IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v390y2011i11p2096-2111.html
   My bibliography  Save this article

Scaling, multifractality, and long-range correlations in well log data of large-scale porous media

Author

Listed:
  • Dashtian, Hassan
  • Jafari, G. Reza
  • Sahimi, Muhammad
  • Masihi, Mohsen

Abstract

Three distinct methods, namely, the spectral density, the multifractal random walk approach, and the multifractal detrended fluctuation analysis are utilized to study the properties of four distinct types of well logs from three oil and gas fields, namely, the natural gamma ray emission, neutron porosity, bulk density, and the sonic transient time logs. Such well logs have never been analyzed by the methods that we utilize in the present study. The results indicate that the well logs exhibit multifractal characteristics, and the estimated Hurst exponents by the three methods are close to each other. Using multifractal detrended fluctuation analysis and the shuffled and surrogated data, we find that the source of multifractality is due to both broad probability density functions of the data and long-range correlations in them. The correlations are persistent and are characterized by a Hurst exponent H>0.5. Despite very significant differences in the geology of the three reservoirs–ranging from shaly sands to fractured carbonate reservoirs–there is a rough universality in the log data in that, the Hurst exponents for all the logs vary in a very narrow range.

Suggested Citation

  • Dashtian, Hassan & Jafari, G. Reza & Sahimi, Muhammad & Masihi, Mohsen, 2011. "Scaling, multifractality, and long-range correlations in well log data of large-scale porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2096-2111.
  • Handle: RePEc:eee:phsmap:v:390:y:2011:i:11:p:2096-2111
    DOI: 10.1016/j.physa.2011.01.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437111000732
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2011.01.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Silva, L.B.M. & Vermelho, M.V.D. & Lyra, M.L. & Viswanathan, G.M., 2009. "Multifractal detrended fluctuation analysis of analog random multiplicative processes," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2806-2811.
    2. Serrano, E. & Figliola, A., 2009. "Wavelet Leaders: A new method to estimate the multifractal singularity spectra," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2793-2805.
    3. Kantelhardt, Jan W. & Rybski, Diego & Zschiegner, Stephan A. & Braun, Peter & Koscielny-Bunde, Eva & Livina, Valerie & Havlin, Shlomo & Bunde, Armin, 2003. "Multifractality of river runoff and precipitation: comparison of fluctuation analysis and wavelet methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 240-245.
    4. Amir Bashan & Ronny Bartsch & Jan W. Kantelhardt & Shlomo Havlin, 2008. "Comparison of detrending methods for fluctuation analysis," Papers 0804.4081, arXiv.org.
    5. Castro e Silva, A. & Moreira, J.G., 1997. "Roughness exponents to calculate multi-affine fractal exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 235(3), pages 327-333.
    6. S. Shadkhoo & G. R. Jafari, 2009. "Multifractal detrended cross-correlation analysis of temporal and spatial seismic data," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 72(4), pages 679-683, December.
    7. F. Schmitt & D. Marsan, 2001. "Stochastic equations generating continuous multiplicative cascades," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(1), pages 3-6, March.
    8. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    9. Ferreira, R.B. & Vieira, V.M. & Gleria, Iram & Lyra, M.L., 2009. "Correlation and complexity analysis of well logs via Lyapunov, Hurst, Lempel–Ziv and neural network algorithms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 747-754.
    10. Hajian, S. & Movahed, M. Sadegh, 2010. "Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4942-4957.
    11. Bashan, Amir & Bartsch, Ronny & Kantelhardt, Jan W. & Havlin, Shlomo, 2008. "Comparison of detrending methods for fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5080-5090.
    12. Wei-Xing Zhou, 2008. "Multifractal detrended cross-correlation analysis for two nonstationary signals," Papers 0803.2773, arXiv.org.
    13. Dean Prichard & James Theiler, 1994. "Generating Surrogate Data for Time Series with Several Simultaneously Measured Variables," Working Papers 94-04-023, Santa Fe Institute.
    14. Zunino, Luciano & Figliola, Alejandra & Tabak, Benjamin M. & Pérez, Darío G. & Garavaglia, Mario & Rosso, Osvaldo A., 2009. "Multifractal structure in Latin-American market indices," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2331-2340.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wei, Yu & Wang, Yudong & Huang, Dengshi, 2011. "A copula–multifractal volatility hedging model for CSI 300 index futures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4260-4272.
    2. Henriques, M.V.C. & Leite, F.E.A. & Andrade, R.F.S. & Andrade, J.S. & Lucena, L.S. & Neto, M. Lucena, 2015. "Improving the analysis of well-logs by wavelet cross-correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 130-140.
    3. Shiri, Yousef & Tokhmechi, Behzad & Zarei, Zeinab & Koneshloo, Mohammad, 2012. "Self-affine and ARX-models zonation of well logging data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5208-5214.
    4. Hernandez-Martinez, Eliseo & Velasco-Hernandez, Jorge X. & Perez-Muñoz, Teresa & Alvarez-Ramirez, Jose, 2013. "A DFA approach in well-logs for the identification of facies associations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 6015-6024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhao, Xiaojun & Shang, Pengjian & Zhao, Chuang & Wang, Jing & Tao, Rui, 2012. "Minimizing the trend effect on detrended cross-correlation analysis with empirical mode decomposition," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 166-173.
    2. Wu, Liang & Chen, Lei & Ding, Yiming & Zhao, Tongzhou, 2018. "Testing for the source of multifractality in water level records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 824-839.
    3. Stosic, Dusan & Stosic, Darko & de Mattos Neto, Paulo S.G. & Stosic, Tatijana, 2019. "Multifractal characterization of Brazilian market sectors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 956-964.
    4. Jiang, Zhi-Qiang & Xie, Wen-Jie & Zhou, Wei-Xing, 2014. "Testing the weak-form efficiency of the WTI crude oil futures market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 235-244.
    5. Xiong, Gang & Yu, Wenxian & Zhang, Shuning, 2015. "Singularity power spectrum distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 431(C), pages 63-73.
    6. Dutta, Srimonti & Ghosh, Dipak & Chatterjee, Sucharita, 2016. "Multifractal detrended Cross Correlation Analysis of Foreign Exchange and SENSEX fluctuation in Indian perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 188-201.
    7. Chatterjee, Sucharita & Ghosh, Dipak, 2021. "Impact of Global Warming on SENSEX fluctuations — A study based on Multifractal detrended cross correlation analysis between the temperature anomalies and the SENSEX fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).
    8. Xiong, Gang & Yu, Wenxian & Zhang, Shuning, 2015. "Time-singularity multifractal spectrum distribution based on detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 351-366.
    9. Chatterjee, Sucharita, 2020. "Analysis of the human gait rhythm in Neurodegenerative disease: A multifractal approach using Multifractal detrended cross correlation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    10. Li, Bao-Gen & Ling, Dian-Yi & Yu, Zu-Guo, 2021. "Multifractal temporally weighted detrended partial cross-correlation analysis of two non-stationary time series affected by common external factors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    11. Xiong, Gang & Zhang, Shuning & Liu, Qiang, 2012. "The time-singularity multifractal spectrum distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4727-4739.
    12. Hasan, Rashid & Mohammed Salim, M., 2017. "Power law cross-correlations between price change and volume change of Indian stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 620-631.
    13. Stavroyiannis, Stavros & Babalos, Vassilios & Bekiros, Stelios & Lahmiri, Salim & Uddin, Gazi Salah, 2019. "The high frequency multifractal properties of Bitcoin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 62-71.
    14. Olivares, Felipe & Zanin, Massimiliano, 2022. "Corrupted bifractal features in finite uncorrelated power-law distributed data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    15. Kristoufek, Ladislav, 2015. "Finite sample properties of power-law cross-correlations estimators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 513-525.
    16. Zhao, Xiaojun & Shang, Pengjian & Lin, Aijing & Chen, Gang, 2011. "Multifractal Fourier detrended cross-correlation analysis of traffic signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3670-3678.
    17. Schumann, Aicko Y. & Kantelhardt, Jan W., 2011. "Multifractal moving average analysis and test of multifractal model with tuned correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2637-2654.
    18. Gulich, Damián & Zunino, Luciano, 2014. "A criterion for the determination of optimal scaling ranges in DFA and MF-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 17-30.
    19. Ardalankia, Jamshid & Osoolian, Mohammad & Haven, Emmanuel & Jafari, G. Reza, 2020. "Scaling features of price–volume cross correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    20. Ruan, Yong-Ping & Zhou, Wei-Xing, 2011. "Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1646-1654.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:390:y:2011:i:11:p:2096-2111. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.