Fast least-squares reverse time migration based on stable pseudo-acoustic wave equations for tilted transverse isotropic media

Conventional tools for seismic imaging normally ignore the anisotropy of the media to produce images of the subsurface, and such omission reduces the quality of the images. Therefore, it is necessary to develop methods which account for subsurface anisotropic properties in order to produce more accurate images. In this paper, we present a least-squares reverse time migration based on the coupled pseudo-acoustic equations for tilted transverse isotropic media. Thus, from the stable pseudo-acoustic wave equation for such media, we derive the linearized modelling (Born modelling) and adjoint migration operators to implement a least-squares reverse time migration. Then, to save time and effort on development, while ensuring optimal performance of the inversion, we based our implementation on the domain-specific language Devito, which, in turn, allowed us to easily verify the correctness of the developed operators. Synthetic examples demonstrate the validity of our approach in dealing with tilted transverse isotropic media.