An rescaled range analysis on the characteristics of coal seam development in the Eastern depression

Mining Science and Technology(China)21(2011)223-227Contents lists available at science DirectMining Science and Technology(China)ELSEVIERjournalhomepagewww.elsevier.com/locate/mstcAn rescaled range analysis on the characteristics of coal seam development in theEastern depression of the liaohe basinZhao Zhongying., Wang Yulin Liu Guangdi, Sun Xiang.. State Key Laboratory of petroleum Resource and Prospecting Chtna Uniwersity of petroleum, Effing 102249, Chinab College of Resource and Emvironment Engineering Liaoning Technical University Liaoning 123000, China"State Key Laboratory of Geological Processes and Mineral Resource, China University of Geosciences, Beijing 100083, ChinaARTICLE INFOA BSTRACTeceived 29 August 2010evaluated for the Liaohe Basin located in China. The Number 3 and Number 9 coal seam thickness seriesfrom 60 nearly equally spaced bores in the Eastern depression of the Liaohe Basin were examined byccepted 23 October 2010a rescaled range analysis. The results indicate that the hurst exponents of the Number 3 and Number 9the bore spacing increases the hurst exponent of the Number 3 series gradually decreases(H changesfrom 0.69 to 0.52)and shifts from persistence to randomness, The Hurst exponent of the Number 9thickness data gradually increases(H changes from 0.68 to 0.91)and always shows the characteristic ofpersistence. A combination of geological characteristics and the series data allow theEastem depressionmore suitable for the Number 9 coal seam to form in the Northeasterm part of the Eastern depressionLiaohe Basinthan the number 3 coal seamCopyright o 2011, China University of Mining Technology. All rights reserved.1. IntroductionQuantitative information is expressed by the Hurst exponent, HThe value of H always lies between 0 and 1 and is equal to 0.Since Mandelbrots coining of the word"fractal"more than two purely random observations, for example, Brownian motion. An Hdecades ago[1, 2 fractal and multi-fractal models have been applied value larger than 0.5 shows persistence while values less than 0.5to several phenomena in the natural sciences to describe the irreg. show anti-persistence. these terms characterize the way in whichlarity of geological features or the time and spatial distribution of the value of a previous time step influences the probability ofgeological objects [3-9 Scale invariance plays an important role in subsequent time steps as they occur within these processesfractal geometry and provides the basis for the definition of the Although these methods have previously been applied toseveral fractal dimensions that are associated with the geometric a number of time series related to geological events, and greatcharacteristics, or the dynamical behavior, of these systems.achievements have been made a space series of geological eventsThe rescaled range analysis, or R/s analysis, first introduced by has not yet been extensively investigated. In this article, weHurst while studying water storage problems related to the Nile describe the use of an R/s analysis method to quantify theiver, has been used to investigate scale properties of time series complexity of coal seam distribution, to reveal the characteristics ofrelated to several geophysical or geological events. These events coal seam development, and to be helpful for the study of coalnclude such things as precipitation, temperature, sea level, the gasification member of the shahejie formation in the Easternock market, earthquakes and landslides, deformation and fracture depression of the liaohe basin, China.of coal and rock, and mine inflows[10-19]. The method providesis it possible to identify a persistent, anti-persistent, or a purely 2 Geological settingandom character in the time seriesThe Liaohe Basin is located in the northem part ofa northeast( NE)trending Palaeogene rift and Neogened into seven tectonic units: the Shen中国煤化工 /estern dep-le central uplil1674-5264/5-see front matter Copyright o 2011, China University of Mining Technology. AllCNMHGdoi:101016/mstc20110201Z Zhongying et al/ Mining Science and Technology(China)21(2011)223-227henyangAnshanStudFig- 1. Location of the Liaohe Basin in China (a), tectonic division of the Liaohe Basin (b) and sequence of the third member of the Shahejie formation in the Eastern depression(c)Eastern slope(Fig1b) The basement is composed of Archean的h-z之頊metamorphic rocks and Mesozoic Upper Jurassic and LowerCretaceous sedimentary-volcanic rocksThe Eastern depression is an NE-trending tectonic unit in theNow let X(a t)be the difference between E()and )r defined asLiaohe Basin with an area of 3950 km. The sedimentary sequencesan be divided into four formations: the Palaeogene Fangshenpao, X(aj, t)->I5(0-5), 1 sjste Shahejie and Dongying, the Neogene Guantao, and the minghuazhen. Among these the third member of the shahejie Forma-The range, R, and the standard variation, S, are given bytion(Es])is the most important coal bearing stratum[20-23lCoal seams are distributed widely in the Eastern depression R()=max x(i, t)with a total area of 200 km. they can be divided into 11 coalmin x(, T)ams, among which Number l to Number 5 coal seams are in theupper coal seam group and Number 6 to Number 11 coal seams S(r)s(=(∑{0-(2(4)Number 9 coal seams are the main coal seams that are controlledby the syndepositional faults and are distributed in the directionFor each value of the space span,of ne, 35 to 45, similar to the strike of the Eastern depressionThe effect of the sedimentary environment causes them to be R()/S()aTHdistributed discontinuously from the southwest(Sw) to the NEmay be obtained, where H denotes the hurst exponent.Equation(5)is known as"Hursts empirical law"and it repre-3. RS analysissents a fitted straight line in a log- log plot of r/S as a function of t.His the slope of the straight line.seam thickness. Let (a1, a2,..., an be a spaced series of bores and (5 4. Results and discussionn)be the coal seam thickness series from the correspondingresIn any given space span, t, the average coal seam thickness is The coal seam thickness data comprisegiven byNumber 3 and Number 9 coal seams taken from 60 bores hay己03m中国煤化工>CNMHGFi 2 Contour map showing coal seam thickness in the third member of the Shahejie formation in the Eastem depression.Z Zhongying et aL/ Mining Science and Technology(China)21(2011)223-227Table 2Types of data set for RiS analysis.Hurst exponents of the data.Hurst exponentNo. 3 coal seamNo 9 coal seamAn array of 20 coal seam thickness measurements. Each datumis the average of every three coal seam thickness data taken inthe order of the 60 bores.series from Point a to point b as a way of determining if the seriesfollowed a fractal distribution. the 30 average thickness datformed data set ll while the 20 averaged data were data set Illnearly equal spacing. The bores are distributed in the direction ofSw (Table 1). Figures 4b and 4c show the Hurst exponent of theto NE in the Easternn( Fig. 2).Let bore"Rong 60"be the first Number 3 coal seam thickness, data set ll and data set Ill. Figre( Point A in Fig. 2)to order the bore numbers in the direction of and 4f show the hurst exponent of the equivalent Number 9 data.SWto NE. Then bore"Niu6"is designated as the 60th bore ( Point B in The Hurst exponents indicate that the thickness series from bothFig. 2). Now the data from these bores form a space series data set Number 3 and Number 9 coal seams follow a fractal distribution. An(data set i in Table 1)taken in the order of the bore number. the increase in bore spacing causes the Hurst exponent of the Number 3average thickness of the Number 3 and Number 9 coal seams is about thickness data to gradually decrease as it shifts from persistence to3.5 m and the maximum thickness is about 12 m( Fig 3).randomness, The Hurst exponent of the Number 9 coal seriesFigures 4a and 4d show the Hurst exponent of the Number 3 and gradually increases and always shows the characteristic of persis-Number 9 coal seam thickness series as estimated by means of rs tence(Table 2). This suggests that the coal seams may haveanalysis of data set L These thickness data follow a fractal distribu- different development features. It is more suitable for thetion and the goodness of fit is greater than 0.98. Their Hurst expo- coal seam to have formed in the Northeastern part ofnents are 0.69 and 0.68, respectively, which indicates the presence of depression than the Number 3 coal seam, which is alsosistence in these coal seam thickness series(Table 2).by the geological characteristics of the Eastern depression.The averages of every two thickness data, and separately ofThe coal seams in the eastern depression formed within a peatevery three thickness data, were calculated in the order of the swamp distributed between an alluvial fan and a surviving lakeBore numberBore numberNo.3 coalNo 9 coal seam3. Plots of coal seam thickness versus bore number in the Eastern depression.06917x044136827x0427305184x0.0977EIsER15R0975E1sR209872Data set I. No. 3 coal seamData set Il. No. 3 coal seamData set IIL. No. 3 coal seamy=06768x04189ey=0.769x0.5883y=0.9117x0.7489R2-0.9843中国煤化工Data set I. No 9 coalCNMHG配4 Double log plot of R/sw.【Z Zhongying et al./ Mining Science and Technology( China)21(2011)223-227g2385a. Xinkai alluvial fan; b, Dongjiagang alluvial fan; c. Shaling alluvial fan; d, North Oulituozi alluvial fan; e Dawan alluvial fan;f. Ciyutuozi alluvial fan; g. Yongle alluvial fan; h Qinglongtai alluvial fan; i East Ping annongchang alluvial fan; j. East Rongxingtun alluvial fan;1. Alluvial fan; 2. Fluvial deposits; 3. Peat swamp; 4. Shore-shallow lake; 5. Erosion area; 6. Bore location; A. No. 3 coal seam; B No 9 coal seamFig. 5. Sketch of the coal-accumulating environment in the third member of the Shahejie formation in the Easterm depression(modified after Reference [20n(Fig. 5). During the formation of the Number 3 coal seam the lake Referencesquickly shrank and the peat swamp disappeared in the North-eastern part of the Eastern depression as the Yongle alluvial fan I11 Mandelbrot BB. The fractal geometry of nature. San Francisca, CA: Freeman:progressed.As a result the area was not suitable for formation of n uals e ature 1984:308 721-2.the Number 3 coal seam. However during the formation of theNumber 9 coal seam the peat swamp existed throughout in the [3I Turcotte DL Fractals and chaos in geology and geophysics. Cambridge, UKareas neighboring the border of a fan delta plain and fan delta front.Areas of lake shore existed in the Northeastern part of the EasternElbrond J. Tang X, editors. Application ofdepression and as a result the area was suitable for the formation of24th APCOM Syrthe number 9 coal seam15) Cheng oM. agterberg Fp. Ballantyne SB. The separation of geochemi16] Wang Z Cheng QM, Cao L Xia QL Chen Z]. fractal modeling of the micro-Derty of quartz mylonite during deformation process. Mat1. An R/S analysis of thickness data from the Number 3 and [7] Zhang w, Liang CH. Study of pitting morphology fractal characteristic ofhejie formation in the Eastern depression of the Liaohe Basin, 18) Rine d hnol 2004: 1432856-ss steel in Fecs environment j China UnivNumber 9 coal seams located in the third member of the sha-China, was presented. The seam thickness data follow a fractaldeposits meaningful? Nat Resour Res 2008; 17: 87-97.suggest the presence of persistence in the coal seam thickness 10) Upor 19( 3 ):321-5wer distribution systatdistribution and their Hurst exponents are 0.69 and 0.68 [9 Liu jH, Liang R Wang CL Fan DP. Application of fractal theory in detecting lowin coal mines Mining Sd Technolng-term storage capacity of reservoirs. Trans Am soc Civ2. As the bore spacing increases the Hurst exponent of the Hurst H, l ck RPa smacks M Long-term storage: an experimental studyNumber 3 thickness seriesdecreases suggesting [12] Miranda JGV. Andrade RFS Rescaled range analysis of pluviometric records inchange from persistence teess. The Hurst exponent3. 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