Theoretical and quantitative evaluation of hybrid PML-ABCs for seismic wave simulation

IF 1.2 4区 地球科学 Q3 Earth and Planetary Sciences
Yuhang Wang , Wei Zhang
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引用次数: 0

Abstract

A good artificial boundary treatment in a seismic wave grid-based numerical simulation can reduce the size of the computational region and increase the computational efficiency, which is becoming increasingly important for seismic migration and waveform inversion tasks requiring hundreds or thousands of simulations. Two artificial boundary techniques are commonly used: perfectly matched layers (PMLs), which exhibit the excellent absorption performance but impose a greater computational burden by using finite layers to gradually reduce wave amplitudes; and absorbing boundary conditions (ABCs), which have the high computational efficiency but are less effective in absorption because they employ the one-way wave equation at the exterior boundary. Naturally, PMLs have been combined with ABCs to reduce the number of PMLs, thus improving the computational efficiency; many studies have proposed such hybrid PMLs. Depending on the equations from which the ABCs are derived, there are two hybrid PML variants: the PML+unstretched ABC (UABC), in which the ABC is derived from a physical equation; or the PML+stretched ABC (SABC), in which the ABC is derived from the PML equation. Even though all the previous studies concluded that hybrid PMLs can improve the absorption performance, none of them quantified how many PMLs can be removed by combining the PML with the ABC compared with the pure PML. In this paper, we systematically study the absorption performance of the two hybrid PML variants. We develop a method to distinguish the artificial reflections from the PML-interior interface and those caused by the PML exterior boundary to accurately approximate the additional absorption achieved by using the UABC and the SABC. The reflection coefficients based on a theoretical derivation and numerical tests both show that the UABC amplifies most reflections and is not recommended in any situation; conversely, the SABC can always diminish reflections, but the additional absorption achieved by the SABC is relatively poor and cannot effectively reduce the number of PMLs. In contrast, we find that simply increasing the damping parameter improves absorption better than the PML+SABC. Our results show that the improvement in absorption achieved by combining the PML with either the SABC or the UABC is not better than that obtained by simply adjusting the damping profile of the PML; thus, combining the PML with the ABC is not recommended in practice.

混合pml - abc用于地震波模拟的理论与定量评价
在基于地震波网格的数值模拟中,良好的人工边界处理可以减小计算区域的大小,提高计算效率,这对于需要成百上千次模拟的地震偏移和波形反演任务变得越来越重要。两种常用的人工边界技术是:完全匹配层(pml),它具有良好的吸收性能,但由于使用有限层来逐渐降低波幅,计算负担较大;吸收边界条件(ABCs)计算效率高,但由于在外边界采用单向波动方程,吸收效果较差。自然,将pml与abc相结合可以减少pml的数量,从而提高计算效率;许多研究提出了这种混合pml。根据导出ABC的方程,有两种混合PML变体:PML+未拉伸ABC (UABC),其中ABC从物理方程导出;或PML+拉伸ABC (SABC),其中ABC由PML方程导出。尽管以往的研究都得出杂交PML可以提高吸收性能的结论,但没有一项研究量化了与ABC相结合的PML与纯PML相比可以去除多少PML。在本文中,我们系统地研究了两种混合PML变体的吸收性能。我们开发了一种区分PML内部界面和PML外部边界引起的人工反射的方法,以准确地近似使用UABC和SABC获得的额外吸收。基于理论推导和数值测试的反射系数都表明,UABC放大了大部分反射,在任何情况下都不推荐使用;相反,SABC总是可以减少反射,但SABC实现的附加吸收相对较差,不能有效地减少pml的数量。相比之下,我们发现仅仅增加阻尼参数比PML+SABC更能改善吸收。我们的研究结果表明,将PML与SABC或UABC结合所获得的吸收改善并不比简单调整PML的阻尼曲线所获得的吸收改善更好;因此,在实践中不建议将PML与ABC结合使用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Earthquake Science
Earthquake Science GEOCHEMISTRY & GEOPHYSICS-
CiteScore
1.10
自引率
8.30%
发文量
42
审稿时长
3 months
期刊介绍: Earthquake Science (EQS) aims to publish high-quality, original, peer-reviewed articles on earthquake-related research subjects. It is an English international journal sponsored by the Seismological Society of China and the Institute of Geophysics, China Earthquake Administration. The topics include, but not limited to, the following ● Seismic sources of all kinds. ● Earth structure at all scales. ● Seismotectonics. ● New methods and theoretical seismology. ● Strong ground motion. ● Seismic phenomena of all kinds. ● Seismic hazards, earthquake forecasting and prediction. ● Seismic instrumentation. ● Significant recent or past seismic events. ● Documentation of recent seismic events or important observations. ● Descriptions of field deployments, new methods, and available software tools. The types of manuscripts include the following. There is no length requirement, except for the Short Notes. 【Articles】 Original contributions that have not been published elsewhere. 【Short Notes】 Short papers of recent events or topics that warrant rapid peer reviews and publications. Limited to 4 publication pages. 【Rapid Communications】 Significant contributions that warrant rapid peer reviews and publications. 【Review Articles】Review articles are by invitation only. Please contact the editorial office and editors for possible proposals. 【Toolboxes】 Descriptions of novel numerical methods and associated computer codes. 【Data Products】 Documentation of datasets of various kinds that are interested to the community and available for open access (field data, processed data, synthetic data, or models). 【Opinions】Views on important topics and future directions in earthquake science. 【Comments and Replies】Commentaries on a recently published EQS paper is welcome. The authors of the paper commented will be invited to reply. Both the Comment and the Reply are subject to peer review.
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