The possibilities of compressed-sensing-based Kirchhoff prestack migration

Abstract

CitationThe possibilities of compressed-sensing-based Kirchhoff prestack migration 2014, 79 (3):S113 GEOPHYSICS ABSTRACTAn 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.

Compressive sensing imaging of microseismic events constrained by the sign-bit

“…In the first case, the target image is not sparse because it consists of continuous nonzero coefficients defining the interfaces of an earth model ( Figure 1). This scenario has recently been explored by Aldawood et al (2014). Two important differences between our example and the work presented in Aldawood et al (2014) deserve clarification.…”

“…This scenario has recently been explored by Aldawood et al (2014). Two important differences between our example and the work presented in Aldawood et al (2014) deserve clarification. First, in this work, CS refers to the theory formalized by the seminal papers of Candes et al (2006) and Donoho (2006), which are characterized by the introduction of a compression matrix Φ different from the identity.…”

“…Under this definition, the results presented by Aldawood et al (2014) would correspond to the solution of a sparse representation problem and not to the application of CS. The second difference is that Aldawood et al (2014) consider the earth's reflectivity sparse, which we also adopt as a reasonable assumption in a vertical direction; however, this is commonly not the case in a lateral direction. For the examples presented in Aldawood et al (2014), vertical sparseness is enough to obtain encouraging results.…”

“…Without the incorporation of a compression element, we opted to call the implementation a sparse representation problem (see, for example, Vera Rodriguez et al, 2012b). Under this definition, the results presented by Aldawood et al (2014) would correspond to the solution of a sparse representation problem and not to the application of CS. The second difference is that Aldawood et al (2014) consider the earth's reflectivity sparse, which we also adopt as a reasonable assumption in a vertical direction; however, this is commonly not the case in a lateral direction.…”

The possibilities of least-squares migration of internally scattered seismic energy

“…Dai et al (2012) adapt LSM to image blended data in a multisource RTM framework. Wang and Sacchi (2007), Herrmann and Li (2012), and Aldawood et al (2014a) improved the leastsquares imaging by imposing sparseness constraints on the least-squares solution to enhance the spatial resolution of the seismic events.…”