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 introducest hree kinds of supplementarye lements etsi n addition to a basic elements et 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 l% tpper 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 32.7Vo 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 previousf inite-element methods