Weighted-averaging finite-element method for scalar wave equation in the frequency domain

Abstract

We develop a new weighted-averaging finite-element method which can be applied to generate synthetic seismograms using scalar wave equation in the frequency domain. Our method introduces three kinds of supplementary element sets in addition to a basic element set which is used in standard finite-element method. By constructing global stiffness and mass matrices for four kinds of element sets and then averaging them with weighting coefficients, we obtain a new global stiffness and mass matrix. With the optimal weighting coefficients minimizing grid dispersion and grid anisotropy, we can reduce the number of grid points required per wavelength to 4 for a 1% upper limit of error. This reduction of the number of grid points, achieved by using the weighted-averaging finite-element method, makes it possible to reduce computer memory to 32.7% of that for the eclectic finite-element method. We confirm the accuracy of our weighted-averaging finite-element method through accuracy analyses for a homogeneous and a horizontal-layer model. By synthetic data example, we reconfirm that our method is more efficient for simulating a geological model than previous finite-element methods.