Finite-difference method for modeling the surface wave propagation with surface topography in anisotropic-viscoelastic media

The growth of urbanization makes it increasingly important to accurately investigate underground spaces. Surface-wave-based inversion methods are becoming popular due to their cost-effectiveness and efficiency in reconstructing underground space. However, these methods may produce inaccurate results in the presence of media anisotropy or/and viscoelasticity. To investigate the influence of media anisotropy or viscoelasticity on surface waves, it is crucial to develop an efficient and accurate forward modeling method in anisotropic-viscoelastic (AV) media. The finite-difference (FD) method is a widely used forward modeling method in surface-wave-based inversion methods. However, implementing the free-surface boundary condition and representing non-flat topography can be challenging. Considering the challenges described above, this study proposes a simple and efficient FD method for modeling surface-wave propagation. The proposed method employs a parameter-modified strategy to implement the stress-free condition by modifying the model parameters near the (non-) flat free-surface boundary. A staircase discretization strategy is then used to represent the non-flat free surface. To suppress the staircase diffractions caused by the staircase discretization strategy, an independent wavefield superposition is adopted with modeling results of different parameter configurations. Compared with conventional FD methods, the proposed method can reduce computational costs while accurately simulating surface waves. Numerical experiments have demonstrated the accuracy and feasibility of the proposed method. The proposed method provides a theoretical basis for surface-wave-based inversion methods and contributes to the development of accurate underground space investigation. •Present a forward modeling method in anisotropic-viscoelastic medium.•A parameter-modified implementation of the free surface is proposed.•A discrete model design method is used to suppress the staircase noise.•The proposed method is simple, efficient and has good code portability.•The proposed method can reduce computational cost and memory requirements.