Abstract：
Sparsity constrained deconvolution can improve the resolution of band-limited seismic data compared to conventional deconvolution. However, such deconvolution methods result in nonunique solutions and suppress weak reflections. The Cauchy function, modified Cauchy function, and Huber function are commonly used constraint criteria in sparse deconvolution. We used numerical experiments to analyze the ability of sparsity constrained deconvolution to restore reflectivity sequences and protect weak reflections under different constraint criteria. The experimental results demonstrate that the performance of sparsity constrained deconvolution depends on the agreement between the constraint criteria and the probability distribution of the reflectivity sequences; furthermore, the modified Cauchy-constrained criterion protects the weak reflections better than the other criteria. Based on the model experiments, the probability distribution of the reflectivity sequences of carbonate and clastic formations is statistically analyzed by using well-logging data and then the modified Cauchy-constrained deconvolution is applied to real seismic data much improving the resolution.
LI Guo-Fa,QIN De-Hai,PENG Geng-Xin et al. Experimental analysis and application of sparsity constrained deconvolution[J]. APPLIED GEOPHYSICS, 2013, 10(2): 191-200.
[1]
Antoine, G., and William, W. S., 2003, Robust inversion of seismic data using the Huber norm: Geophysics, 68(4), 1310 - 1319.
[2]
Canadas, G., 2002, A mathematical framework for blind deconvolution inversion problems: the 72nd SEG Annual Meeting, 2202 - 2205.
Debski, W., and Tarantola, A., 1995, Information on elastic parameters obtained from the amplitudes of reflected waves: Geophysics, 60, 1426 - 1436
[5]
Huber, P. J., 1981, Robust statistics: John Wiley and Sons, New York.
[6]
Liu, X. W., Nin, J. R., and Zhang, G. L., 2009, Cauchy sparse constrained Bayesian estimation based seismic blind deconvolution frame and algorithm: Geophysical Prospecting for Petroleum (in Chinese), 48(5), 459 - 646.
[7]
Kaaresen, K. F., and Taxt, T. M., 1998, Multichannel blind deconvolution of seismic signals: Geophysics, 63(6), 2093 - 2017.
[8]
Meng, X. H., 2005, Study of blind deconvolution and application of method: Oil Geophysical Prospecting (in Chinese), 40(6), 642 - 645.
[9]
Oldenburg, D. W., Levy, S., and Whittall, K. P., 1981 Wavelet estimation and deconvolution: Geophysics, 46(11), 1528 - 1542.
[10]
Ralph, A. W., 1978, Minimum entropy deconvolution: Geoexploration, 16(1 - 2), 21 - 35.
[11]
Sacchi, M. D., 1997, Reweighting strategies in seismic deconvolution: Geophysical Journal International, 129(3), 651 - 656.
[12]
Sacchi, M. D., 1999, Statistical and transform methods for seismic signal processing: University of Alberta, Edmonton, Canada.
[13]
Sacchi, M. D., and Ulrych, T. J, 2000, Nonminimum-phase wavelet estimation using higher order statistics: The Leading Edge, 19(1), 80 - 83
[14]
Tarantola, A., 1984, Inversion of seismic reflection data in the acoustic approximation: Geophysics, 49, 1259 - 1266.
[15]
Ulrych, T. J., and Sacchi, M. D., 2001, A tutorial: A bayes tour of inversion: Geophysics, 66, 55 - 69.
[16]
Youzwishen, C. F., 2001, Non-linear sparse and block constraints for seismic inversion problems. M. Sc. thesis, University of Alberta.
[17]
Zhang, F. C., Liu, J. Y., and Yang, P. J., 2008, Modified Cauchy-constrained seismic blind deconvolution: Oil Geophysical Prospecting (in Chinese), 43(4), 391 - 396.
2013, Vol. 10 
