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多尺度有限差分法模拟复杂介质波传问题
引用本文:马坚伟,杨慧珠,朱亚平.多尺度有限差分法模拟复杂介质波传问题[J].物理学报,2001,50(8):1415-1420.
作者姓名:马坚伟  杨慧珠  朱亚平
作者单位:(1)The Center of Wave Phenomenon,Department of Geophysics,Colorado School of Mines,Colorado 80401,USA; (2)清华大学工程力学系,地震波勘探研究所,北京100084
基金项目:国家自然科学基金(批准号:19872037)资助的课题.
摘    要:利用有限差分和紧支集正交小波变换对波动方程的时间、空间进行联合近似求解,提出一种适合于一般边界非均匀耗散介质中波传问题数值模拟的快速自适应混合算法——多尺度有限差分(multiresolution finite difference缩写为MRFD)方法.将波传问题的求解转换到小波域中进行,利用小波基的自适应性与消失矩特性,使偏微分算子矩阵稀疏化,有效改善了计算量等.地球物理勘探中的数值实例显示了算法具有良好效率 关键词: MRFD 小波变换 多尺度 波传问题

关 键 词:MRFD  小波变换  多尺度  波传问题
收稿时间:2000-12-26
修稿时间:3/5/2001 12:00:00 AM

SIMULATION OF ACOUSTIC WAVE PROPAGATION IN COMPLEX MEDIA USING MRFD METHOD
MA JIAN-WEI,YANG HUI-ZHU and ZHU YA-PING.SIMULATION OF ACOUSTIC WAVE PROPAGATION IN COMPLEX MEDIA USING MRFD METHOD[J].Acta Physica Sinica,2001,50(8):1415-1420.
Authors:MA JIAN-WEI  YANG HUI-ZHU and ZHU YA-PING
Abstract:This paper is devoted to the simulation of acoustic wave propagation in complex media, applying the finite difference scheme and the orthonormal compactly supported wavelet transform approximation,to the time and the space dimension of the wave equation, respectively. A new method, which is a fast adaptive arithmetic, named Multiresolution Finite Difference (MRFD) is first proposed to solve the problem of the wave propagation in multi-layered medium with nonperiodic boundary condition. Thus the problem is solved in the wavelet domain rather than in the traditional Euclidian space. Due to adaptive and vanishing-moment property of the wavelet basis, the difference operator and solution vector have sparseness in the wavelet domain. MRFD is a promising method because of some advantages such as lighter computational burden, efficiency of convergence and robustness. Numerical results in geophysics exploration show the effectiveness and potential of the method.
Keywords:MRFD  wavelet transform  multiresolution analysis  wave propagation
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