论文部分内容阅读
在地震波传播数值模拟的过程中,需要使用吸收边界条件达到衰减人为边界反射的目的,其中完全匹配层(PML)吸收边界条件被认为是目前最理想的吸收边界条件.但在三维地震波传播数值模拟中直接应用常规的PML吸收边界条件存在编程实现复杂、计算资源需求高等不足之处.本文基于传统的NPML吸收边界条件,提出了一种改进的方法.该方法通过引入伸展函数和辅助变量,把PML介质中的三维弹性波动方程分解成正常计算项和衰减项,其中衰减项的计算只在PML区域内部进行,其值只与坐标轴的方向相关,可通过离散数值迭代求解.分析和试验结果表明,该方法避免了卷积运算,减少了辅助变量的个数,具有理论方程简洁、编程实现简单、计算资源需求少等优点,能更有效地解决三维地震波传播数值模拟中的吸收边界问题.
In the process of numerical simulation of seismic wave propagation, it is necessary to use absorption boundary conditions to attenuate the artificial boundary reflection, in which perfectly matched layer (PML) absorption boundary conditions are considered as the most ideal absorption boundary conditions.But in the numerical simulation of three-dimensional seismic wave propagation , The direct application of conventional PML absorbing boundary conditions has the disadvantages of complex programming and high computational resource requirements.Based on the traditional NPML absorbing boundary conditions, an improved method is proposed in this paper.By introducing the extension function and auxiliary variables, The three-dimensional elastic wave equation in PML media is decomposed into normal and attenuation terms, of which the calculation of the attenuation term is only carried out inside the PML region, the value of which is only related to the direction of the coordinate axis and can be solved iteratively by discrete numerical analysis and test results It shows that this method avoids the convolution operation and reduces the number of auxiliary variables. It has the advantages of simple theoretical equation, simple programming and less resource requirements, which can more effectively solve the problem of absorbing boundary in 3D seismic wave propagation numerical simulation.