Numerical Modeling for Elastic Wavee Propagation With a Hybrid of the Pseudo-Spectrum and Finite-Element Methods

Abstract

A numerical hybrid method was developed to model elastic wave propagation. This algorithm was implemented with both the pseudo-spectrum and the finite-element methods. The pseudo-spectrum is currently a popular numerical method in earthquake seismology studies due to its high efficiency and accuracy. On the other hand, its most significant drawback is the difficulty of implementing a free surface or absorption boundary owing to the nature of its periodic boundary. In addition, since the grid space must be defined globally within a model to prevent grid dispersion depending on the region of strong velocity contrasts, computations may become very expensive. However, these drawbacks can be overcome with a hybrid of the pseudo-spectrum and the finite-element techniques. With the implementation based on the finite-element formulation, grid spacing can be determined according to local velocity within a velocity model. In so doing, the coding of the boundary conditions becomes much easier as well. The advantages of this proposed hybrid method consist of both reducing the amount of computational time and memory needed and obtaining both accurate and stable results during calculation. Some examples are shown to demonstrate the advantages of the hybrid method. This method can also be easily expanded to 3-D situations with minor modifications.

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