Viscoacoustic least-squares reverse-time migration using the L1-2 norm sparsity constraint

Abstract

Abstract Least-squares reverse-time migration (LSRTM) has become an advanced technique for complex structures imaging of the subsurface, as it can provide a higher resolution and more balanced amplitude migrated image than conventional reverse-time migration (RTM). However, the intrinsic attenuation of the subsurface introduces amplitude attenuation and phase dispersion of the seismic wavefield, which leads to an inexact inverted image kinematically and dynamically. Moreover, the imperfect geometry, limited bandwidth of seismic data, and inappropriate modeling kernel etc., would inevitably introduce two side-effects in the migrated image, resulting in degradation of LSRTM imaging potential. To alleviate these issues, we present a data-domain sparsity constraint viscoacoustic LSRTM algorithm in this paper. In particular, we use the decoupled constant Q fractional Laplacian viscoacoustic wave equation as the modeling kernel to describe the attenuation effects of the subsurface, while a model constraint constructed in the misfit function via the L1-2 norm is carried out to clear the migrated artifacts and boost the imaging resolution. Thanks to the excellent performance in sparsity, the drawbacks of unconstrained LSRTM can be effectively mitigated by the L1-2 norm-based regularization. In this paper, we adopt the alternating direction of multipliers method to iteratively address the constrained L1-2 minimization problem by implementing a proximal operator, and three synthetic examples are used to evaluate the effectiveness and practicability of the proposed strategy. Migration results prove that the proposed scheme can effectively compensate for the attenuation effects, improve the resolution, and suppress the migration artifacts of inverted images even in the complex imaging situations.