Least-squares reverse time migration with first-order scattering wave equation penalty

Abstract

Least-square reverse time migration (LSRTM) can obtain high-resolution and high-amplitude preserved imaging results. Compared to the traditional migration methods, LSRTM can be robust and free of low-frequency artefacts. Under the first-order Born approximation, the corresponding scattering wave equation can only describe the wavefield under the approximate of weak perturbation. Nevertheless, in complicated media, weak scattering potential and small scatter assumptions are generally difficult to be satisfied. For inversion, with full wavefield information, the inversion results can be contaminated by artefacts caused by a strong scattering interface that to high-order scattered waves from strong scattering interfaces. To handle this problem, the first-order scattering wave equation is introduced as a penalty term to the LSRTM objective function, which can suppress the artefacts caused by the weak scattering hypothesis of the Born approximation. As a result, the LSRTM converts to an alternative optimisation problem: firstly, we need to find the optimal solution in the first-order scattered wavefield space. That is, by calculating a virtual source corresponding to the time-domain augmented wave equation, reconstructing an accurate first-order scattered wavefield based on the first-order scattering wave equation; secondly, an updated gradient of the reflectivity is then calculated based on the reconstructed first-order scattered wavefield. Therefore, the inverted reflectivity calculated according to the first-order scattered wavefield can be capable of obtaining the imaging results with high precision and high-amplitude preservation. Synthetic and real dataset results illustrate the effectiveness of the proposed method.