Vertical transversely isotropic elastic least-squares reverse time migration based on elastic wavefield vector decomposition

Anisotropic elastic reverse time migration (RTM) is a promising technique for imaging complex oil and gas reservoirs. However, the migrated images often suffer from low spatial resolution, migration artifacts, wave-mode crosstalk, and unbalanced amplitude response. Conventional vertical transversely isotropic elastic least-squares reverse time migration (VTI-elastic LSRTM) defines stiffness parameter perturbations as elastic images, which have different physical meanings from VTI-elastic RTM images. We have developed a VTI-elastic LSRTM method based on elastic wavefield vector decomposition that is a natural extension of VTI-elastic RTM. More specifically, our method applies least-squares inversion to VTI-elastic RTM and defines the compressional- and shear-wave reflectivity as elastic images (PP, PS, SP, and SS images). When computing the elastic images, we decompose the elastic wavefields into compressional and shear wavefields and cross-correlate the corresponding wave modes. We derive the reverse time demigration operator by taking the adjoint of the RTM operator. Using the migration and demigration operators, we formulate the VTI-elastic LSRTM as a linear inverse problem with the least-squares criterion. The conjugate gradient method is used to solve the optimization problem. Three numerical examples are presented to test the feasibility of our method. The VTI-elastic LSRTM images have higher resolution, fewer migration artifacts and wave-mode crosstalk, and improved amplitude response when compared with VTI-elastic RTM images.