The Spectral Element Method For Elastic Wave Simulation In A Formation With A Topographic Traction Free Surface

In numerical modeling of seismic wavefield and earthquake engineering, the seismic wave propagational mechanisms in various complex mediums need to be studied in order to get better seismic data field-acquisition, seismic data processing, seismic data interpretation, as well as the formation property inversed by seismic wave (elastic wave), yet numerical modeling is an effective method. Considerable efforts have been devoted to developing highly accurate numerical techniques for the solution of elastic wave equations and modeling of elastic waveforms in all kinds of complex geological media, hoping to find an effective elastic waveform modeling method that can be used to calculate the complex model both accurately and effectively.According to the former work, in this paper, based on strong and wake forms of elastic wave equations, using the Galerkin arithmetic, the Chebyshev spectral element method(SEM) for elastic waveform modeling is modified by discretizing the wave equation in space and time domains and introducing preconditioned conjugate gradiens(PCG)—element by element(EBE) method in the space domain, staggered predictor/corrector method in the time domain, respectively. The modeling accuracy of the SEM is compared with a popularly used finite difference-method (FDM) for a homogeneous model, a medium with a horizontal interface and a medium with an inclined interface by using the SEM to model the wave propagation in these mediums. Each of the modeling results is in good agreement with each other. To show the algorithm capability, the proposed method is used to model the wave propagation in a medium with a heave free surface, and in a layered medium with a topographic traction free surface. The modeling results show that by introducing EBE method with optimized tensor multiplication technique, the proposed method is able to deal with complex model efficiently with irregularly free surfaces in high accuracy. The results of study show that the SEM has its particular excellence in modeling model with a complex free surface, and it can be extend to other seismic wave modelings with complex interface and realistic geological structure.