瑞雷波有限差分数值模拟中不同自由表面边界条件的对比

发布时间：2019-03-12 16:01

【摘要】：自由表面边界条件是决定瑞雷波数值模拟效果的关键因素。本文基于标准交错网格高阶有限差分法,在二维各向同性弹性介质背景下,针对应力镜像法(SIM)、改进应力镜像法(MSIM)、横向各向同性介质替换法(MS)和声学—弹性边界近似法(AEA)等四种最具代表性的自由表面边界条件进行了数值模拟,并在均匀半空间模型中从波场快照、波形曲线和频散曲线三个角度进行了对比分析。在相同条件下,上述四种方法均能生成符合勘探地球物理规律的波场快照,各自对应的数值解与解析解的拟合误差都随网格剖分精度的提高而减小,SIM和AEA数值模拟的稳定性和精度都明显高于MSIM和MS。基于层状介质模型的进一步研究表明:对于简单模型,SIM和AEA都能得到比MSIM和MS更高精度的数值模拟结果;对于复杂模型,AEA的精度最高,是最适合瑞雷波数值模拟的自由表面边界条件。
[Abstract]:The free surface boundary condition is the key factor to determine the effect of Rayleigh wave numerical simulation. In this paper, based on the standard staggered grid high-order finite difference method and in the context of two-dimensional isotropic elastic medium, an improved stress mirror method, (MSIM), is proposed for the stress mirror method (SIM),). Four of the most representative free surface boundary conditions, the transverse isotropic medium replacement method (MS) and the acoustic-elastic boundary approximation method (AEA), are numerically simulated and a snapshot of the wave field in a homogeneous half-space model is carried out. The three angles of waveform curve and dispersion curve are compared and analyzed. Under the same conditions, the above four methods can all generate wave field snapshots in accordance with the geophysical law of exploration, and the fitting errors of the corresponding numerical solutions and analytical solutions decrease with the increase of mesh generation accuracy. The stability and accuracy of SIM and AEA numerical simulation are obviously higher than those of MSIM and MS.. The further research based on the layered medium model shows that for the simple model, both SIM and AEA can obtain more accurate numerical simulation results than those of MSIM and MS. For complex models, AEA has the highest accuracy and is the most suitable free surface boundary condition for Rayleigh wave numerical simulation.
【作者单位】：中国地质大学地球物理与空间信息学院;地球内部多尺度成像湖北省重点实验室;
【基金】：国家自然科学基金项目(41574114、41174113) 中国地质大学(武汉)教学实验室开放基金项目(SKJ2016098)联合资助
【分类号】：P631.4

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