Coherence estimation algorithm using Kendall’s concordance measurement on seismic data
Yang Tao1,2, Gao Jing-Huai1,2, Zhang Bing1,2, and Wang Da-Xing3
1. Institute of Wave and Information, Xi'an Jiaotong University, Xi’an 710049, China.
2. National Engineering Laboratory for Offshore Oil Exploration, Xi'an 710049, China.
3. Exploration and Development Research Institute of Petrochina Changqing Oil Field Company, Xi'an 710018, China.
Abstract The coherence method is always used to describe the discontinuity and heterogeneity of seismic data. In traditional coherence methods, a linear correlation coefficient is always used to measure the relationship between two random variables (i.e., between two seismic traces). However, mathematically speaking, a linear correlation coefficient cannot be applied to describe nonlinear relationships between variables. In order to overcome this limitation of liner correlation coefficient. We proposed an improved concordance measurement algorithm based on Kendall’s tau. That mainly concern the sensitivity of the liner correlation coefficient and concordance measurements on the waveform. Using two designed numerical models tests sensitivity of waveform similarity affected by these two factors. The analysis of both the numerical model results and real seismic data processing suggest that the proposed method, combining information divergence measurement, can not only precisely characterize the variations of waveform and the heterogeneity of an underground geological body, but also does so with high resolution. In addition, we verified its effectiveness by the actual application of real seismic data from the north of China.
This work was supported by the Major Programs of National Natural Science Foundation of China (No. 41390454) and the Major Research Plan of the National Natural Science Foundation of China (No. 91330204).
Cite this article:
. Coherence estimation algorithm using Kendall’s concordance measurement on seismic data[J]. APPLIED GEOPHYSICS, 2016, 13(3): 529-538.
[1]
Bahorich, M. S., and Farmer, S. L., 1995, 3-D seismic discontinuity for faults and stratigraphic features: The coherence cube: The Leading Edge, 14, 1053−1058.
[2]
Chopra, S., and Marfurt, K., 2007, Seismic attributes for prospect identification and reservoir characterization: Society of Exploration Geophysicists Geophysical Developments, 11, Tulsa, Oklahoma.
[3]
Cohen, I., and Coifman, R. R., 2002, Local discontinuity measures for 3-D seismic data: Geophysics, 67, 1933−1945.
[4]
Dou, X. Y., Han, L. G., Wang, E. L., Dong, X. H., Yang, Q., and Yan, G. H., 2014, A fracture enhancement method based on the histogram equalization of eigenstructure-based coherence: Applied Geophysics, 11, 179−185.
[5]
Gersztenkorn, A., and Marfurt, K. J., 1999, Eigenstructure-based coherence computations as an aid to 3-D structural and stratigraphic mapping: Geophysics, 64, 1468−1479.
[6]
Kendall, M. G., 1938, A new measure of rank correlation: Biometrika, 30, 81−93.
[7]
Kruskal, W. H., 1958, Ordinal Measures of Association: Journal of the American Statistical Association, 53, 814−861.
[8]
Lehmann, E. L., and D'Abrera, H. J. M., 1975, Nonparametric statistical methods based on ranks: Journal of the Royal Statistical Society, 83(140), 347−353.
[9]
Levy, S., and Oldenburg, D., 1987, Automatic phase correction of common-midpoint stacked data: Geophysics, 52, 51−59.
[10]
Li, Y., Lu, W., Zhang, S., and Xiao, H., 2006, Dip-scanning coherence algorithm using eigenstructure analysis and supertrace technique: Geophysics, 71, V61−V66.
[11]
Lu, W., Li, Y., Zhang, S., Xiao, H., and Li, Y., 2005, Higher-order-statistics and supertrace-based coherence-estimation algorithm: Geophysics, 70, P13−P18.
[12]
Marfurt, K. J., Kirlin, R. L., Farmer, S. L., and Bahorich, M. S., 1998, 3-D seismic attributes using a semblance-based coherency algorithm: Geophysics, 63, 1150−1165.
[13]
Marfurt, K. J., Sudhaker, V., Gersztenkorn, A., Crawford, K.D., and Nissen, S.E., 1999, Coherency calculations in the presence of structural dip: Geophysics, 64, 104−111.
[14]
Nelsen, R. B., 1999, Lecture Notes in Statistics: Dependence, 3(1), 139−146.
[15]
Rényi, A., 1959, On a theorem of P. Erd?s and its application in information theory: Mathematica (Cluj), 1(24), 341-344.
[16]
Rényi, A., 1961, On measures of entropy and information: in Neyman, J., Ed., Fourth Berkeley Symposium on Mathematical Statistics and Probability: University of California Press, Berkeley, 1, 547-561.
[17]
Salicrú, M., 1994, Measures of information associated with Csiszar's divergences: Kybernetika Praha, 30(5), 563-573.
[18]
Wang, J., and Lu, W. K., 2010, Coherence cube enhancement based on local histogram specification: Applied Geophysics, 7, 249-256.
[19]
Wang, Y., Lu, W., and Zhang, P., 2015, An improved coherence algorithm with robust local slope estimation: Journal of Applied Geophysics, 114, 146−157.
[20]
Yang, T., Zhang, B., and Gao, J., 2013, A fast coherence algorithm for seismic data interpretation based on information divergence: SEG Technical Program Expanded Abstracts, 2554−2558.
[21]
Zhao, H., Gao, J., and Liu, F., 2014, Frequency-dependent reflection coefficients in diffusive-viscous media: Geophysics, 79, T143−T155.