In acoustic or seismic exploration, propagation characteristics of seismic waves in various complex media are required in order to acquire, process, and interpret seismic data and to use seismic data to invert formation properties. Numerical simulation is an efficient way to realize this goal. Therefore, considerable efforts are made to solve elastic wave equations and to simulate elastic wave propagation under various complex geologic conditions.

For seeking a more efficient numerical method with high computation accuracy for simulating elastic wave propagation in complex geologic structures, many kinds of numerical modeling methods have been developed. However, for a given problem, a superior algorithm for general modeling cases is difficult to find and a specific algorithm is always chosen according to the specific situation because of the complexity of the problems researched.

So based on strong and weak forms of elastic wave equations, CHE Chengxuan, WANG Xiuming and LIN Weijun of Institute of Acoustics, Chinese Academy of Sciences carried out a series of studies and developed a Chebyshev spectral element method (SEM) using the Galerkin variational principle.

They discretize the wave equation in the spatial and time domains and introduce the preconditioned conjugate gradient (PCG)-element by element (EBE) method in the spatial domain and the staggered predictor/corrector method in the time domain. They verify the accuracy of the proposed method by comparing it with a finite-difference method (FDM) for a homogeneous solid medium and a double layered solid medium with an inclined interface. The modeling results using the two methods are in good agreement with each other. Meanwhile, to show the algorithm capability, they use the suggested method to simulate the wave propagation in a layered medium with a topographic traction free surface. By introducing the EBE algorithm with an optimized tensor product technique, the proposed SEM is especially suitable for numerical simulation of wave propagations in complex models with irregularly free surfaces at a fast convergence rate, while keeping the advantage of the finite element method.

This research result was published on the recently issued journal of APPLIED GEOPHYSICS (Vol.7, No.2 (June 2010), P. 174 - 184).