A TRANSMITTING BOUNDARY WITH TIME-VARYING COMPUTATIONAL ARTIFICIAL WAVE VELOCITIES

The treatment of artificial boundary is a key issue in the numerical simulation of seismic wave propagation, among which multi-transmitting formula (MTF) is a widely used artificial boundary method, but it also suffers from the conflict between simulation accuracy and stability. In order to improve the simulation accuracy of those lower order boundary conditions which have the advantage of good stability, we have developed a time-varying artificial velocity-based multi-transmitting formula, which can adapt to the large temporal variation in the transmitting angle of out-going waves for complex wave propagation problem, and discussed the key issue of the identification of time-varying artificial wave velocity. At the current time instant the neighborhood of an artificial boundary is divided into a number of observation windows, and a group of selection windows are constructed for each observation window. These selection windows are apart from each observation window at shift angles varying in the range of −90° ~ 90°. By adopting an image comparison technique, one can seek out the selection window whose wave field is most like that of the observation window, thus the shift angle of the selection window is the out-going wave’s transmitting angle in the local area near the artificial boundary. The image recognized transmitting angles are subsequently utilized to update the computational artificial velocities of the multi-transmitting formula, which bring about a wave-motion numerical simulation with time-varying artificial wave velocity-based transmitting boundary. The proposed method is tested in numerical simulations of SH wave propagation which include a simple single pulse wave propagation, and complex wave propagation that are a compound of several plane waves with different transmitting angles. Numerical results validates that the time-varying artificial wave velocity-based multi-transmitting formula has good adaptability to the complex wave components with quite different transmitting angles, and therefore its simulation accuracy is much better than the traditional transmitting boundary which uses empirical fixed artificial wave velocity. This work has provided a novel research idea for the development and improvement of high-precision and computationally stable artificial boundary conditions.