复杂介质中地震波模拟的无单元法
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摘要
复杂介质中地震波的传播多是通过求取单程或双程波动方程的数值解进行模拟的。波动方程的数值解法多种多样,本文将工程和岩石力学领域中广泛应用的一种无网格算法——无单元法应用于地震模拟。由于无单元法的节点完全独立存在,因此在计算成本上与有限元相比优势明显;再采用滑动最小二乘的拟合方法使得无单元法具有精度高、独立变量解高次连续等优点。本文在介绍无单元法原理的基础上,通过薄膜震动算例表明该方法与有限差分法相比有精度优势;然后将无单元法用于叠前地震模拟,并讨论了几种吸收边界方法在地震模拟中与无单元法的结合。模型计算的结果表明,辅以有效的吸收边界,无单元法能够获得波场完整、走时精确的理论地震图,其精度和稳定性皆令人满意。
Propagation of seismic wave in complex medium is mostly simulated by numeric solution of oneway or two-way wave equation. The numeric solution of wave equation is various. A mesh-free algorithm--element-free method that is widely usedfor engineering mechanics and litho-mechanics fields is used for seismic simulation in the paper. It exists clear superiority in computational cost in comparison with finite-element algorithm because of independent existence of node in element-free method; besides, using moving least squares fitting method makes element-free method have the advantages of high precision and smooth high-order derivatives of independent variables solution. On the basis of introducing the principle of element-free method, the paper showed the superiority in precision by the case of damping film vibration in comparison with finite-element algorithm; then the element-free method for prestack seismic simulation isased and the combination of several absorbing boundary conditions with element-free method in seismic simulation is discussed. The results of model calculation showed that element-free method adding in effective absorbing boundary can gain complete and travel-time-precious seismic wave section with satisfactory in both precision and stability.
Propagation of seismic wave in complex medium is mostly simulated by numeric solution of oneway or two-way wave equation. The numeric solution of wave equation is various. A mesh-free algorithm--element-free method that is widely usedfor engineering mechanics and litho-mechanics fields is used for seismic simulation in the paper. It exists clear superiority in computational cost in comparison with finite-element algorithm because of independent existence of node in element-free method; besides, using moving least squares fitting method makes element-free method have the advantages of high precision and smooth high-order derivatives of independent variables solution. On the basis of introducing the principle of element-free method, the paper showed the superiority in precision by the case of damping film vibration in comparison with finite-element algorithm; then the element-free method for prestack seismic simulation isased and the combination of several absorbing boundary conditions with element-free method in seismic simulation is discussed. The results of model calculation showed that element-free method adding in effective absorbing boundary can gain complete and travel-time-precious seismic wave section with satisfactory in both precision and stability.
引文
[1]Belytschko T,Lu Y Y and Gu L.Element-free Galerkin method.International Journal for Numerical Methods in Engineering,1994,37:229~256
[2]Zhu T,Zhang J and Atluri S.A local boundary integral equation(LBIE)method in computational mechanics and a meshless discretization approach.Computational Mechanics,1998,21:223~235
[3]Melenk J and Babuska I.The partition of unity meth-od:basic theory and applications.Computer Methods in Applied Mechanics and Engineering,1996,139:289~314
[4]Lu Y Y,Belytschko T and Tabbara M.Element-free Garlerkin method for wave propagation and dynamic fracture.Computer Methods in Applied Mechanics and Engineering,1995,126:131~153
[5]Zhu T and Atluri S N.A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element-free galerkin method.Computational Mechanics,1998,21:211~222
[6]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.中国地震,2003,19(3):236~242
[7]周维垣,寇晓东.无单元法及其在岩土工程中的应用.岩土工程学报,1998,20(1):5~9
[8]Clayton R and Engquist B.Absorbing boundary conditions for acoustic and elastic wave equations.Bulletin of the Seismological Society of America,1977,67:1529~1540
[9]Liao Z P.Extrapolation nonreflecting boundary conditions.Wave Motion,1996,24:117~138
[10]Sarma G S,Mallick K and Gadhinglajkar V R.Nonreflecting boundary condition in finite-element formulation for an elastic wave equation.Geophysics,1998,63:1006~1016
[2]Zhu T,Zhang J and Atluri S.A local boundary integral equation(LBIE)method in computational mechanics and a meshless discretization approach.Computational Mechanics,1998,21:223~235
[3]Melenk J and Babuska I.The partition of unity meth-od:basic theory and applications.Computer Methods in Applied Mechanics and Engineering,1996,139:289~314
[4]Lu Y Y,Belytschko T and Tabbara M.Element-free Garlerkin method for wave propagation and dynamic fracture.Computer Methods in Applied Mechanics and Engineering,1995,126:131~153
[5]Zhu T and Atluri S N.A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element-free galerkin method.Computational Mechanics,1998,21:211~222
[6]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.中国地震,2003,19(3):236~242
[7]周维垣,寇晓东.无单元法及其在岩土工程中的应用.岩土工程学报,1998,20(1):5~9
[8]Clayton R and Engquist B.Absorbing boundary conditions for acoustic and elastic wave equations.Bulletin of the Seismological Society of America,1977,67:1529~1540
[9]Liao Z P.Extrapolation nonreflecting boundary conditions.Wave Motion,1996,24:117~138
[10]Sarma G S,Mallick K and Gadhinglajkar V R.Nonreflecting boundary condition in finite-element formulation for an elastic wave equation.Geophysics,1998,63:1006~1016
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