An immersed absorbing boundary condition for scalar wavefield modeling under topography

Abstract

The irregular surface is an important aspect that needs be considered in finite-difference (FD) numerical simulations of seismic waves. To avoid the artificial edge reflections from the irregular surface, an effective absorbing boundary condition (ABC) should be designed with consideration of the topography. However, the FD methods usually use a rectangular grid discretization that causes a staircase problem in approximating the irregular surface. Additionally, the current ABC often assumes a horizontal interface between the interior computational domain and the top absorbing domain, which is the not case when an irregular surface exists. To avoid the spurious scattering caused by the staircase and adjust the ABC to irregular surfaces, we develop an immersed ABC for scalar wavefield modeling. We place the irregular surface at fractional grid nodes according to the true topography and we predict the wavefields at ghost grid points by a plane-wave transmitting boundary condition (BC). The ghost grid points refer to those grid nodes required by the interior FD calculations and the wavefield prediction is implemented along the normal direction of the surface, which means wavefield absorption along the normal direction. Numerical examples are presented to verify the feasibility of our immersed ABC under topography.