Zhang Hailan

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

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.

An element by element spectral element method for elastic wave modeling

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