[1] KOESTER J, KULKE H.Sedimentology and petroleum geology: Book review[M]. New York: Springer-Verlag, 1993.
[2] SHIRI Y, TOKHMECHI B, ZAREI Z, et al.Self-affine and ARX-models zonation of well logging data[J]. Physica A: Statistical Mechanics and Its Applications, 2012, 391(21): 5208-5214.
[3] MALAMUD B D, TURCOTTE D L.Advances in geophysics[M]. Amsterdam: Elsevier, 1999: 1-90.
[4] DANOS M.Fractals and chaos in geology and geophysics[M]. 2nd ed. London: Cambridge University Press, 2006.
[5] DELIGNIÈRES D. Correlation properties of (discrete) fractional Gaussian noise and fractional Brownian motion[J]. Mathematical Problems in Engineering, 2015, 2015: 1-7.
[6] HURST H E.Long-term storage capacity of reservoirs[J]. Transactions of the Amererical Society of Civil Engineers, 1951, 116: 770-808.
[7] TURCOTTE D L.Fractals and chaos in geology and geophysics[M]. London: Cambridge University Press, 1992.
[8] MOKTADIR Z, KRAFT M, WENSINK H.Multifractal properties of pyrex and silicon surfaces blasted with sharp particles[J]. Physica A: Statistical Mechanics and Its Applications, 2008, 387(8/9): 2083-2090.
[9] BANSAL A R, DIMRI V P.Self-affine gravity covariance model for the Bay of Bengal[J]. Geophysical Journal International, 2005, 161(1): 21-30.
[10] FEDI M.Global and local multiscale analysis of magnetic susceptibility data[J]. Pure and Applied Geophysics, 2003, 160(12): 2399-2417.
[11] DIMRI V.Application of fractals in earth sciences[M]. Florida, USA: CRC Press, 2000.
[12] MILNE B T.Measuring the fractal geometry of landscapes[J]. Applied Mathematics and Computation, 1988, 27(1): 67-79.
[13] DAS S.Functional fractional calculus[M]. Berlin: Springer Science & Business Media, 2011.
[14] WITT A, MALAMUD B D.Quantification of long-range persistence in geophysical time series: Conventional and benchmark-based improvement techniques[J]. Surveys in Geophysics, 2013, 34(5): 541-651.
[15] MANDELBROT B B.Intermittent turbulence in self-similar cascades: Divergence of high moments and dimension of the carrier[J]. Journal of Fluid Mechanics, 1974, 62(2): 331-358.
[16] MANDELBROT B B.Pure and applied geophysics PAGEOPH[M]. Berlin: Springer, 1989: 5-42.
[17] DIMRI V P, GANGULI S S.Fractal theory and its implication for acquisition, processing and interpretation(API) of geophysical investigation: A review[J]. Journal of the Geological Society of India, 2019, 93(2): 142-152.
[18] GANGULI S S, DIMRI V P.Interpretation of gravity data using eigenimage with Indian case study: A SVD approach[J]. Journal of Applied Geophysics, 2013, 95: 23-35.
[19] ALI S, SHAHZAD S J H, RAZA N, et al. Stock market efficiency: A comparative analysis of Islamic and conventional stock markets[J]. Physica A: Statistical Mechanics and Its Applications, 2018, 503: 139-153.
[20] DASHTIAN H, JAFARI G R, SAHIMI M, et al.Scaling, multifractality, and long-range correlations in well log data of large-scale porous media[J]. Physica A: Statistical Mechanics and Its Applications, 2011, 390(11): 2096-2111.
[21] HERNANDEZ-MARTINEZ E, VELASCO-HERNANDEZ J X, PEREZ-MUÑOZ T, et al. A DFA approach in well-logs for the identification of facies associations[J]. Physica A: Statistical Mechanics and Its Applications, 2013, 392(23): 6015-6024.
[22] TANG Y J, CHANG Y F, LIOU T S, et al. Evolution of the temporal multifractal scaling properties of the Chiayi earthquake(ML=6.4), Taiwan[J]. Tectonophysics, 2012, 546/547: 1-9.
[23] TELESCA L, LOVALLO M, MAMMADOV S, et al.Power spectrum analysis and multifractal detrended fluctuation analysis of Earth’s gravity time series[J]. Physica A: Statistical Mechanics and Its Applications, 2015, 428: 426-434.
[24] SUBHAKAR D, CHANDRASEKHAR E.Reservoir characterization using multifractal detrended fluctuation analysis of geophysical well-log data[J]. Physica A: Statistical Mechanics and Its Applications, 2016, 445: 57-65.
[25] STANLEY H E, MEAKIN P.Multifractal phenomena in physics and chemistry[J]. Nature, 1988, 335(6189): 405-409.
[26] MOLINO-MINERO-RE E, GARCÍA-NOCETTI F, BENÍTEZ-PÉREZ H. Application of a time-scale local hurst exponent analysis to time series[J]. Digital Signal Processing: A Review Journal, 2015, 37(1): 92-99.
[27] TOKHMECHI B, RASOULI V, AZIZI H, et al.Hybrid clustering-estimation for characterization of thin bed heterogeneous reservoirs[J]. Carbonates and Evaporites, 2019, 34(3): 917-929.
[28] SAHIMI M.Flow and transport in porous media and fractured rock: From classical to modern approaches[M]. New Jersey, USA: John Wiley & Sons, 2010.
[29] AMINIKHANGHAHI S, COOK D J.A survey of methods for time series change point detection[J]. Knowledge and Information Systems, 2017, 51(2): 339-367.
[30] CHOPRA S, MARFURT K J.Seismic attributes for prospect identification and reservoir characterization[R]. Tulsa: Society of Exploration Geophysicists and European Association of Geoscientists and Engineers, 2007.
[31] HUANG Y P, GENG J H, GUO T L.New seismic attribute: Fractal scaling exponent based on gray detrended fluctuation analysis[J]. Applied Geophysics, 2015, 12(3): 343-352.
[32] NATH S K, DEWANGAN P.Detection of seismic reflections from seismic attributes through fractal analysis[J]. Geophysical Prospecting, 2002, 50(3): 341-360.
[33] LOUIE J N, MELA K.Correlation length and fractal dimension interpretation from seismic data using variograms and power spectra[J]. Geophysics, 2001, 66(5): 1372-1378.
[34] DONG J, LANG Z, GONG W, et al.Development of oil development and gas prediction software system based on fractal dimension of amplitude spectrum[J]. Computer Applications of Petroleum, 2018, 26(1): 6-8.
[35] KANTELHARDT J W, KOSCIELNY-BUNDE E, REGO H H A, et al. Detecting long-range correlations with detrended fluctuation analysis[J]. Physica A: Statistical Mechanics and Its Applications, 2001, 295(3/4): 441-454.
[36] HU K, IVANOV P C, CHEN Z, et al.Effect of trends on detrended fluctuation analysis[J]. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 2001, 64(1): 1-19.
[37] CHEN Z, IVANOV P C, HU K, et al.Effect of nonstationarities on detrended fluctuation analysis[J]. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 2002, 65(4): 1-17.
[38] HAVLIN S, BULDYREV S V, BUNDE A, et al.Scaling in nature: From DNA through heartbeats to weather[J]. Physica A: Statistical Mechanics and Its Applications, 1999, 273(1/2): 46-69.
[39] OSSADNIK S M, BULDYREV S V, GOLDBERGER A L, et al.Correlation approach to identify coding regions in DNA sequences[J]. Biophysical Journal, 1994, 67(1): 64-70.
[40] BILLAT V L, MILLE-HAMARD L, MEYER Y, et al.Detection of changes in the fractal scaling of heart rate and speed in a marathon race[J]. Physica A: Statistical Mechanics and Its Applications, 2009, 388(18): 3798-3808.
[41] BUDINSKI-PETKOVIĆ L, LONČAREVIĆ I, JAKŠIĆ ZM, et al. Fractal properties of financial markets[J]. Physica A: Statistical Mechanics and Its Applications, 2014, 410: 43-53.
[42] SU Z Y, WU T.Music walk, fractal geometry in music[J]. Physica A: Statistical Mechanics and Its Applications, 2007, 380(1/2): 418-428.
[43] KANTELHARDT J W.Encyclopedia of complexity and systems science[M]. Berlin: Springer, 2015: 1-37.
[44] CAO G, HE L Y, CAO J.Multifractal detrended analysis method and its application in financial markets[M]. Beilin: Springer, 2018.
[45] MATIA K, ASHKENAZY Y, STANLEY H E.Multifractal properties of price fluctuations of stocks and commodities[J]. Europhysics Letters, 2003, 61(3): 422-428.
[46] THEILER J, GALDRIKIAN B, LONGTIN A, et al.Using surrogate data to detect nonlinearity in time series[J]. Nonlinear Modeling and Forecasting, 1992(XII): 163-188.
[47] HENRY B, LOVELL N, CAMACHO F.Nonlinear dynamics time series analysis[J]. Nonlinear Biomedical Signal Processing: Dynamic Analysis and Modeling, 2001(2): 1-39.
[48] THEILER J, EUBANK S, LONGTIN A, et al.Testing for nonlinearity in time series: The method of surrogate data[J]. Physica D: Nonlinear Phenomena, 1992, 58(1/2/3/4): 77-94.
[49] ZENG J G, SHU YQ, ZHONG Y.Fractal and chaotic characteristics of seismic data[J]. Oil Geophysical Prospecting, 1995, 30(6): 743-748.
[50] WU Chao, CHEN Mian, JIN Yan.Real-time prediction method of borehole stability[J]. Petroleum Exploration and Development, 2008, 35(1): 80-84.
[51] LI W K, TONG H.Time series: Advanced methods[M]. Amsterdam: Elsevier, 2015.
[52] YAO R, PAKZAD S N.Autoregressive statistical pattern recognition algorithms for damage detection in civil structures[J]. Mechanical Systems and Signal Processing, 2012, 31: 355-368.
[53] CHAMOLI A, RAM BANSAL A, DIMRI V P.Wavelet and rescaled range approach for the Hurst coefficient for short and long time series[J]. Computers and Geosciences, 2007, 33(1): 83-93.
[54] MADAN S, SRIVASTAVA K, SHARMILA A, et al.A case study on discrete wavelet transform based Hurst exponent for epilepsy detection[J]. Journal of Medical Engineering and Technology, 2018, 42(1): 9-17.
[55] HOSSEINI S A, AKBARZADEH T M R, NAGHIBI-SISTANI M B. Intelligent technologies and techniques for pervasive computing[M]. Pennsylvania, USA: IGI Global, 2013: 20-36.
[56] LJUNG L.MATLAB system identification toolbox[R]. Massachusetts, USA: MathWorks, 2007.
[57] OHLSSON H, LJUNG L, BOYD S.Segmentation of ARX-models using sum-of-norms regularization[J]. Automatica, 2010, 46(6): 1107-1111.
[58] BASSEVILLE M.Detection of abrupt changes in signal processing[M]. New Jersey, USA: Prentice Hall, Englewood Cliffs, 1990: 99-101.
[59] GUSTAFSSON F.Adaptive filtering and change detection[R]. New York: Citeseer, 2000.
[60] BALAKRISHNAN V.System identification: Theory for the user[M]. 2nd ed. New Jersey, USA: Prentice-Hall, 2002.
[61] DOCTORALE E, SCIENCES D E S, INGENIEUR P L. Initialization of output error identification algorithms[M]. Beilin: Springer, 2006.
[62] MCQUARRIE N.Crustal scale geometry of the Zagros fold-thrust belt, Iran[J]. Journal of Structural Geology, 2004, 26(3): 519-535.
[63] RAHIMI R, BAGHERI M, MASIHI M.Characterization and estimation of reservoir properties in a carbonate reservoir in Southern Iran by fractal methods[J]. Journal of Petroleum Exploration and Production Technology, 2018, 8(1): 31-41.
[64] BO Y Y, LEE G H, KIM H J, et al.Comparison of wavelet estimation methods[J]. Geosciences Journal, 2013, 17(1): 55-63.
[65] ASHCROFT W.A petroleum geologist’s guide to seismic reflection[M]. New Jersey, USA: John Wiley & Sons, 2011.
[66] LIU Ming, ZHANG Shicheng, MOU Jianye.Fractal nature of acid- etched wormholes and the influence of acid type on wormholes[J]. Petroleum Exploration and Development, 2012, 39(5): 630-635.
[67] CHEN Y, ZHANG L, LI J.Nano-scale pore structure and fractal dimension of lower Silurian Longmaxi Shale[J]. Chemistry and Technology of Fuels and Oils, 2018, 54(3): 354-366.
[68] JIANG F, CHEN D, CHEN J, et al.Fractal analysis of shale pore structure of continental gas shale reservoir in the Ordos Basin, NW China[J]. Energy & Fuels, 2016, 30(6): 4676-4689.
[69] CHEN L, JIANG Z X, JIANG S, et al.Nanopore structure and fractal characteristics of lacustrine shale: Implications for shale gas storage and production potential[J]. Nanomaterials, 2019, 9(3): 390.
[70] WANG X, JIANG Z, JIANG S, et al.Full-scale pore structure and fractal dimension of the Longmaxi shale from the southern Sichuan Basin: Investigations using FE-SEM, gas adsorption and mercury intrusion porosimetry[J]. Minerals, 2019, 9(9): 543-555.
[71] KROHN C E.Fractal measurements of sandstones, shales, and carbonates[J]. Journal of Geophysical Research: Solid Earth, 1988, 93(B4): 3297-3305.
[72] SONG Z, MA C, ZHANG M.The fractal properties of calcination of limestone and its sulfidation with H2S[R]. Wuhan, China: 2010 Asia-Pacific Power and Energy Engineering Conference, 2010.
[73] WU X, LONG S, LI G.Fractal study on the complexity of limestone surface pore structure[J]. Advanced Materials Research, 2012, 548: 275-280.
