多人工波速优化透射边界在谱元法地震波动模拟中的应用

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

将作者最近发展的多人工波速优化透射边界(记为c_(aj)-MTF)应用于高精度谱元法的地震波动模拟中,并与经典的廖氏透射(MTF)边界、完美匹配层(PML)边界、黏弹性边界以及一阶旁轴近似边界进行了比较分析.结果显示:(1)c_(aj)-MTF边界与MTF边界在形式上非常接近,它继承了后者公式简单、易于实现、精度可控、计算量低以及通用性好的优点;(2)不同于传统MTF边界的单一人工波速参数配置,c_(aj)-MTF边界所具有的多个人工波速参数可以分别取为P波和S波波速,此时边界计算波速与介质物理波速相匹配,能够大幅度提高复杂波动情形下的边界精度;(3)c_(aj)-MTF边界的精度略低于PML边界,不过要明显优于MTF边界、黏弹性边界以及一阶旁轴近似边界;(4)c_(aj)-MTF边界相比于PML边界的优势在于形式简洁且普遍适用.本研究为谱元法的地震波动模拟提供了一种便捷、高效的人工边界条件(即吸收边界条件)实现方法.

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 multitransmitting formula(MTF) boundary,perfectly matched layer(PML) boundary,viscousspring 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_(aj)-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_(aj)-MTF has multiple artificial wave velocities. In the simulation of elastic waves,the computational wave velocity parameters of c_(aj)-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_(aj)-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_(aj)-MTF is superior to PML as it has much simpler formulations and better versatility. This work provides a convenient and highefficient artificial boundary(or absorbing boundary) for spectral-element simulation of seismic wave propagation.