Numerical modeling for 3D acoustic wave equation in the frequency domain

We investigate a frequency-domain finite-element method for three-dimensional modeling of the acoustic wave equation. Frequency-domain modeling has several advantages over time-domain modeling, even though it requires huge computational memory compared to time-domain modeling. One of these advantages is that multi-shot modeling can be performed more efficiently in the frequency domain than in the time domain, and another is the ability to work on a frequency-by-frequency basis, which makes it possible to distribute frequencies across processors. Considering that frequency-domain modeling is popular in waveform inversion because of source wavelet estimation and multi-shot modeling, 3D frequency-domain finite-element modeling can be effectively used in 3D waveform inversion. We derive a numerical dispersion relationship for the 3D frequency-domain finite-element method and then analyze numerical dispersion on the basis of dispersion curves. From the dispersion analysis, we determine the minimum number of grid points per wavelength. The validity of the 3D finite-element modeling algorithm is examined for a three-layered model and the SEG/EAGE salt model.