Anisotropic elastic least-squares reverse time migration with density variations in vertical transverse isotropic media

Elastic least-squares reverse time migration (ELSRTM) has the potential to provide higher-quality migration images related to the lithology and fluid by imaging multi-component seismic data than conventional elastic reverse time migration (ERTM). Oil and gas are widely stored in fractures and sedimentary rocks. The sedimentary rocks and the rocks with fractures will produce anisotropy. The anisotropy effect should be corrected in migration. In order to correct the anisotropic effect to the images of ELSRTM, a new anisotropic ELSRTM scheme is developed to image the multi-component seismic data in vertical transverse isotropic (VTI) media. This new ELSRTM method can invert high-quality images and correct the anisotropic effect in VTI media. Many ELSRTM methods assume that the density is constant. However, the constant-density assumption will generate false migration results when the density of media is variation. We derive the elastic VTI de-migration operator in the media with density variations based on Born approximation. The adjoint state equations and gradient formulas with respect to medium images in VTI media with density variations are also derived by the adjoint state method. Using the new elastic de-migration operator, adjoint state equations, and gradients in VTI media with density variations, we can produce high-resolution subsurface elastic reflectivity images. Numerical examples from the graben VTI model and modified HESS VTI model demonstrate that the proposed ELSRTM can not only generate the images with high quality but also correct the anisotropic effect in VTI media with density variations.