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 引用本文: 李小军, 张恂, 邢浩洁. 基于动态人工波速的透射边界. 力学学报, 待出版.
Li Xiaojun, Zhang Xun, Xing Haojie. A transmitting boundary with time-varying computational artificial wave velocities. Chinese Journal of Theoretical and Applied Mechanics, in press.
 Citation: Li Xiaojun, Zhang Xun, Xing Haojie. A transmitting boundary with time-varying computational artificial wave velocities. Chinese Journal of Theoretical and Applied Mechanics, in press.

## A TRANSMITTING BOUNDARY WITH TIME-VARYING COMPUTATIONAL ARTIFICIAL WAVE VELOCITIES

• 摘要: 人工边界处理是近场地震波动数值模拟的关键问题, 其中透射边界(multi-transmitting formula, MTF)是一种应用较为广泛的人工边界方法, 但它也存在计算精度与稳定性相互冲突的问题. 为提高稳定性较好的低阶边界的模拟精度, 发展出一种动态人工波速透射边界, 能够适应复杂波动中外行波透射角随时间大幅度变化的情形, 并探讨了动态人工波速识别这一关键问题. 通过在当前时刻波场中沿人工边界附近划定观察窗口, 并在一段时间之前某时刻波场中构建出一组与边界法线夹角在−90° ~ 90°范围变化的筛选窗口, 设计出一种对这两个时刻局部窗口中的波场进行比对的图像处理方法来识别外行波的透射角度. 将识别得到的透射角度用于动态更新透射边界的人工波速, 实现基于动态人工波速透射边界的波动模拟. 在SH波动数值模拟中分别以单一脉冲波的简单波动和多个平面波叠加的复杂波动为例, 证明所发展的动态人工波速透射边界对于不同透射角的波动成分均具有较好的适应性, 模拟精度显著优于采用经验固定人工波速的传统透射边界. 该方法为发展和完善高精度且计算稳定的人工边界提供了一个全新的研究思路.

Abstract: 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.

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