Application of an optimized transmitting boundary with multiple artificial wave velocities in spectral-element simulation of seismic wave propagation

This paper applied an optimized transmitting boundary with multiple artificial velocities （denoted as c_aj-MTF） that is recently proposed by the authors to the high-accuracy spectral-element simulation of seismic wave propagation, and made a comparison study with several other classical artificial （or absorbing） boundary conditions including Liao’s multi-transmitting formula （MTF） boundary, perfectly matched layer （PML） boundary, viscous-spring boundary and the first-order Clayton-Engquist paraxial-approximation boundary. The results obtained from theoretical analysis and numerical tests are as follows: ① The formulation of c_{a j}-MTF is very similar to that of MTF, so it has most of the advantages of the latter, i.e., very simple expressions, easy to be implemented, adjustable accuracy, minimal computation cost, and general applicability. ② Unlike the traditional MTF boundary that has only a single artificial wave velocity （i.e., computational wave velocity）, c_{a j}-MTF has multiple artificial wave velocities. In the simulation of elastic waves, the computational wave velocity parameters of c_{a j}-MTF can be set to be P- and S-wave velocities, respectively. On this situation, the consistency between computational and physical wave velocities makes a significant improvement in the boundary accuracy. ③ c_{a j}-MTF boundary has an slightly lower accuracy than that of PML boundary, whereas it is significantly superior to MTF, viscous-spring boundary and the first-order paraxial-approximation boundary. ④ c_{a j}-MTF is superior to PML as it has much simpler formulations and better versatility. This work provides a convenient and high-efficient artificial boundary （or absorbing boundary） for spectral-element simulation of seismic wave propagation.