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Modeling of elastic wave propagation on a curved free surface using an improved finite-difference algorithm

Science China(Physics,Mechanics & Astronomy) 2004年第5期47卷 633-648页

作者： wang xiuming1,{1., arrc, po.bo. 113., techno.o.y park, bentley, wa 6102, australia 2. Institute of Acoustics, Chinese Academy of Sciences, Beijing 1.0080, China 3. Present address: Institute of Acoustics, Chinese Academy of Sciences, Beijing 1.0080, China csiro.petro.eum ARRC Bentley Australia Institute of Acoustics Chinese Academy of Sciences Beijing China

Based on existing direct and imaging methods of a staggered finite-difference scheme, an improved algorithm for staggered finite-difference is proposed to implement rugged topographic free boundary conditions. This method assumes that the free surface can be implemented with horizontal and vertical free surface segments and their corners; the free surface passes through the grid points of shear stress components, instead of the normal stress components. Imaging is carried out for stress components in both horizontal and vertical directions, thus increasing the accuracy. To update particle- velocities, imaging and updating are first performed in the horizontal direction, and then in the vertical direction. The numerical results for elastic flat horizontal free surface with the imaging method and those for flat free surfaces of various slope angles with the proposed method are compared, and are shown to be in good agreement. The advantage of the proposed method is that only the stresses are dealt with in implementing the free surface into the staggered algorithm, which improves computation efficiency.

关键词： elastic wave simulation, curved free surface, staggered finite-difference, algorithm stability.

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An element by element spectral element method for elastic wave modeling

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Progress in Natural Science:Materials International 2006年第1期16卷 21-29页

作者： LIN Weijun1. wang xiuming1,2 and {1. hailan 1.1.Institute of Acoustics, Chinese Academy of Sciences, Beijing 1.0080, China 2. csiro.petro.eum, arrc, po.bo. 113., techno.o.y park, bentley, wa 6102, australia) Institute of Acoustics Chinese Academy of Sciences Beijing 100080 China csiro.petro.eum ARRC PO BOX 1130 Technology Park Bentley WA 6102 Australia

The spectral element method which combines the advantages of spectral method with those of finite element method, provides an efficient tool in simulating elastic wave equation in complex medium. Based on weak form of elastodynamic equations, mathematical formulations for Legendre spectral element method are presented. The wave field on an element is discretized using high-order La-grange interpolation, and integration over the element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This results in a diagonal mass matrix which leads to a greatly simplified algorithm. In addition, the element by element technique is introduced in our method to reduce the memory sizes and improve the computation efficiency. Finally, some numerical examples are presented to demonstrate the spectral accuracy and the efficiency. Because of combinations of the finite element scheme and spectral algorithms, this method can be used for complex models, including free surface boundaries and strong heterogeneity.

关键词： spectral element Legendre polynomial elastic wave modeling element by element.

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