Several absorbing boundary conditions have been suggested to reduce the reflections at the artificial grid boundary Bayliss et al. (1982); Berenger (1994); Engquist and Majda (1977). One kind of absorbing boundary condition is based on the one-way wave equation, and others are based on absorbing layers. In this paper, I introduce a high order one-way wave equation absorbing boundary condition, which can be solved using low order partial differential equations.
To simulate the wavefield in an open domain, absorbing boundary condition will be transparent to outgoing waves and be an obstacle to incoming waves. So, for a rectangular domain, the wavefield at the grid boundary satisfies the one-way wave equation. For example, the wavefield at the right boundary satisfies the leftgoing wave equation, and the wavefield at the left boundary satisfies the rightgoing wave equation. Solving the internal equation, which is a full wave equation in modeling and a one-way wave equation in migration, and using absorbing boundary conditions, we can simulate the wavefield in an open domain.