Reciprocity-aware adaptive tile low-rank factorization for large-scale 3D multidimensional deconvolution

ABSTRACT Low-rank regularization is an effective technique for addressing ill-posed inverse problems when the solution tends to be rank-deficient. Global low-rank assumptions do not always hold for seismic wavefields; however, local low-rank features are observed in many practical situations. To leverage this feature, the unknown parameter is partitioned into tiles, each represented via low-rank factorization. This framework is applied to regularize multidimensional deconvolution in the frequency domain, considering two key factors. First, the unknown variable, referred to as Green’s function, must maintain symmetry according to the reciprocity principle of wave propagation. To ensure symmetry within the tile-based low-rank framework, diagonal tiles are represented as the product of a low-rank factor and its transpose when numerically rank-deficient. Otherwise, they are represented by preconditioned dense forms. Symmetry in off-diagonal is achieved by parameterizing subdiagonal tiles as the product of two distinct low-rank factors, with the corresponding superdiagonal tiles assigned as their transposes. Second, the local rank of Green’s function is allowed to vary with frequency. The numerical rank and optimal tile size at each frequency are estimated based on the solution from a benchmark solver. This approach is referred to as reciprocity-aware, factorization-based adaptive tile low-rank regularization. To enhance the applicability of the local low-rank approximation, receivers are reordered using a Hilbert space-filling curve, ensuring that receivers close in physical space are close in index in the unknown Green’s function matrix. Our method is applied to a large-scale 3D deconvolution problem, demonstrating improved accuracy over the benchmark solver, especially in scenarios with added random noise and sparse source sampling.