3D coupled acoustic-elastic migration with topography and bathymetry based on spectral-element and adjoint methods

In the context of the adjoint method, we considered 3D coupled acoustic-elastic migration in the presence of surface topography and/or bathymetry. Isotropic elastic imaging involves three primary kernels, related to mass density and shear and bulk moduli, and various secondary kernels, for example, related to P-wave impedance and compressional and shear-wave speeds. Similar to reverse-time migration, these kernels reflect the constructive interference between a forward wavefield generated by active sources and an adjoint wavefield triggered by simultaneously back propagating recorded reflections from all receivers. Forward and adjoint wavefields were simulated using a spectral-element method, which, due to its weak nature, captures free-surface topography in land surveys and bathymetry in marine acquisition. To avoid storing the entire 3D forward wavefield, required for calculating its interaction with the adjoint wavefield, we only saved information on domain boundaries and reconstructed the forward wavefield while simulating the adjoint wavefield. Their interactions were calculated and integrated on the fly, thereby eliminating storage issues but doubling memory and CPU requirements. Our 3D images confirmed a previous conclusion based on 2D simulations, namely, that the impedance kernel best highlights reflectors, whereas wave-speed kernels constrain large-scale structures, i.e., the background model.