The fourth-order absorbing boundary condition with optimized coefficients for the simulation of the acoustic equation*

This paper introduces the fourth-order absorbing boundary condition (ABC) into staggered-grid finite difference forward modeling of the first-order stress–velocity acoustic equation, and develops a new method to optimize coefficients of the fourth-order ABC to further improve its overall absorbing effect. Theoretical analysis and the results of numerical tests demonstrate that the fourth-order ABC with optimized coefficients has much higher absorbing efficiency than both the conventional second-order and fourth-order ABCs without optimized coefficients, for waves with large incident angles. Compared with the perfectly matched layer (PML) with 40 layers, the fourth-order ABC not only has a much better absorbing effect, but also uses far less computer memory for calculation. We present the fourth-order ABC with optimized coefficients as an ideal artificial boundary for the simulation of the acoustic equation based on extensive and complex structure models.