1. School of Information and Communication Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China; 2. China National Offshore Oil Corporation, Beijing 116503, China
Abstract：Seismic wavelet extraction plays an important role in seismic data processing. The seismic wavelet is determined by the amplitude spectrum and phase spectrum; thus estimating the amplitude spectrum of seismic wavelets is a key step. The common methods for extracting amplitude spectra of seismic wavelets are subject to limitations on the reflectivity type and the seismic wavelet form, failing to achieve a wide application in actual seismic data processing. To obtain the accurate amplitude spectra of seismic wavelets, we proposed prior knowledge embedded deep learning. Firstly, given the prior information, i.e. smoothness of the seismic wavelet amplitude spectrum, the observed seismic data were preprocessed. Then, the smoothed amplitude spectrum of seismograms was input into a 12-layer deep neural network to obtain the amplitude spectrum of the seismic wavelet. Compared with traditional spectrum simulation, the proposed method can obtain an accurate estimation of the unimodal and non-unimodal amplitude spectra of seismic wavelets without any hypothesis about reflectivity. Moreover, it can avoid the parameter estimation in polynomial fitting methods and the calculation error induced by opera-ting band estimation. Specifically, it has superior anti-noise performance, and the advantage of this method has been proved by model examples and actual data tests.
Symes W W. The seismic reflection inverse problem[J]. Inverse Problems, 2009, 25(12):123008.
[2]
Chen H L, Gao J H, Liu N H, et al. Multi-trace semi-blind nonstationary deconvolution[J]. IEEE Geo-science and Remote Sensing Letters, 2019, 16(8):1195-1199.
[3]
Walden A T, White R E. Seismic wavelet estimation:a frequency domain solution to a geophysical noisy input-output problem[J]. IEEE Transactions on Geoscience and Remote Sensing, 1998, 36(1):287-297.
[4]
Tan T H. Wavelet spectrum estimation[J]. Geophy-sics, 1999, 64(6):1836-46.
[5]
Edgar J A, Van der Baan M. How reliable is statistical wavelet estimation?[J]. Geophysics, 2011, 76(4):V59-V68.
[6]
Wiggins R A. Minimum entropy deconvolution[J]. Geo-exploration, 1978, 16(1-2):21-35.
[7]
Van der Baan M. Time-varying wavelet estimation and deconvolution by kurtosis maximization[J]. Geo-physics, 2008, 73(2):V11-V18.
[8]
Van der Baan M, Fomel S. Nonstationary phase estimation using regularized local kurtosis maximization[J]. Geophysics, 2009, 74(6):A75-A80.
[9]
Van der Baan M, Fomel S, Perz M. Nonstationary phase estimation:A tool for seismic interpretation[J]. The Leading Edge, 2010, 29(9):1020-1026.
[10]
Robinson E A, Treitel S. Geophysical Signal Analysis[M]. Prentice-Hall, 2000.
[11]
Robinson E A, Treitel S. Digital imaging and deconvolution[C]. The ABCs of Seismic Exploration and Processing, 2008.
[12]
Margrave G F, Lamoureux M P, Henley D C. Gabor deconvolution:estimating reflectivity by nonstationary deconvolution of seismic data[J]. Geophysics, 2011, 76(3):W15-W30.
[13]
高静怀, 汪玲玲, 赵伟.基于反射地震记录变子波模型提高地震道分辨率[J]. 地球物理学报, 2009, 52(5):1289-1300.GAO Jinghuai, WANG Lingling, ZHAO Wei. Enhancing resolution of seismic traces based on the changing wavelet model of the seismogram[J]. Chinese Journal of Geophysics, 2009, 52(5):1289-1300.
[14]
Gao J H, Yang S L, Wang D X, et al. Estimation of quality factor Q from the instantaneous frequency at the envelope peak of a seismic signal[J]. Journal of Computational Acoustics, 2011, 19(1):155-179.
[15]
Gao J H, Zhang B. Estimation of seismic wavelets based on the multivariate scale mixture of Gaussians model[J]. Entropy, 2010, 12(1):14-33.
[16]
Wang L L, Gao J H, Zhao W, et al. Enhancing resolution of nonstationary seismic data by molecular-Gabor transform[J]. Geophysics, 2013, 78(1):V31-V41.
[17]
Otis R M, Smith R B. Homomorphic deconvolution by log spectral averaging[J]. Geophysics, 1977, 42(6):1146-1157.
[18]
Rosa A L R, Ulrych T J. Processing via spectral mo-deling[J]. Geophysics, 1991, 56(8):1244-1251.
[19]
唐博文, 赵波, 吴艳辉, 等. 一种实现谱模拟反褶积的新途径[J]. 石油地球物理勘探, 2010, 45(增刊1):66-70.TANG Bowen, ZHAO Bo, WU Yanhui, et al. A new way to realize spectral modeling deconvolution[J]. Oil Geophysical Prospecting, 2010, 45(S1):66-70.
[20]
Gao J H, Zhang B, Han W M, et al. A new approach for extracting the amplitude spectrum of the seismic wavelet from the seismic traces[J]. Inverse Problems, 2017, 33(10):103012.
[21]
Wang L X, Mendel J M. Adaptive minimum prediction-error deconvolution and source wavelet estimation using Hopfield neural networks[J]. Geophysics, 1992, 57(5):882-840.
[22]
Chen H L, Gao J H, Jiang X D, et al. Optimization-inspired deep learning high-resolution inversion for seismic data[J]. Geophysics, 2021, 86(3):A27-A57.
[23]
唐杰, 孟涛, 韩盛元, 等. 基于多分辨率U-Net网络的地震数据断层检测方法[J]. 石油地球物理勘探, 2021, 56(3):436-445.TANG Jie, MENG Tao, HAN Shengyuan, et al. A fault detection method of seismic data based on MultiRes-Unet[J]. Oil Geophysical Prospecting, 2021, 56(3):436-445.
[24]
Yilmaz O. Seismic Data Processing[M]. SEG Press, 1987.
[25]
Neidell N S. Could the processed seismic wavelet be simpler than we think?[J]. Geophysics, 1991, 56(4):681-690.
[26]
Wang Y H. Generalized seismic wavelets[J]. Geophysical Journal International, 2015, 203:1172-1178.
[27]
Walden A T, Hosken J W J. The nature of the non-Gaussianity of primary reflection coefficients and its significance for deconvolution[J]. Geophysical Prospecting, 1986, 34(5):1038-1066.
[28]
Saggaf M M, Robinson E A. A unified framework for the deconvolution of traces of nonwhite reflectivity[J]. Geophysics, 2000, 65(6):1660-1676.
[29]
Samorodnitsky G, Taqqu M S. Stable Non-Gaussian Random Processes Stochastic Models with Infinite Variance[M]. Chapman and Hall, New York, 1994.
[30]
Pavel C, Wolfgang H, Weron R. Statistical Tools for Finance and Insurance[M]. Springer, Berlin, 2005.
[31]
Weron R. On the Chambers-Mallows-Stuck method for simulating skewed stable random variables[J]. Statistics & Probability Letters, 1996, 28(2):165-171.
[32]
Painter S, Beresford G, Paterson L. On the distribution of seismic reflection coefficients and seismic amplitudes[J]. Geophysics, 1995, 60(5):1187-1194.
[33]
宋常州, 张旭明. 地震资料高分辨率处理技术应用[J]. 石油地球物理勘探, 2009, 44(1):44-48.SONG Changzhou, ZHANG Xuming. Seismic data high resolution processing technique and its application[J]. Oil Geophysical Prospecting, 2009, 44(1):44-48.
