Adaptive parameter-related implementation of the free surface in elastic anisotropic full-waveform modeling

The near-surface anisotropy is one of the factors that lead to errors in static corrections, seismic imaging, and inaccurate surface velocity building. Therefore, it is important to study the propagation features of seismic waves in the near-surface with anisotropy. The finite-difference method is commonly used in seismic wave forward modeling, however, the numerical implementation of the free surface is nontrivial in this method, in particular to its implementation in the anisotropic media which is less studied. Here, we propose an adaptive parameter-related free surface implementation. This method is developed from the physical viewpoint with the average medium theory and limit theorem, in which the stress-free condition is implemented by modifications of the original constitutive relation and density at the free-surface points without additional computational requirements. Numerical experiments with the increasing complexity of anisotropy in both 2D and 3D demonstrate that this method can produce precise simulation results with a spatial sampling of 10 grid points per minimum wavelength. In addition, a time-space discontinues grid strategy can be introduced in this implementation to allow the usage of the coarse grid in the deeper part where the oversampling for the surface waves is not required, which increases the flexibility and the computational efficiency of the proposed method.