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An rescaled range analysis on the characteristics of coal seam development in the Eastern depression of the Liaohe Basin
Mining Science and Technology (China) 21 (2011) 223e227
Contents lists available at ScienceDirect
Mining Science and Technology (China) journal homepage: www.elsevier.com/locate/mstc
An rescaled range analysis on the characteristics of coal seam development in the Eastern depression of the Liaohe Basin Zhao Zhongying a, *, Wang Yulin b, Liu Guangdi a, Sun Xiang c a
State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum, Beijing 102249, China College of Resource and Environment Engineering, Liaoning Technical University, Liaoning 123000, China c State Key Laboratory of Geological Processes and Mineral Resource, China University of Geosciences, Beijing 100083, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 August 2010 Received in revised form 30 September 2010 Accepted 23 October 2010
The characteristics of coal seam development, and the prospects of a favorable coal-forming area, were evaluated for the Liaohe Basin located in China. The Number 3 and Number 9 coal seam thickness series from 60 nearly equally spaced bores in the Eastern depression of the Liaohe Basin were examined by a rescaled range analysis. The results indicate that the Hurst exponents of the Number 3 and Number 9 coal seam thickness series are 0.69 and 0.68, respectively. This suggests the presence of persistence. As the bore spacing increases the Hurst exponent of the Number 3 series gradually decreases (H changes from 0.69 to 0.52) and shifts from persistence to randomness. The Hurst exponent of the Number 9 thickness data gradually increases (H changes from 0.68 to 0.91) and always shows the characteristic of persistence. A combination of geological characteristics and the series data allow the conclusion that it is more suitable for the Number 9 coal seam to form in the Northeastern part of the Eastern depression than the Number 3 coal seam. Copyright Ó 2011, China University of Mining & Technology. All rights reserved.
Keywords: Rescaled range analysis Hurst exponent Coal seam thickness Eastern depression Liaohe Basin
1. Introduction Since Mandelbrot’s coining of the word “fractal” more than two decades ago [1,2] fractal and multi-fractal models have been applied to several phenomena in the natural sciences to describe the irregularity of geological features or the time and spatial distribution of geological objects [3e9]. Scale invariance plays an important role in fractal geometry and provides the basis for the definition of the several fractal dimensions that are associated with the geometric characteristics, or the dynamical behavior, of these systems. The rescaled range analysis, or R/S analysis, first introduced by Hurst while studying water storage problems related to the Nile River, has been used to investigate scale properties of time series related to several geophysical or geological events. These events include such things as precipitation, temperature, sea level, the stock market, earthquakes and landslides, deformation and fracture of coal and rock, and mine inflows [10e19]. The method provides important statistical information about a record over time, namely, is it possible to identify a persistent, anti-persistent, or a purely random character in the time series.
* Corresponding author. Tel.: þ86 10 89734480. E-mail address: [email protected] (Z. Zhongying).
Quantitative information is expressed by the Hurst exponent, H. The value of H always lies between 0 and 1 and is equal to 0.5 for purely random observations, for example, Brownian motion. An H value larger than 0.5 shows persistence while values less than 0.5 show anti-persistence. These terms characterize the way in which the value of a previous time step influences the probability of subsequent time steps as they occur within these processes. Although these methods have previously been applied to a number of time series related to geological events, and great achievements have been made, a space series of geological events has not yet been extensively investigated. In this article, we describe the use of an R/S analysis method to quantify the complexity of coal seam distribution, to reveal the characteristics of coal seam development, and to be helpful for the study of coal gasification member of the Shahejie formation in the Eastern depression of the Liaohe Basin, China. 2. Geological setting The Liaohe Basin is located in the northern part of China. It is a northeast (NE)-trending Palaeogene rift and Neogene sag basin that can be divided into seven tectonic units: the Shenbei depression, the Damintun depression, the Western depression, the Eastern depression, the Western slope, the central uplift, and the
1674-5264/$ e see front matter Copyright Ó 2011, China University of Mining & Technology. All rights reserved. doi:10.1016/j.mstc.2011.02.011
224
Z. Zhongying et al. / Mining Science and Technology (China) 21 (2011) 223e227
Fig. 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 (Fig. 1b). The basement is composed of Archean metamorphic rocks and Mesozoic Upper Jurassic and Lower Cretaceous sedimentary-volcanic rocks. The Eastern depression is an NE-trending tectonic unit in the Liaohe Basin with an area of 3950 km2. The sedimentary sequences can be divided into four formations: the Palaeogene Fangshenpao, the Shahejie and Dongying, the Neogene Guantao, and the Minghuazhen. Among these the third member of the Shahejie Formation (Es3) is the most important coal bearing stratum [20e23]. Coal seams are distributed widely in the Eastern depression with a total area of 200 km2. They can be divided into 11 coal seams, among which Number 1 to Number 5 coal seams are in the upper coal seam group and Number 6 to Number 11 coal seams are in the lower coal seam group (Fig. 1c). The Number 3 and Number 9 coal seams are the main coal seams that are controlled by the syndepositional faults and are distributed in the direction of NE, 35 to 45 , similar to the strike of the Eastern depression. The effect of the sedimentary environment causes them to be distributed discontinuously from the southwest (SW) to the NE (Fig. 2). 3. R/S analysis As an introduction to R/S analysis, let us consider the case of coal seam thickness. Let {a1, a2, ., an} be a spaced series of bores and {x1, x2, ., xn} be the coal seam thickness series from the corresponding bores. In any given space span, s, the average coal seam thickness is given by
hxis ¼
s 1X
s i¼1
xðiÞ
(1)
Now let X(aj, s) be the difference between x(i) and hxis , defined as j X xðiÞ hxis ; X aj ; s ¼
1js
(2)
i¼1
The range, R, and the standard variation, S, are given by
RðsÞ ¼ max Xði; sÞ min Xði; sÞ 1is
SðsÞ ¼
s 1X
s i¼1
1is
xðiÞ hxis
2
(3)
!1=2 (4)
For each value of the space span, s, an R/S number that follows the power law
RðsÞ=SðsÞfsH
(5)
may be obtained, where H denotes the Hurst exponent. Equation (5) is known as “Hurst’s empirical law” and it represents a fitted straight line in a log-log plot of R/S as a function of s. H is the slope of the straight line. 4. Results and discussion The coal seam thickness data comprise thickness data from Number 3 and Number 9 coal seams taken from 60 bores having
Fig. 2. Contour map showing coal seam thickness in the third member of the Shahejie formation in the Eastern depression.
Z. Zhongying et al. / Mining Science and Technology (China) 21 (2011) 223e227 Table 1 Types of data set for R/S analysis.
Table 2 Hurst exponents of the data.
Data set
Description
I
An array of 60 coal seam thickness measurements. Each datum is from every coal seam taken in the order of the 60 bores. An array of 30 coal seam thickness measurements. Each datum is the average of every two coal seam thickness data paired in the order of the 60 bores. An array of 20 coal seam thickness measurements. Each datum is the average of every three coal seam thickness data taken in the order of the 60 bores.
II
III
225
Data set
nearly equal spacing. The bores are distributed in the direction of SW to NE in the Eastern depression (Fig. 2). Let bore “Rong60” be the first bore (Point A in Fig. 2) to order the bore numbers in the direction of SW to NE. Then bore “Niu6” is designated as the 60th bore (Point B in Fig. 2). Now the data from these bores form a space series data set (data set I in Table 1) taken in the order of the bore number. The average thickness of the Number 3 and Number 9 coal seams is about 3.5 m and the maximum thickness is about 12 m (Fig. 3). Figures 4a and 4d show the Hurst exponent of the Number 3 and Number 9 coal seam thickness series as estimated by means of R/S analysis of data set I. These thickness data follow a fractal distribution and the goodness of fit is greater than 0.98. Their Hurst exponents are 0.69 and 0.68, respectively, which indicates the presence of persistence in these coal seam thickness series (Table 2). The averages of every two thickness data, and separately of every three thickness data, were calculated in the order of the
I II III
Hurst exponent No. 3 coal seam
No. 9 coal seam
0.69 0.68 0.52
0.68 0.77 0.91
series from Point A to Point B as a way of determining if the series followed a fractal distribution. The 30 average thickness data formed data set II while the 20 averaged data were data set III (Table 1). Figures 4b and 4c show the Hurst exponent of the Number 3 coal seam thickness, data set II and data set III. Figures 4e and 4f show the Hurst exponent of the equivalent Number 9 data. The Hurst exponents indicate that the thickness series from both Number 3 and Number 9 coal seams follow a fractal distribution. An increase in bore spacing causes the Hurst exponent of the Number 3 thickness data to gradually decrease as it shifts from persistence to randomness. The Hurst exponent of the Number 9 coal series gradually increases and always shows the characteristic of persistence (Table 2). This suggests that the coal seams may have different development features. It is more suitable for the Number 9 coal seam to have formed in the Northeastern part of the Eastern depression than the Number 3 coal seam, which is also confirmed by the geological characteristics of the Eastern depression. The coal seams in the Eastern depression formed within a peat swamp distributed between an alluvial fan and a surviving lake
Fig. 3. Plots of coal seam thickness versus bore number in the Eastern depression.
Fig. 4. Double log plot of R/S vs. s.
226
Z. Zhongying et al. / Mining Science and Technology (China) 21 (2011) 223e227
Fig. 5. Sketch of the coal-accumulating environment in the third member of the Shahejie formation in the Eastern depression (modified after Reference [20]).
(Fig. 5). During the formation of the Number 3 coal seam the lake quickly shrank and the peat swamp disappeared in the Northeastern part of the Eastern depression as the Yongle alluvial fan progressed. As a result the area was not suitable for formation of the Number 3 coal seam. However, during the formation of the Number 9 coal seam the peat swamp existed throughout in the areas neighboring the border of a fan delta plain and fan delta front. Areas of lake shore existed in the Northeastern part of the Eastern depression and as a result the area was suitable for the formation of the Number 9 coal seam.
5. Conclusions 1. An R/S analysis of thickness data from the Number 3 and Number 9 coal seams located in the third member of the Shahejie formation in the Eastern depression of the Liaohe Basin, China, was presented. The seam thickness data follow a fractal distribution and their Hurst exponents are 0.69 and 0.68 (Number 3 and Number 9, respectively). The Hurst exponents suggest the presence of persistence in the coal seam thickness series. 2. As the bore spacing increases the Hurst exponent of the Number 3 thickness series gradually decreases suggesting a change from persistence to randomness. The Hurst exponent of the Number 9 coal seam data gradually increases and always shows the characteristics of persistence. 3. The R/S analysis combined with the known geological characteristics suggests that it is more suitable for the Number 9 coal seam to have formed in the Northeastern part of the Eastern depression than the Number 3 coal seam.
Acknowledgements This research was supported by National Basic Research Program of China (No. 2007CB209503).
References [1] Mandelbrot BB. The fractal geometry of nature. San Francisco, CA: Freeman; 1982. [2] Mandelbrot BB, Passoja DE, Paullay AJ. Fractal character of fracture surfaces of metals. Nature 1984;308:721e2. [3] Turcotte DL. Fractals and chaos in geology and geophysics. Cambridge, UK: Cambridge University Press; 1992. [4] Agterberg FP, Cheng QM, Wright DF. Fractal modeling of mineral deposits. In: Elbrond J, Tang X, editors. Application of Computers and Operations Research in the Mineral Industry: Proc. 24th APCOM Symposium, v. 1. Montreal, Canada: Canadian Institute of Mining, Metallurgy and Petroleum; 1993. [5] Cheng QM, Agterberg FP, Ballantyne SB. The separation of geochemical anomalies from background by fractal methods. J Geochem Explor 1994;51: 109e30. [6] Wang Z, Cheng QM, Cao L, Xia QL, Chen ZJ. Fractal modeling of the microstructure property of quartz mylonite during deformation process. Math Geosci 2006;39:53e68. [7] Zhang W, Liang CH. Study of pitting morphology fractal characteristic of corroded surface of 304 stainless steel in FeCl3 environment. J China Univ Mining Technol 2004;14(1):86e9. [8] Raines GL. Are fractal dimensions of the spatial distribution of mineral deposits meaningful? Nat Resour Res 2008;17:87e97. [9] Liu JH, Liang R, Wang CL, Fan DP. Application of fractal theory in detecting low current faults of power distribution system in coal mines. Mining Sci Technol 2009;19(3):321e5. [10] Hurst HE. Long-term storage capacity of reservoirs. Trans Am Soc Civil Eng 1951;116:770. [11] Hurst HE, Black RP, Simaike YM. Long-term storage: an experimental study. London, UK: Constable; 1965. [12] Miranda JGV, Andrade RFS. Rescaled range analysis of pluviometric records in northeast Brazil. Theor Appl Climatol 1999;63:79e88. [13] Rangarajan G, Sant DA. Fractal dimensional analysis of Indian climatic dynamics. Chaos Soliton Fract 2004;19:285e91. [14] Beretta A, Roman HE, Raicich F, Cresciani F. Long time correlations of sea-level and local atmospheric pressure fluctuations at Trieste. Physica A Stat Mech Appl 2005;347:695e703. [15] Zhuang XT, Zhang XL, Tian Y. Hurst index and problem of fractal structure in stock market. J Northeastern University (Nat Sci) 2003;24(9):862e5. In Chinese. [16] Xu YB, Burton PW. Time varying seismicity in Greece: Hurst’s analysis and Monte Carlo simulation applied to a new earthquake catalog for Greece. Tectonophysics 2006;423:125e36. [17] He KQ, Sun LN, Wang SJ. Displacement fractal parameter Hurst index and its application to prediction of debris landslides. Chin J Rock Mech Eng 2009;28(6):1107e15. In Chinese. [18] Wang EY, He X, Liu Z. R/S statistic rule of EME during deformation and fracture of coal and rock. J China Univ Mining Technol 1998;27(4):349e51. In Chinese.
Z. Zhongying et al. / Mining Science and Technology (China) 21 (2011) 223e227 [19] Yang YG, Yuan JF, Chen SZ. R/S analysis and its application in the forecast of mine inflows. J China Univ Mining Technol 2006;16(4):425e8. [20] Wang YL, Zhao ZY, Jiang ZG. Gathered coal features of No.3 coal measure in eastern depressed sand of Liaohe Basin. Coal Sci Technol 2008;36(4):89e92. In Chinese. [21] Zhao ZY, Wang YL, Sun X. Fuzzy comprehensive appraisement of selected areas for coalbed methane in eastern sag of Liaohe Basin. Xinjiang Petroleum Geol 2008;29(2):206e8. In Chinese.
227
[22] Zhang WH, Liu JX, Wu ZP, Liu JG. Paleogene passage system in the northern part of Liaohe eastern depression and its effect on hydrocarbon migration. J Univ Petroleum China 2005;29(5):19e22. In Chinese. [23] Wang YL, Gao YJ, Zhao ZY, Jiang ZG. Characters of coal classification and coal rank distribution in third member of Shahejie Formation in eastern depression of Liaohe Basin. Coal Geol Exploration 2007;35(2):14e6. In Chinese.
Contents lists available at ScienceDirect
Mining Science and Technology (China) journal homepage: www.elsevier.com/locate/mstc
An rescaled range analysis on the characteristics of coal seam development in the Eastern depression of the Liaohe Basin Zhao Zhongying a, *, Wang Yulin b, Liu Guangdi a, Sun Xiang c a
State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum, Beijing 102249, China College of Resource and Environment Engineering, Liaoning Technical University, Liaoning 123000, China c State Key Laboratory of Geological Processes and Mineral Resource, China University of Geosciences, Beijing 100083, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 August 2010 Received in revised form 30 September 2010 Accepted 23 October 2010
The characteristics of coal seam development, and the prospects of a favorable coal-forming area, were evaluated for the Liaohe Basin located in China. The Number 3 and Number 9 coal seam thickness series from 60 nearly equally spaced bores in the Eastern depression of the Liaohe Basin were examined by a rescaled range analysis. The results indicate that the Hurst exponents of the Number 3 and Number 9 coal seam thickness series are 0.69 and 0.68, respectively. This suggests the presence of persistence. As the bore spacing increases the Hurst exponent of the Number 3 series gradually decreases (H changes from 0.69 to 0.52) and shifts from persistence to randomness. The Hurst exponent of the Number 9 thickness data gradually increases (H changes from 0.68 to 0.91) and always shows the characteristic of persistence. A combination of geological characteristics and the series data allow the conclusion that it is more suitable for the Number 9 coal seam to form in the Northeastern part of the Eastern depression than the Number 3 coal seam. Copyright Ó 2011, China University of Mining & Technology. All rights reserved.
Keywords: Rescaled range analysis Hurst exponent Coal seam thickness Eastern depression Liaohe Basin
1. Introduction Since Mandelbrot’s coining of the word “fractal” more than two decades ago [1,2] fractal and multi-fractal models have been applied to several phenomena in the natural sciences to describe the irregularity of geological features or the time and spatial distribution of geological objects [3e9]. Scale invariance plays an important role in fractal geometry and provides the basis for the definition of the several fractal dimensions that are associated with the geometric characteristics, or the dynamical behavior, of these systems. The rescaled range analysis, or R/S analysis, first introduced by Hurst while studying water storage problems related to the Nile River, has been used to investigate scale properties of time series related to several geophysical or geological events. These events include such things as precipitation, temperature, sea level, the stock market, earthquakes and landslides, deformation and fracture of coal and rock, and mine inflows [10e19]. The method provides important statistical information about a record over time, namely, is it possible to identify a persistent, anti-persistent, or a purely random character in the time series.
* Corresponding author. Tel.: þ86 10 89734480. E-mail address: [email protected] (Z. Zhongying).
Quantitative information is expressed by the Hurst exponent, H. The value of H always lies between 0 and 1 and is equal to 0.5 for purely random observations, for example, Brownian motion. An H value larger than 0.5 shows persistence while values less than 0.5 show anti-persistence. These terms characterize the way in which the value of a previous time step influences the probability of subsequent time steps as they occur within these processes. Although these methods have previously been applied to a number of time series related to geological events, and great achievements have been made, a space series of geological events has not yet been extensively investigated. In this article, we describe the use of an R/S analysis method to quantify the complexity of coal seam distribution, to reveal the characteristics of coal seam development, and to be helpful for the study of coal gasification member of the Shahejie formation in the Eastern depression of the Liaohe Basin, China. 2. Geological setting The Liaohe Basin is located in the northern part of China. It is a northeast (NE)-trending Palaeogene rift and Neogene sag basin that can be divided into seven tectonic units: the Shenbei depression, the Damintun depression, the Western depression, the Eastern depression, the Western slope, the central uplift, and the
1674-5264/$ e see front matter Copyright Ó 2011, China University of Mining & Technology. All rights reserved. doi:10.1016/j.mstc.2011.02.011
224
Z. Zhongying et al. / Mining Science and Technology (China) 21 (2011) 223e227
Fig. 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 (Fig. 1b). The basement is composed of Archean metamorphic rocks and Mesozoic Upper Jurassic and Lower Cretaceous sedimentary-volcanic rocks. The Eastern depression is an NE-trending tectonic unit in the Liaohe Basin with an area of 3950 km2. The sedimentary sequences can be divided into four formations: the Palaeogene Fangshenpao, the Shahejie and Dongying, the Neogene Guantao, and the Minghuazhen. Among these the third member of the Shahejie Formation (Es3) is the most important coal bearing stratum [20e23]. Coal seams are distributed widely in the Eastern depression with a total area of 200 km2. They can be divided into 11 coal seams, among which Number 1 to Number 5 coal seams are in the upper coal seam group and Number 6 to Number 11 coal seams are in the lower coal seam group (Fig. 1c). The Number 3 and Number 9 coal seams are the main coal seams that are controlled by the syndepositional faults and are distributed in the direction of NE, 35 to 45 , similar to the strike of the Eastern depression. The effect of the sedimentary environment causes them to be distributed discontinuously from the southwest (SW) to the NE (Fig. 2). 3. R/S analysis As an introduction to R/S analysis, let us consider the case of coal seam thickness. Let {a1, a2, ., an} be a spaced series of bores and {x1, x2, ., xn} be the coal seam thickness series from the corresponding bores. In any given space span, s, the average coal seam thickness is given by
hxis ¼
s 1X
s i¼1
xðiÞ
(1)
Now let X(aj, s) be the difference between x(i) and hxis , defined as j X xðiÞ hxis ; X aj ; s ¼
1js
(2)
i¼1
The range, R, and the standard variation, S, are given by
RðsÞ ¼ max Xði; sÞ min Xði; sÞ 1is
SðsÞ ¼
s 1X
s i¼1
1is
xðiÞ hxis
2
(3)
!1=2 (4)
For each value of the space span, s, an R/S number that follows the power law
RðsÞ=SðsÞfsH
(5)
may be obtained, where H denotes the Hurst exponent. Equation (5) is known as “Hurst’s empirical law” and it represents a fitted straight line in a log-log plot of R/S as a function of s. H is the slope of the straight line. 4. Results and discussion The coal seam thickness data comprise thickness data from Number 3 and Number 9 coal seams taken from 60 bores having
Fig. 2. Contour map showing coal seam thickness in the third member of the Shahejie formation in the Eastern depression.
Z. Zhongying et al. / Mining Science and Technology (China) 21 (2011) 223e227 Table 1 Types of data set for R/S analysis.
Table 2 Hurst exponents of the data.
Data set
Description
I
An array of 60 coal seam thickness measurements. Each datum is from every coal seam taken in the order of the 60 bores. An array of 30 coal seam thickness measurements. Each datum is the average of every two coal seam thickness data paired in the order of the 60 bores. An array of 20 coal seam thickness measurements. Each datum is the average of every three coal seam thickness data taken in the order of the 60 bores.
II
III
225
Data set
nearly equal spacing. The bores are distributed in the direction of SW to NE in the Eastern depression (Fig. 2). Let bore “Rong60” be the first bore (Point A in Fig. 2) to order the bore numbers in the direction of SW to NE. Then bore “Niu6” is designated as the 60th bore (Point B in Fig. 2). Now the data from these bores form a space series data set (data set I in Table 1) taken in the order of the bore number. The average thickness of the Number 3 and Number 9 coal seams is about 3.5 m and the maximum thickness is about 12 m (Fig. 3). Figures 4a and 4d show the Hurst exponent of the Number 3 and Number 9 coal seam thickness series as estimated by means of R/S analysis of data set I. These thickness data follow a fractal distribution and the goodness of fit is greater than 0.98. Their Hurst exponents are 0.69 and 0.68, respectively, which indicates the presence of persistence in these coal seam thickness series (Table 2). The averages of every two thickness data, and separately of every three thickness data, were calculated in the order of the
I II III
Hurst exponent No. 3 coal seam
No. 9 coal seam
0.69 0.68 0.52
0.68 0.77 0.91
series from Point A to Point B as a way of determining if the series followed a fractal distribution. The 30 average thickness data formed data set II while the 20 averaged data were data set III (Table 1). Figures 4b and 4c show the Hurst exponent of the Number 3 coal seam thickness, data set II and data set III. Figures 4e and 4f show the Hurst exponent of the equivalent Number 9 data. The Hurst exponents indicate that the thickness series from both Number 3 and Number 9 coal seams follow a fractal distribution. An increase in bore spacing causes the Hurst exponent of the Number 3 thickness data to gradually decrease as it shifts from persistence to randomness. The Hurst exponent of the Number 9 coal series gradually increases and always shows the characteristic of persistence (Table 2). This suggests that the coal seams may have different development features. It is more suitable for the Number 9 coal seam to have formed in the Northeastern part of the Eastern depression than the Number 3 coal seam, which is also confirmed by the geological characteristics of the Eastern depression. The coal seams in the Eastern depression formed within a peat swamp distributed between an alluvial fan and a surviving lake
Fig. 3. Plots of coal seam thickness versus bore number in the Eastern depression.
Fig. 4. Double log plot of R/S vs. s.
226
Z. Zhongying et al. / Mining Science and Technology (China) 21 (2011) 223e227
Fig. 5. Sketch of the coal-accumulating environment in the third member of the Shahejie formation in the Eastern depression (modified after Reference [20]).
(Fig. 5). During the formation of the Number 3 coal seam the lake quickly shrank and the peat swamp disappeared in the Northeastern part of the Eastern depression as the Yongle alluvial fan progressed. As a result the area was not suitable for formation of the Number 3 coal seam. However, during the formation of the Number 9 coal seam the peat swamp existed throughout in the areas neighboring the border of a fan delta plain and fan delta front. Areas of lake shore existed in the Northeastern part of the Eastern depression and as a result the area was suitable for the formation of the Number 9 coal seam.
5. Conclusions 1. An R/S analysis of thickness data from the Number 3 and Number 9 coal seams located in the third member of the Shahejie formation in the Eastern depression of the Liaohe Basin, China, was presented. The seam thickness data follow a fractal distribution and their Hurst exponents are 0.69 and 0.68 (Number 3 and Number 9, respectively). The Hurst exponents suggest the presence of persistence in the coal seam thickness series. 2. As the bore spacing increases the Hurst exponent of the Number 3 thickness series gradually decreases suggesting a change from persistence to randomness. The Hurst exponent of the Number 9 coal seam data gradually increases and always shows the characteristics of persistence. 3. The R/S analysis combined with the known geological characteristics suggests that it is more suitable for the Number 9 coal seam to have formed in the Northeastern part of the Eastern depression than the Number 3 coal seam.
Acknowledgements This research was supported by National Basic Research Program of China (No. 2007CB209503).
References [1] Mandelbrot BB. The fractal geometry of nature. San Francisco, CA: Freeman; 1982. [2] Mandelbrot BB, Passoja DE, Paullay AJ. Fractal character of fracture surfaces of metals. Nature 1984;308:721e2. [3] Turcotte DL. Fractals and chaos in geology and geophysics. Cambridge, UK: Cambridge University Press; 1992. [4] Agterberg FP, Cheng QM, Wright DF. Fractal modeling of mineral deposits. In: Elbrond J, Tang X, editors. Application of Computers and Operations Research in the Mineral Industry: Proc. 24th APCOM Symposium, v. 1. Montreal, Canada: Canadian Institute of Mining, Metallurgy and Petroleum; 1993. [5] Cheng QM, Agterberg FP, Ballantyne SB. The separation of geochemical anomalies from background by fractal methods. J Geochem Explor 1994;51: 109e30. [6] Wang Z, Cheng QM, Cao L, Xia QL, Chen ZJ. Fractal modeling of the microstructure property of quartz mylonite during deformation process. Math Geosci 2006;39:53e68. [7] Zhang W, Liang CH. Study of pitting morphology fractal characteristic of corroded surface of 304 stainless steel in FeCl3 environment. J China Univ Mining Technol 2004;14(1):86e9. [8] Raines GL. Are fractal dimensions of the spatial distribution of mineral deposits meaningful? Nat Resour Res 2008;17:87e97. [9] Liu JH, Liang R, Wang CL, Fan DP. Application of fractal theory in detecting low current faults of power distribution system in coal mines. Mining Sci Technol 2009;19(3):321e5. [10] Hurst HE. Long-term storage capacity of reservoirs. Trans Am Soc Civil Eng 1951;116:770. [11] Hurst HE, Black RP, Simaike YM. Long-term storage: an experimental study. London, UK: Constable; 1965. [12] Miranda JGV, Andrade RFS. Rescaled range analysis of pluviometric records in northeast Brazil. Theor Appl Climatol 1999;63:79e88. [13] Rangarajan G, Sant DA. Fractal dimensional analysis of Indian climatic dynamics. Chaos Soliton Fract 2004;19:285e91. [14] Beretta A, Roman HE, Raicich F, Cresciani F. Long time correlations of sea-level and local atmospheric pressure fluctuations at Trieste. Physica A Stat Mech Appl 2005;347:695e703. [15] Zhuang XT, Zhang XL, Tian Y. Hurst index and problem of fractal structure in stock market. J Northeastern University (Nat Sci) 2003;24(9):862e5. In Chinese. [16] Xu YB, Burton PW. Time varying seismicity in Greece: Hurst’s analysis and Monte Carlo simulation applied to a new earthquake catalog for Greece. Tectonophysics 2006;423:125e36. [17] He KQ, Sun LN, Wang SJ. Displacement fractal parameter Hurst index and its application to prediction of debris landslides. Chin J Rock Mech Eng 2009;28(6):1107e15. In Chinese. [18] Wang EY, He X, Liu Z. R/S statistic rule of EME during deformation and fracture of coal and rock. J China Univ Mining Technol 1998;27(4):349e51. In Chinese.
Z. Zhongying et al. / Mining Science and Technology (China) 21 (2011) 223e227 [19] Yang YG, Yuan JF, Chen SZ. R/S analysis and its application in the forecast of mine inflows. J China Univ Mining Technol 2006;16(4):425e8. [20] Wang YL, Zhao ZY, Jiang ZG. Gathered coal features of No.3 coal measure in eastern depressed sand of Liaohe Basin. Coal Sci Technol 2008;36(4):89e92. In Chinese. [21] Zhao ZY, Wang YL, Sun X. Fuzzy comprehensive appraisement of selected areas for coalbed methane in eastern sag of Liaohe Basin. Xinjiang Petroleum Geol 2008;29(2):206e8. In Chinese.
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[22] Zhang WH, Liu JX, Wu ZP, Liu JG. Paleogene passage system in the northern part of Liaohe eastern depression and its effect on hydrocarbon migration. J Univ Petroleum China 2005;29(5):19e22. In Chinese. [23] Wang YL, Gao YJ, Zhao ZY, Jiang ZG. Characters of coal classification and coal rank distribution in third member of Shahejie Formation in eastern depression of Liaohe Basin. Coal Geol Exploration 2007;35(2):14e6. In Chinese.