An imaging condition for acoustic reverse time migration with implicit angle-dependent weighting factors and its extended applications for imaging elastic P-P and S-S data

The imaging condition is a crucial component of the reverse time migration. In its conventional form, it involves cross-correlating the extrapolated source- and receiver-side wavefields. Effective imaging conditions are usually developed to suppress imaging artefacts (e.g. low-wavenumber artefacts) and enhance the image quality. For acoustic reverse time migration, not only the scalar pressure but also their spatial and/or time derivatives are used in the imaging condition, similar to the gradient terms of adjoint tomography. These operations implicitly introduce additional angle-domain weighting factors to the image results. In this study, based on an analysis of angle-dependent properties of the existing imaging conditions, we propose a new imaging condition tailored for acoustic reverse time migration. It can be implemented efficiently using the variables within the finite-difference solver. Without explicitly measuring wave propagation directions, the proposed imaging condition can naturally suppress the low-wavenumber artefacts while maintaining a relatively wider imaging aperture, thereby corresponding to a broader wavenumber sampling range. Additionally, the evolved imaging conditions for imaging elastic P-P and S-S scattering and reflections are also formulated. In the angle domain, we conduct a comparative analysis between existing imaging conditions and the newly proposed ones. Various numerical examples are provided to demonstrate the advantages of the new imaging conditions. A comprehensive understanding of their angle-domain properties may be further beneficial to constructing reasonable inversion strategies for full waveform inversion.