Transform-Domain Multidimensional Deconvolution – Sparsity V/S Low-Rank

Summary Seismic interferometry using multidimensional deconvolution is a robust framework to retrieve the Green’s function of the subsurface. Although conceptually elegant, the multidimensional deconvolution system is ill-conditioned in nature, i.e., the point-spread-function matrix contains small singular values. To overcome the numerical instability, the least-squares system can be solved by using the sparsity of the seismic wavefields in the curvelet-domain. However, the curvelet-domain-based sparsity-promotion solvers come with a very high computational cost and memory requirements due to transform-domain redundancy, thus making it not a practical solution for large-scale seismic data acquisition. To overcome the computational and memory requisite of the curvelet-based solver, in this work we present a computationally tractable factorization-based rank-minimization algorithm to perform multidimensional deconvolution. The proposed algorithm is suitable for large-scale seismic data since it avoids singular-value decompositions and uses a low-rank-based factorized formulation instead. Using a carefully selected, simple but geologically complex model, we demonstrate that the factorization-based rank-minimization framework is computationally feasible, both in terms of speed and memory usage, for the large-scale seismic data volumes while performing the multidimensional deconvolution.