Sparse seismic deconvolution via recurrent neural network

Abstract We propose a new efficient method to perform deconvolution of post-stacking post-migration seismic data. We employ recurrent neural networks (RNNs) to obtain super resolution reflectivity images. The network is designed and trained to take into account time and space relations. The robustness of the proposed method is experimentally validated for both synthetic data and real data with challenging structures and difficult signal-to-noise ratio (SNR) environment. We explore the system's behavior for different training and testing scenarios and discuss potential problems for future research. We show that training with synthetic data of simple structures solely can yield enhanced and detailed real data inversion results. The proposed method can be applied to large volumes of three-dimensional (3D) seismic data.

[1]  Emmanuel J. Candès,et al.  Super-Resolution from Noisy Data , 2012, Journal of Fourier Analysis and Applications.

[2]  Tadeusz J. Ulrych,et al.  Processing via spectral modeling , 1991 .

[3]  Xiaoou Tang,et al.  Image Super-Resolution Using Deep Convolutional Networks , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  N. Ricker.  THE FORM AND NATURE OF SEISMIC WAVES AND THE STRUCTURE OF SEISMOGRAMS , 1940 .

[5]  Martín Abadi,et al.  TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems , 2016, ArXiv.

[6]  Carlos Fernandez-Granda.  Support detection in super-resolution , 2013, ArXiv.

[7]  D. Donoho.  Superresolution via sparsity constraints , 1992 .

[8]  Peng Jiang,et al.  Deep-Learning Inversion of Seismic Data , 2019, IEEE Transactions on Geoscience and Remote Sensing.

[9]  Yanghua Wang,et al.  Seismic Inverse Q Filtering , 2008 .

[10]  Israel Cohen,et al.  Multichannel blind seismic deconvolution using dynamic programming , 2008, Signal Process..

[11]  Israel Cohen,et al.  Multichannel Deconvolution of Seismic Signals Using Statistical MCMC Methods , 2010, IEEE Transactions on Signal Processing.

[12]  Mrinal K. Sen,et al.  Stacking velocity estimation using recurrent neural network , 2018, SEG Technical Program Expanded Abstracts 2018.

[13]  Jürgen Schmidhuber,et al.  Long Short-Term Memory , 1997, Neural Computation.

[14]  William S.D. Wilcock,et al.  Exploration Seismology, 2nd edition , 1997 .

[15]  A. J. Berkhout,et al.  Resolution in seismic trace inversion by parameter estimation , 1985 .

[16]  Sanyi Yuan,et al.  Sparse reflectivity inversion for nonstationary seismic data , 2014 .

[17]  Shai Dekel,et al.  Stable Support Recovery of Stream of Pulses With Application to Ultrasound Imaging , 2015, IEEE Transactions on Signal Processing.

[18]  Caroline Chaux,et al.  A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal , 2014, IEEE Transactions on Signal Processing.

[19]  Kjetil F. Kaaresen,et al.  Multichannel blind deconvolution of seismic signals , 1998 .

[20]  David C. Henley,et al.  Gabor deconvolution: Estimating reflectivity by nonstationary deconvolution of seismic data , 2011 .

[21]  Chiyuan Zhang,et al.  Machine-learning Based Automated Fault Detection in Seismic Traces , 2014 .

[22]  Yanghua Wang.  Frequencies of the Ricker wavelet , 2015 .

[23]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[24]  고봉환,et al.  Minimum Entropy Deconvolution을 이용한 회전체 시스템의 결함 모니터링 , 2013 .

[25]  Yves Goussard,et al.  Multichannel seismic deconvolution , 1993, IEEE Trans. Geosci. Remote. Sens..

[26]  Ronald R. Coifman,et al.  Local discontinuity measures for 3-D seismic data , 2002 .

[27]  Israel Cohen,et al.  Detection and extraction of fault surfaces in 3D seismic data , 2006 .

[28]  Israel Cohen,et al.  Seismic signal recovery based on Earth Q model , 2017, Signal Process..

[29]  Tomer Michaeli,et al.  Deep-STORM: super-resolution single-molecule microscopy by deep learning , 2018, 1801.09631.

[30]  Jerry M. Mendel,et al.  A novel approach to seismic signal processing and modeling , 1981 .

[31]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[32]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Thomas M. Cover,et al.  Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing) , 2006 .

[34]  Jr. G. Forney,et al.  Viterbi Algorithm , 1973, Encyclopedia of Machine Learning.

[35]  Wenlong Wang,et al.  Automatic Salt Detection with Machine Learning , 2018, 80th EAGE Conference and Exhibition 2018.

[36]  Leiv-J. Gelius,et al.  INVERSE Q-FILTERING. A SPECTRAL BALANCING TECHNIQUE* , 1987 .

[37]  Kevin P. Dorrington,et al.  Genetic‐algorithm/neural‐network approach to seismic attribute selection for well‐log prediction , 2004 .

[38]  Tadeusz J. Ulrych,et al.  Estimation of quality factors from CMP records , 2002 .

[39]  Tony Kusuma,et al.  A Neural Network Approach to Automate Velocity Picking , 1994 .

[40]  Einar Kjartansson,et al.  Constant Q-wave propagation and attenuation , 1979 .

[41]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[42]  Thang H. Nguyen.  High resolution seismic reflectivity inversion , 2008 .

[43]  Michael E. Murat,et al.  AUTOMATED FIRST ARRIVAL PICKING: A NEURAL NETWORK APPROACH1 , 1992 .

[44]  Mauricio D. Sacchi,et al.  Fast 3D Blind Seismic Deconvolution via Constrained Total Variation and GCV , 2013, SIAM J. Imaging Sci..

[45]  Tomaso Poggio,et al.  Automated fault detection without seismic processing , 2017 .

[46]  Mauricio D. Sacchi,et al.  A Fast and Automatic Sparse Deconvolution in the Presence of Outliers , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[47]  H. L. Taylor,et al.  Deconvolution with the l 1 norm , 1979 .

[48]  Xaq Pitkow,et al.  Skip Connections Eliminate Singularities , 2017, ICLR.

[49]  Israel Cohen,et al.  Three-dimensional sparse seismic deconvolution based on earth Q model , 2019, Signal Process..

[50]  Emmanuel J. Candès,et al.  Towards a Mathematical Theory of Super‐resolution , 2012, ArXiv.

[51]  Ali Cafer Gürbüz,et al.  Seismic Tunnel Imaging and Detection , 2006, 2006 International Conference on Image Processing.

[52]  Biondo L. Biondi,et al.  3D Seismic Imaging , 2006 .

[53]  Mrinal K. Sen,et al.  Automatic NMO correction and velocity estimation by a feedforward neural network , 1998 .

[54]  Israel Cohen,et al.  Multichannel Seismic Deconvolution Using Markov–Bernoulli Random-Field Modeling , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[55]  Israel Cohen,et al.  Dynamic Programming For Multichannel Blind Seismic Deconvolution , 2007 .

[56]  Nitish Srivastava,et al.  Dropout: a simple way to prevent neural networks from overfitting , 2014, J. Mach. Learn. Res..

[57]  Rui Zhang,et al.  Seismic sparse-layer reflectivity inversion using basis pursuit decomposition , 2011 .

[58]  Israel Cohen,et al.  Detection And Extraction of Fault Surfaces In 3-D Seismic Data , 2005 .

[59]  Jean-Christophe Pesquet,et al.  Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed ${\ell _1}/{\ell _2}$ Regularization , 2014, IEEE Signal Processing Letters.