Abstract
Detrended fluctuation analysis and detrended cross correlation analysis are used in this work to identify and characterize correlated well log data. This is performed by first separating the different fluctuations due to external trends, and evaluating the autocorrelation and cross-correlation exponents to determine whether scale properties persist as the size of the series changes. Two new methodologies were developed to identify optimal values of the cross-correlation coefficients and graphically display them, which we call the automatic search procedure and correlation map. The methodologies were applied to well logs from the Jequitinhonha Basin, Brazil, to verify the existence of scale property in these data. For practical purposes, our goal is to use a local analysis framework to detect all points of high cross-correlation among different physical parameters in the same well, and among one same physical parameter in different wells. The correlated events suggested the continuity of geological features, including the vertical displacements of rock layers. In particular, it was possible to identify layers of calcilutites in a specific depth range. These rocks are of particular importance to the study of stratigraphic correlations due to their great regional extent and regular layering.
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References
Hurst, H.E.: Long-term storage capacity of reservoirs. Trans. Am. Soc. Civ. Eng. 116, 770–808 (1951)
Peng, C.K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., Goldberger, A.L.: Mosaic organization of DNA nucleotides. Phys. Rev. E 49, 1685–1689 (1994)
Podobnik, B., Stanley, H.E.: Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series. Phys. Rev. Lett. 100, 084–102 (2008)
Zebende, G.F.: DCCA cross-correlation coefficient: Quantifying level of cross-correlation. Physica A 390, 614–618 (2011)
Lowrie, W.: Fundamentals of Geophysics. Cambridge University Press, New York (1997)
Dimri, V.P.: Fractal Behaviour of the Earth System. Springer, New York (2005)
Voss, R.F.: Fractals in nature: from characterization to simulation. In: Peitgen, H.-O., Saupe, D. (eds.) Science of Fractal Images, pp. 21–70. Springer, New York (1988)
Carvalho, M.D., Antunes, R.L.: Oligocene calcilutites from the Jequitinhonha Basin, similarity to the “blue mark” calcilutites from the Campos Basin (in Portuguese). Boletim Geociências Petrobras 2, 291–292 (1988)
Kantelhardt, J.W., Koscielny-Bunde, E., Rego, H.H.A., Havlin, S., Bunde, A.: Detecting long-range correlations with detrended fluctuation analysis. Physica A 295, 441–454 (2001)
Podobnik, B., Jiang, Z.Q., Zhou, W.X., Stanley, H.E.: Statistical tests for power-law cross-correlated processes. Phys. Rev. E 84, 066118 (2011)
Ashkenazy, Y., Ivanov, P.C., Havlin, S., Peng, C., Goldberger, A.L., Stanley, H.E.: Magnitude and sign correlations in heartbeat fluctuations. Phys. Rev. Lett. 86, 1900–1903 (2001)
Marinho, E.B.S., Souza, A.M.Y.R., Andrade, R.F.S.: Using detrended cross-correlation analysis in geophysical data. Physica A 392, 2195–2201 (2013)
Ferreira, R.B., Vieira, V.M., Gleria, I., Lyra, M.: Correlation and complexity analysis of well logs via Lyapunov, Hurst, Lempel-Ziv and neural network algorithms. Physica A 388, 747–754 (2009)
Dolan, S.S., Bean, J.C., Riollet, B.: The broad-band fractal nature of heterogeneity in the upper crust from petrophysical logs. Geophys. J. Int. 132, 489–507 (1998)
Acknowledgements
This work was carried out with the support of the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brazil (CAPES) – Financing Code 001. E. Marinho and A. Bassrei thank CNPq for supporting the National Institute of Science and Technology of Petroleum Geophysics (INCT-GP). E. Marinho thanks CAPES for a PhD scholarship. A. Bassrei and R. Andrade thank CNPq for their research fellowships.
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Marinho, E.B.S., Bassrei, A. & Andrade, R.F.S. Correlation analysis: application of DFA and DCCA in well log profiles. Comput Geosci 27, 551–559 (2023). https://doi.org/10.1007/s10596-023-10220-7
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DOI: https://doi.org/10.1007/s10596-023-10220-7