A 2-D Local Correlative Misfit for Least-Squares Reverse Time Migration With Sparsity Promotion

Least-squares reverse time migration (LSRTM) attempts to produce a high-quality image for complicated subsurface structures. However, large amplitude discrepancies between the synthetic and observed seismic data are problematic for high-resolution imaging. Alternatively, correlative LSRTM (CLSRTM) misfit has been proposed to improve the imaging quality of complicated structures. However, the CLSRTM ignores the local characteristics of the 2-D seismic data. Thus, we developed a 2-D local correlative misfit for LSRTM (2-D-LCLSRTM) to improve the imaging resolution. In this case, a 2-D sliding window was used to obtain local-scale seismic data. A 2-D correlation method was then used to measure the similarity between the local-scale synthetic and observed data. Consequently, the 2-D-LCLSRTM misfit could reduce amplitude constraints and emphasize phase similarity, which has a potential for improving deep structure as it can boost weak seismic signals. To suppress the migration artifacts, we incorporated the sparsity promotion method with the 2-D-LCLSRTM misfit and used the fast iterative shrinkage-thresholding algorithm (FISTA) to solve it iteratively. In the numerical examples, a Marmousi model, a Salt model, and a marine field seismic dataset were used to test the effectiveness of the 2-D-LCLSRTM method. Compared with the commonly used RTM and sparsity promotion-based CLSRTM methods, the 2-D-LCLSRTM with sparsity promotion can better image deep reflectors and obtain high-resolution imaging results.