Model parameter design for modeling surface topography in VTI elastic finite-difference near-surface simulations

The near-surface anisotropy is one of the factors leading to an inaccurate velocity estimation in the shallow area, which has a strong impact on the static correction of land data and seismic imaging of the subsurface in depth. To investigate the anisotropy influence, the consideration of medium anisotropy in near-surface seismic modeling becomes necessary. In the oil and gas industry, finite-difference (FD) methods are commonly used for seismic wave modeling, thanks to their simplicity, accuracy, and high efficiency. However, for near-surface modeling, the implementation of free-surface boundary conditions and nonflat topography representation are the two main obstacles preventing the effectiveness of FD methods. To address these two issues in the vertical transversely isotropic anisotropic scenarios, we have developed a simple and efficient method for the discrete model design which can be easily applied to the conventional Cartesian-grid FD modeling. Our method involves: (1) the parameter-averaging method for implicitly implementing the stress-free condition by a modification of model anisotropy parameters near the (non) flat free-surface boundary and (2) an independent wavefield superposition with modeling results of different parameter configurations to accurately represent the rugged topography and significantly reduce the staircase diffractions caused by a staircase approximation of continuous surface in the Cartesian-grid discretization. For validation of this method, we conduct several numerical tests in 2D and 3D spaces. The accuracy is demonstrated by a comparison of the spectral-element solutions of SPECFEM in modeling the seismic wave propagation in the presence of an irregular free surface. From the aspect of computational efficiency, it is more promising in practical applications due to the use of wavefield superposition strategy in this method which does not require finer spatial sampling to eliminate the staircase diffractions.