Full Waveform Inversion of Visco-Acoustic Media Based on the Symplectic Stereo-Modeling Method

Visco-acoustic full waveform inversion (FWI) is a widely used high-resolution seismic inversion method. It aims to achieve a joint inversion of the velocity and quality factor (Q) models. The resolution of inversion results highly depends on the accuracy of the seismic wave simulation. In this letter, the symplectic stereo-modeling (SSM) method is used to solve the visco-acoustic wave equation. We compare a series of numerical properties between SSM and the traditional finite difference (FD) methods such as Lax–Wendroff correction (LWC) method, including numerical dispersion, accuracy, efficiency, numerical errors, stability, etc. The results show that the maximum numerical dispersion error of SSM is about 9%, while that of LWC is about 24%. Meanwhile, SSM is closer to the analytical solution, computationally efficient and stable. We derive the velocity and Q gradients for visco-acoustic FWI based on the adjoint-state method using the SSM method, namely, SSM-based FWI. For the visco-acoustic Marmousi model, the results show that the proposed method has high inversion accuracy and minor numerical dispersion. Furthermore, for the field data, we implement a three-stage FWI for different frequency ranges and demonstrate the effectiveness of the proposed method.