The possibilities of compressed-sensing-based Kirchhoff prestack migration

An approximate subsurface reflectivity distribution of the earth is usually obtained through the migration process. However, conventional migration algorithms, including those based on the least-squares approach, yield structure descriptions that are slightly smeared and of low resolution caused by the common migration artifacts due to limited aperture, coarse sampling, band-limited source, and low subsurface illumination. To alleviate this problem, we use the fact that minimizing the L1-norm of a signal promotes its sparsity. Thus, we formulated the Kirchhoff migration problem as a compressed-sensing (CS) basis pursuit denoise problem to solve for highly focused migrated images compared with those obtained by standard and least-squares migration algorithms. The results of various subsurface reflectivity models revealed that solutions computed using the CS based migration provide a more accurate subsurface reflectivity location and amplitude. We applied the CS algorithm to image synthetic data from a fault model using dense and sparse acquisition geometries. Our results suggest that the proposed approach may still provide highly resolved images with a relatively small number of measurements. We also evaluated the robustness of the basis pursuit denoise algorithm in the presence of Gaussian random observational noise and in the case of imaging the recorded data with inaccurate migration velocities.

[1]  Michael W. Marcellin,et al.  JPEG2000 - image compression fundamentals, standards and practice , 2013, The Kluwer international series in engineering and computer science.

[2]  S. Operto,et al.  Joint ray + Born least-squares migration and simulated annealing optimization for target-oriented quantitative seismic imaging , 2011 .

[3]  Daniel Cohen-Or,et al.  ℓ1-Sparse reconstruction of sharp point set surfaces , 2010, TOGS.

[4]  Yaxun Tang.  Target-oriented wave-equation least-squares migration/inversion with phase-encoded Hessian , 2009 .

[5]  Bart De Moor,et al.  Kernel-based Data Fusion for Machine Learning - Methods and Applications in Bioinformatics and Text Mining , 2009, Studies in Computational Intelligence.

[6]  Michael P. Friedlander,et al.  Probing the Pareto Frontier for Basis Pursuit Solutions , 2008, SIAM J. Sci. Comput..

[7]  Antoine Guitton,et al.  Regularizing seismic inverse problems by model reparameterization using plane-wave construction , 2006 .

[8]  G. Schuster,et al.  Least-squares migration of incomplete reflection data , 1999 .

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

[10]  Joan L. Mitchell,et al.  JPEG: Still Image Data Compression Standard , 1992 .

[11]  Mark Noble,et al.  Robust elastic nonlinear waveform inversion: Application to real data , 1990 .

[12]  Wafik B. Beydoun,et al.  Reference velocity model estimation from prestack waveforms: Coherency optimization by simulated annealing , 1989 .

[13]  R. Clayton,et al.  An iterative inversion of back‐scattered acoustic waves , 1988 .

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

[15]  Armando Manduca,et al.  Highly Undersampled Magnetic Resonance Image Reconstruction via Homotopic $\ell_{0}$ -Minimization , 2009, IEEE Transactions on Medical Imaging.

[16]  Clifford H. Thurber,et al.  Parameter estimation and inverse problems , 2005 .

[17]  D. L. Donoho,et al.  Rapid MR Imaging with "Compressed Sensing" and Randomly Under-Sampled 3DFT Trajectories , 2004 .

[18]  Albert Tarantola,et al.  Inversion of seismic waveforms using neural networks , 1992 .

[19]  A. Tarantola,et al.  Retrieving Both the Impedance Variations And Background Velocity In Reflection Seismics Using Least-squares Waveform Inversion , 1988 .