滑动最小二乘法求解地震波波动方程
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摘要
本文首次将固体力学领域中的滑动最小二乘拟合法用于求解地震波波动方程.与有限差分法相比,该方法所采用的拟合思想使得解在全空间域更加连续,同时仍然保持高精度的特性;与有限元法相比,该方法绕过变分原理,经过算法的有限差分化之后,其所需的计算量及数据存储量均可大大降低.薄膜震动的数值算例表明了该方法的上述特点.最后,通过对几个模型的合成地震模拟试验,进一步证明了滑动最小二乘法用于波动方程数值模拟的可行性.
In this paper,the moving least squares(MLS) fitting criterion commonly used in solid mechanics is discussed for solving seismic wave equations.The fitting in MLS instead of interpolation in finite difference method(FDM) makes the solution more continuous in the whole space domain without any loss of accuracy.On the other hand,although the absence of variational principle which is necessary in finite element method(FEM) save little computational volume,the cost could further be cut down greatly by a differentiated method.An example of vibrant film shows the merits of the MLS method.Furthermore,some synthetic seismograms obtained by MLS method prove its effectivity for wave equation seismic modeling.
In this paper,the moving least squares(MLS) fitting criterion commonly used in solid mechanics is discussed for solving seismic wave equations.The fitting in MLS instead of interpolation in finite difference method(FDM) makes the solution more continuous in the whole space domain without any loss of accuracy.On the other hand,although the absence of variational principle which is necessary in finite element method(FEM) save little computational volume,the cost could further be cut down greatly by a differentiated method.An example of vibrant film shows the merits of the MLS method.Furthermore,some synthetic seismograms obtained by MLS method prove its effectivity for wave equation seismic modeling.
引文
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[2]张永刚.地震波场数值模拟方法[J].石油物探,2003,42(2):143~148.
[3]Alford R M,Kelly K R,and Boore D M.Accuracy of finite-difference modeling of the acoustic wave equation[J].Geo-physics,1974,39:834~842.
[4]张文生,宋海斌.三维正交各向异性介质三分量高精度有限差分正演模拟[J].石油地球物理勘探,2001,36(4):422~432.
[5]Marfurt K J.Accuracy of finite-difference and finite-elementmodeling of the scalar and elastic wave equations[J].Geo-physics,1984,49:533~549.
[6]张美根,王妙月,李小凡,等.各向异性弹性波场的有限元数值模拟[J].地球物理学进展,2002,17(3):384~389.
[7]Belytschko T,Lu Y Y,and Gu L.Element-free Galerkinmethods[J].International Journal for Numerical Methods inEngineering,1994,37:229~256.
[8]王杰光,曾德顺.滑动最小二乘插值函数配点法[J].力学季刊,2002,23(1):120~125.
[9]贾晓峰,王润秋,胡天跃.求解波动方程的任意差分精细积分法[J].中国地震,2003,19(3):236~242.
[10]廖振鹏.法向透射边界条件[J].中国科学(E辑),1996,26(2):185~192.
[2]张永刚.地震波场数值模拟方法[J].石油物探,2003,42(2):143~148.
[3]Alford R M,Kelly K R,and Boore D M.Accuracy of finite-difference modeling of the acoustic wave equation[J].Geo-physics,1974,39:834~842.
[4]张文生,宋海斌.三维正交各向异性介质三分量高精度有限差分正演模拟[J].石油地球物理勘探,2001,36(4):422~432.
[5]Marfurt K J.Accuracy of finite-difference and finite-elementmodeling of the scalar and elastic wave equations[J].Geo-physics,1984,49:533~549.
[6]张美根,王妙月,李小凡,等.各向异性弹性波场的有限元数值模拟[J].地球物理学进展,2002,17(3):384~389.
[7]Belytschko T,Lu Y Y,and Gu L.Element-free Galerkinmethods[J].International Journal for Numerical Methods inEngineering,1994,37:229~256.
[8]王杰光,曾德顺.滑动最小二乘插值函数配点法[J].力学季刊,2002,23(1):120~125.
[9]贾晓峰,王润秋,胡天跃.求解波动方程的任意差分精细积分法[J].中国地震,2003,19(3):236~242.
[10]廖振鹏.法向透射边界条件[J].中国科学(E辑),1996,26(2):185~192.
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