二维各向同性介质地震波全波场的有限差分模拟
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摘要
对地震波场的有限差分方程进行了详细的推导,采用改进的中心线算法对有限差分方程中的大型稀疏线性方程组进行求解,并对算法的稳定性进行了分析。通过对二维双层弹性介质中的地震波全波场的模拟,获得了清晰的地震波波场特征,包括面波及体波波场特征。
The finite difference equations of the seismic wave field are derived detailedly,used improved center-line method to solve the FD equations with large-spare array,and the stability of the method is analyzed.Through the full wave field modeling in 2D elastic media with horizontal and dip interfaces,the characteristics of the full seismic wave field,including surface wave and body wave,can be modeled clearly.
The finite difference equations of the seismic wave field are derived detailedly,used improved center-line method to solve the FD equations with large-spare array,and the stability of the method is analyzed.Through the full wave field modeling in 2D elastic media with horizontal and dip interfaces,the characteristics of the full seismic wave field,including surface wave and body wave,can be modeled clearly.
引文
[1]冯英杰,杨长春,吴萍.地震波有限差分模拟综述[J].地球物理学进展,2007,22(2):487-491.
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[6]王秀明,张海澜,王东.利用高阶交错网格有限差分法模拟地震波在非均匀孔隙介质中的传播[J].地球物理学报,2003,46(6):842-849.
[7]王德利,何樵登,韩立国.裂隙型单斜介质中多方位地面三分量记录模拟[J].地球物理学报,2005,48(2):386-393.
[8]谢靖.物探数据处理的数学方法[M].北京:地质出版社,1981.
[8]何倡礼.解病态线性方程组的奇异值分解法及其应用[M].武汉:中国地质大学出版社,1990.
[10]吕玉增,熊彬,薛霆虓.地球物理数据处理基础[M].北京:地质出版社,2011.
[11]张志海,杨建辉.求解线性方程组的一种迭代方法算法的一种改进[J].CT理论与应用研究,1994,3(4):20-23.
[12]高望东,姜家辉,张勇.求解大型线性稀疏方程组的中心线法[J].工程数学学报,1997,14(1):92-98.
[13]Renolds A.Boundary condtions for the numerical solution of wave propagation problems[J].Geophysics,1978,43(6):1099-1110.
[14]Clayton R,Engquist B.Absorbing boundary conditions for wave equation migration[J].Geophysics,1980,45(5):895-904.
[15]Stacey R.Improved transparent boundary formulations for the elastic wave equation[J].Bulletin of the Seismological Society of A-merica,1988,78(6):2089-2097.
[16]Javaherian A.产生有限差分合成地震图的最佳震源时间函数[J].地震学报,1994,16(1):18-23.
[17]董清华.震源数值模拟[J].世界地震工程,2000,16(3):27-32.
[2]Alterman Z,Karal F C.Propagation of seismic wave in layered media by finite difference methods[J].Bulletin of the SeismologicalSociety of America,1968,58(1):367-398.
[3]Aford R M,Kelly K R,Ward R W,et al.Accuracy of finite-difference modeling of acoustic wave equation[J].Geophysics,1974,39(6):834-842.
[4]Kelly K R,Ward R W,Treitel S,et al.Synthetic seismograms:a finite-difference approach[J].Geophysics,1976,41:2-27.
[5]Boore D M.Finite-difference methods for seismic wave propagation in heterogeneous materials[M]//Methods in ComputationalPhysics.Bolt B A.New York:Academic Press,1972,11:1-37.
[6]王秀明,张海澜,王东.利用高阶交错网格有限差分法模拟地震波在非均匀孔隙介质中的传播[J].地球物理学报,2003,46(6):842-849.
[7]王德利,何樵登,韩立国.裂隙型单斜介质中多方位地面三分量记录模拟[J].地球物理学报,2005,48(2):386-393.
[8]谢靖.物探数据处理的数学方法[M].北京:地质出版社,1981.
[8]何倡礼.解病态线性方程组的奇异值分解法及其应用[M].武汉:中国地质大学出版社,1990.
[10]吕玉增,熊彬,薛霆虓.地球物理数据处理基础[M].北京:地质出版社,2011.
[11]张志海,杨建辉.求解线性方程组的一种迭代方法算法的一种改进[J].CT理论与应用研究,1994,3(4):20-23.
[12]高望东,姜家辉,张勇.求解大型线性稀疏方程组的中心线法[J].工程数学学报,1997,14(1):92-98.
[13]Renolds A.Boundary condtions for the numerical solution of wave propagation problems[J].Geophysics,1978,43(6):1099-1110.
[14]Clayton R,Engquist B.Absorbing boundary conditions for wave equation migration[J].Geophysics,1980,45(5):895-904.
[15]Stacey R.Improved transparent boundary formulations for the elastic wave equation[J].Bulletin of the Seismological Society of A-merica,1988,78(6):2089-2097.
[16]Javaherian A.产生有限差分合成地震图的最佳震源时间函数[J].地震学报,1994,16(1):18-23.
[17]董清华.震源数值模拟[J].世界地震工程,2000,16(3):27-32.
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