratory of Mathematical Geology inSichuan China They are grateful to Professor HongJun Liu
at ChengduUniversity of Technology for providing construc-tive advice for this studyThey also thank LetPub (httpwwwletpubcom) for its linguistic assistance during the prepara-tion of this manuscript
References
[1] A Darehshiri M Panji and A R Mokhtari ldquoIdentifyinggeochemical anomalies associated with Cu mineralization instream sediment samples in Gharachaman area northwest ofIranrdquo Journal of African Earth Sciences vol 110 pp 92ndash99 2015
[2] X Lu and P Zhao ldquoGeologic anomaly analysis for space-timedistribution of mineral deposits in the middle-lower Yangtzearea southeastern Chinardquo Nonrenewable Resources vol 17 no3 pp 187ndash196 1998
[3] Z Pengda C Qiuming and X Qinglin ldquoQuantitative predic-tion for deep mineral explorationrdquo Journal of China Universityof Geosciences vol 19 no 4 pp 309ndash318 2008
[4] Q Cheng ldquoSingularity theory and methods for mapping geo-chemical anomalies caused by buried sources and for predictingundiscovered mineral deposits in covered areasrdquo Journal ofGeochemical Exploration vol 122 pp 55ndash70 2012
[5] A P Freedman and B Parsons ldquoGeoid anomalies over twoSouth Atlantic fracture zonesrdquo Earth and Planetary ScienceLetters vol 100 no 1ndash3 pp 18ndash41 1990
[6] P Shen Y Shen T Liu L Meng H Dai and Y YangldquoGeochemical signature of porphyries in the Baogutu porphyrycopper belt western Junggar NW Chinardquo Gondwana Researchvol 16 no 2 pp 227ndash242 2009
[7] J Zhao S Chen and R Zuo ldquoIdentifying geochemical anoma-lies associated with AundashCu mineralization using multifractaland artificial neural network models in the Ningqiang districtShaanxi Chinardquo Journal of Geochemical Exploration vol 164pp 54ndash64 2016
[8] P Zhao J Chen J Chen S Zhang and Y Chen ldquoThelsquothree-componentrsquo digital prospecting method a new approachfor mineral resource quantitative prediction and assessmentrdquoNatural Resources Research vol 14 no 4 pp 295ndash303 2005
[9] Q Cheng and P Zhao ldquoSingularity theories and methodsfor characterizing mineralization processes and mapping geo-anomalies for mineral deposit predictionrdquoGeoscience Frontiersvol 2 no 1 pp 67ndash79 2011
[10] Y Chen P Zhao J Chen and J Liu ldquoApplication of the geo-anomaly unit concept in quantitative delineation and assess-ment of gold ore targets in western Shandong uplift terraineastern ChinardquoNatural Resources Research vol 10 no 1 pp 35ndash49 2001
[11] D E Allen A K Singh and R J Powell ldquoExtreme marketrisk-an extreme value theory approachrdquo Mathematics andComputers in Simulation vol 94 pp 310ndash328 2011
[12] Q Chen and X Lv ldquoThe extreme-value dependence betweenthe crude oil price and Chinese stock marketsrdquo InternationalReview of Economics and Finance vol 39 pp 121ndash132 2015
[13] KWhan J Zscheischler R Orth et al ldquoImpact of soil moistureon extreme maximum temperatures in Europerdquo Weather andClimate Extremes vol 9 pp 57ndash67 2015
[14] D Faranda J M Freitas P Guiraud and S Vaienti ldquoSamplinglocal properties of attractors via extreme value theoryrdquo ChaosSolitons and Fractals vol 74 pp 55ndash66 2015
[15] E Vanem ldquoNon-stationary extreme value models to accountfor trends and shifts in the extreme wave climate due to climatechangerdquo Applied Ocean Research vol 52 pp 201ndash211 2015
Mathematical Problems in Engineering 11
[16] D Rivas F Caleyo A Valor and J M Hallen ldquoExtreme valueanalysis applied to pitting corrosion experiments in low carbonsteel comparison of block maxima and peak over thresholdapproachesrdquo Corrosion Science vol 50 no 11 pp 3193ndash32042008
[17] F Ashkar and S-E El Adlouni ldquoAdjusting for small-samplenon-normality of design event estimators under a generalizedPareto distributionrdquo Journal of Hydrology vol 530 pp 384ndash3912015
[18] J D Castillo and I Serra ldquoLikelihood inference for generalizedPareto distributionrdquo Computational Statistics amp Data Analysisvol 83 pp 116ndash128 2015
[19] A T Ergun and J Jun ldquoTime-varying higher-order conditionalmoments and forecasting intraday VaR and Expected ShortfallrdquoThe Quarterly Review of Economics and Finance vol 50 no 3pp 264ndash272 2010
[20] R Gencay and F Selcuk ldquoExtreme value theory and value-at-risk relative performance in emerging marketsrdquo InternationalJournal of Forecasting vol 20 pp 287ndash303 2004
[21] J H T Kim and J Kim ldquoA parametric alternative to the Hillestimator for heavy-tailed distributionsrdquo Journal of Banking ampFinance vol 54 pp 60ndash71 2015
[22] Z-H Feng Y-M Wei and K Wang ldquoEstimating risk for thecarbon market via extreme value theory an empirical analysisof the EU ETSrdquo Applied Energy vol 99 pp 97ndash108 2012
[23] C-C Lee and C-P Chang ldquoNew evidence on the convergenceof per capita carbon dioxide emissions from panel seeminglyunrelated regressions augmented Dickey-Fuller testsrdquo Energyvol 33 no 9 pp 1468ndash1475 2008
[24] G Cao and M Zhang ldquoExtreme values in the Chinese andAmerican stock markets based on detrended fluctuation anal-ysisrdquo Physica A Statistical Mechanics and its Applications vol436 pp 25ndash35 2015
that the EVT model of the geological anomaly is good atmineral deposit prediction and it has good prospectingsignificance
5 Conclusion
In this study the proposed EVT model of the geologicalanomaly was applied to identify geochemical anomaliesassociated with Cu and Au mineralizationThe results of thisstudy led to the following
(1) The characteristics of the geological anomaly and theprinciple of EVT were studied knowledge of the dis-tribution of the EVT coincides with the distributionof the geological anomaly data The designed EVTmodel of the geological anomaly takes full accountof the characteristic of the geological anomaly andthe practical features of the EVT The thresholdselection and parameter estimates of the model weredetermined
(2) The proposed EVT model of the geological anomalywas successfully applied to identify the geologicalanomaly region in the Jiguanzui Cu-Au mining areaThe results show that the anomaly threshold of Cu is8164006 and that of Au is 754736 the shape param-eter of Cu is 03162 and that of Au is 03342 and thescale parameter of Cu is 4409216 and that of the Auis 315699 The abnormal probability distribution wasalso determined Testing the results of the model byfitting the excess threshold of the sample data showedthat the results of the theoretical distribution andactual distribution of the sample data were consistent
(3) The geological anomalies of Cu and Au predictedby the EVT model are consistent with the rangeof ore bodies of the actual engineering explorationThe EVT model has a high indicating function withrespect to ore prospecting and it is applicable for theexploration of mineral deposits
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This study was supported by the GeophysiochemistryProspecting Institute of the Academy of Geological Scienceof China and the Program for the Core of High Spec-trum of Primary Halo Geochemical Prospecting Project (no12120114002001) and the project of the special funds foruniversities was supported by the central governmentmdashtheconstruction of discipline platform inmanagement engineer-ing theory and quantitative methods (no 80000-14Z019002)The authors are grateful to the First Geological Brigade ofthe Hubei Geological Bureau for providing the data Theywould also like to express their appreciation for the teammembers of the Key Laboratory of Mathematical Geology inSichuan China They are grateful to Professor HongJun Liu
at ChengduUniversity of Technology for providing construc-tive advice for this studyThey also thank LetPub (httpwwwletpubcom) for its linguistic assistance during the prepara-tion of this manuscript
References
[1] A Darehshiri M Panji and A R Mokhtari ldquoIdentifyinggeochemical anomalies associated with Cu mineralization instream sediment samples in Gharachaman area northwest ofIranrdquo Journal of African Earth Sciences vol 110 pp 92ndash99 2015
[2] X Lu and P Zhao ldquoGeologic anomaly analysis for space-timedistribution of mineral deposits in the middle-lower Yangtzearea southeastern Chinardquo Nonrenewable Resources vol 17 no3 pp 187ndash196 1998
[3] Z Pengda C Qiuming and X Qinglin ldquoQuantitative predic-tion for deep mineral explorationrdquo Journal of China Universityof Geosciences vol 19 no 4 pp 309ndash318 2008
[4] Q Cheng ldquoSingularity theory and methods for mapping geo-chemical anomalies caused by buried sources and for predictingundiscovered mineral deposits in covered areasrdquo Journal ofGeochemical Exploration vol 122 pp 55ndash70 2012
[5] A P Freedman and B Parsons ldquoGeoid anomalies over twoSouth Atlantic fracture zonesrdquo Earth and Planetary ScienceLetters vol 100 no 1ndash3 pp 18ndash41 1990
[6] P Shen Y Shen T Liu L Meng H Dai and Y YangldquoGeochemical signature of porphyries in the Baogutu porphyrycopper belt western Junggar NW Chinardquo Gondwana Researchvol 16 no 2 pp 227ndash242 2009
[7] J Zhao S Chen and R Zuo ldquoIdentifying geochemical anoma-lies associated with AundashCu mineralization using multifractaland artificial neural network models in the Ningqiang districtShaanxi Chinardquo Journal of Geochemical Exploration vol 164pp 54ndash64 2016
[8] P Zhao J Chen J Chen S Zhang and Y Chen ldquoThelsquothree-componentrsquo digital prospecting method a new approachfor mineral resource quantitative prediction and assessmentrdquoNatural Resources Research vol 14 no 4 pp 295ndash303 2005
[9] Q Cheng and P Zhao ldquoSingularity theories and methodsfor characterizing mineralization processes and mapping geo-anomalies for mineral deposit predictionrdquoGeoscience Frontiersvol 2 no 1 pp 67ndash79 2011
[10] Y Chen P Zhao J Chen and J Liu ldquoApplication of the geo-anomaly unit concept in quantitative delineation and assess-ment of gold ore targets in western Shandong uplift terraineastern ChinardquoNatural Resources Research vol 10 no 1 pp 35ndash49 2001
[11] D E Allen A K Singh and R J Powell ldquoExtreme marketrisk-an extreme value theory approachrdquo Mathematics andComputers in Simulation vol 94 pp 310ndash328 2011
[12] Q Chen and X Lv ldquoThe extreme-value dependence betweenthe crude oil price and Chinese stock marketsrdquo InternationalReview of Economics and Finance vol 39 pp 121ndash132 2015
[13] KWhan J Zscheischler R Orth et al ldquoImpact of soil moistureon extreme maximum temperatures in Europerdquo Weather andClimate Extremes vol 9 pp 57ndash67 2015
[14] D Faranda J M Freitas P Guiraud and S Vaienti ldquoSamplinglocal properties of attractors via extreme value theoryrdquo ChaosSolitons and Fractals vol 74 pp 55ndash66 2015
[15] E Vanem ldquoNon-stationary extreme value models to accountfor trends and shifts in the extreme wave climate due to climatechangerdquo Applied Ocean Research vol 52 pp 201ndash211 2015
Mathematical Problems in Engineering 11
[16] D Rivas F Caleyo A Valor and J M Hallen ldquoExtreme valueanalysis applied to pitting corrosion experiments in low carbonsteel comparison of block maxima and peak over thresholdapproachesrdquo Corrosion Science vol 50 no 11 pp 3193ndash32042008
[17] F Ashkar and S-E El Adlouni ldquoAdjusting for small-samplenon-normality of design event estimators under a generalizedPareto distributionrdquo Journal of Hydrology vol 530 pp 384ndash3912015
[18] J D Castillo and I Serra ldquoLikelihood inference for generalizedPareto distributionrdquo Computational Statistics amp Data Analysisvol 83 pp 116ndash128 2015
[19] A T Ergun and J Jun ldquoTime-varying higher-order conditionalmoments and forecasting intraday VaR and Expected ShortfallrdquoThe Quarterly Review of Economics and Finance vol 50 no 3pp 264ndash272 2010
[20] R Gencay and F Selcuk ldquoExtreme value theory and value-at-risk relative performance in emerging marketsrdquo InternationalJournal of Forecasting vol 20 pp 287ndash303 2004
[21] J H T Kim and J Kim ldquoA parametric alternative to the Hillestimator for heavy-tailed distributionsrdquo Journal of Banking ampFinance vol 54 pp 60ndash71 2015
[22] Z-H Feng Y-M Wei and K Wang ldquoEstimating risk for thecarbon market via extreme value theory an empirical analysisof the EU ETSrdquo Applied Energy vol 99 pp 97ndash108 2012
[23] C-C Lee and C-P Chang ldquoNew evidence on the convergenceof per capita carbon dioxide emissions from panel seeminglyunrelated regressions augmented Dickey-Fuller testsrdquo Energyvol 33 no 9 pp 1468ndash1475 2008
[24] G Cao and M Zhang ldquoExtreme values in the Chinese andAmerican stock markets based on detrended fluctuation anal-ysisrdquo Physica A Statistical Mechanics and its Applications vol436 pp 25ndash35 2015
[16] D Rivas F Caleyo A Valor and J M Hallen ldquoExtreme valueanalysis applied to pitting corrosion experiments in low carbonsteel comparison of block maxima and peak over thresholdapproachesrdquo Corrosion Science vol 50 no 11 pp 3193ndash32042008
[17] F Ashkar and S-E El Adlouni ldquoAdjusting for small-samplenon-normality of design event estimators under a generalizedPareto distributionrdquo Journal of Hydrology vol 530 pp 384ndash3912015
[18] J D Castillo and I Serra ldquoLikelihood inference for generalizedPareto distributionrdquo Computational Statistics amp Data Analysisvol 83 pp 116ndash128 2015
[19] A T Ergun and J Jun ldquoTime-varying higher-order conditionalmoments and forecasting intraday VaR and Expected ShortfallrdquoThe Quarterly Review of Economics and Finance vol 50 no 3pp 264ndash272 2010
[20] R Gencay and F Selcuk ldquoExtreme value theory and value-at-risk relative performance in emerging marketsrdquo InternationalJournal of Forecasting vol 20 pp 287ndash303 2004
[21] J H T Kim and J Kim ldquoA parametric alternative to the Hillestimator for heavy-tailed distributionsrdquo Journal of Banking ampFinance vol 54 pp 60ndash71 2015
[22] Z-H Feng Y-M Wei and K Wang ldquoEstimating risk for thecarbon market via extreme value theory an empirical analysisof the EU ETSrdquo Applied Energy vol 99 pp 97ndash108 2012
[23] C-C Lee and C-P Chang ldquoNew evidence on the convergenceof per capita carbon dioxide emissions from panel seeminglyunrelated regressions augmented Dickey-Fuller testsrdquo Energyvol 33 no 9 pp 1468ndash1475 2008
[24] G Cao and M Zhang ldquoExtreme values in the Chinese andAmerican stock markets based on detrended fluctuation anal-ysisrdquo Physica A Statistical Mechanics and its Applications vol436 pp 25ndash35 2015
