Least‐squares reverse time migration based on an efficient pure qP‐wave equation

Abstract

Seismic waves propagating in anisotropic earth media suffer from waveform distortion, which leads to degraded resolution in seismic data imaging if this adverse effect is not corrected. Additionally, the wavefields simulated by the traditional coupled pseudo‐acoustic wave equations contain undesired shear wave artefacts and are unstable when Thomsen's anisotropy parameter ε is less than δ. To address these issues, many pure qP‐wave equations are proposed to describe wave propagation in anisotropic media. However, these equations are either low precision or high accuracy but computationally expensive. Considering the trade‐off between the computation efficiency and simulation accuracy, we derive a pure qP‐wave equation from the exact dispersion formula in tilted transverse isotropic media. The newly derived equation has only two higher order partial derivatives, which can better balance the accuracy and efficiency than the previous pure qP‐wave equations. The least‐squares reverse time migration method can balance amplitudes, suppress migration artefacts and improve imaging resolution. Then, based on the newly derived pure qP‐wave equation, we derive the Born modelling operator and adjoint migration operator and develop an anisotropic least‐squares reverse time migration method. To achieve the accelerated convergence, we introduce a generalized minimum residual algorithm to implement the anisotropic least‐squares reverse time migration method. Numerical simulation results show that the proposed pure qP‐wave equation outperforms the previous equations in balancing the trade‐off between accuracy and efficiency. In addition, synthetic examples demonstrate the effectiveness and robustness of our proposed anisotropic least‐squares reverse time migration method in correcting the deviations due to anisotropic effects.