Journal of the Korean Society of Mineral and Energy Resources Engineers ISSN:2288-0291(Print) 2288-2790(Online) 한국자원공학회지

We developed a weighted-averaging finite-element method for an accurate and efficient time-domain elastic wave modeling technique. Our method, based on frequency-domain weighted-averaging finite-element methods, is achieved by composing stiffness and mass matrices for four kinds of different-size finite-element sets and then averaging them with weighting coefficients. Unlike the frequency-domain weighted-averaging finite-element methods, in the time domain we cannot use both consistent and lumped mass matrices because using the consistent matrix degrades computational efficiency. For this reason, we only use lumped mass matrices to approximate mass terms. By determining optimal weighting coefficients via a Marquardt-Levenberg method which is one of least-square inversion techniques, we can reduce the number of grid points per shear wavelength to 8 to keep the errors within 1%. By comparing numerical solutions obtained by the time-domain weighted-averaging finite-element method with analytic or numerical solutions for an infinite homogeneous, a semi-infinite homogeneous, and a two-layer model, we ensured that the time-domain weighted-averaging finite-element method yields correct solutions. We could also generate synthetic seismograms for a vertical-step model successfully.