3-D Image-Domain Least-Squares Reverse Time Migration With L1 Norm Constraint and Total Variation Regularization

Data-domain least-squares reverse time migration (DDLSRTM) has been proved to be a more effective imaging tool for complex structures, relative to the standard reverse time migration (RTM) approach. One of the difficulties in DDLSRTM is that the enormous computational costs may impede its application in large-scale 3-D data. To mitigate this problem, with the help of point spread functions (PSFs) and spatial interpolation, we have developed a novel 3-D image-domain least-squares reverse time migration (IDLSRTM) approach, which requires once migration and modeling calculations. However, because of the incomplete acquisition geometry of seismic recordings, IDLSRTM is a highly ill-posed inverse problem. The inverted image from the conventional IDLSRTM approach may suffer from the migration artifacts caused by the coarse source and receiver sampling and spatial discontinuity and instability caused by the truncated PSFs. To solve the ill-posedness and improve image quality, the L1 norm constraint and total variation (TV) regularization are introduced into the objective function of IDLSRTM. The alternating direction method of multipliers (ADMMs) algorithm is developed to solve this optimization problem. Through some 3-D synthetic and field data, it can determine that the proposed IDLSRTM approach computationally efficiently produces a high-fidelity reflection image with good spatial continuity and fewer migration artifacts. It has shown this approach to be a cost-effective and practical inversion-based imaging tool for 3-D field datasets.