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In this paper, a frequency-domain element-free method (EFM) for seismic modeling and reverse-time migration is presented. The application of time-domain EFM has been demonstrated successfully in seismic data processing and its advantages are shown. The absence of elements makes the EFMmore flexible than the finite element method and it can be applied to more complex problems such as for irregular surfaces. Because of the utilization of the moving-least-squares fitting method, the dependent variable and its derivative are both continuous and precise in EFM. However, the large computation time of time-domain EFM limits its usefulness. We have developed an algorithm for frequency-domain EFM that reduces its computation time. Unlike time-domain propagators, the developed algorithm solves array equations to calculate a single-frequency wavefield. Without time iteration, there is very little accumulated error and, because of the spectrum of the source, we only need to calculate parts of the frequencies. The independence of each frequency makes it convenient to manipulate single-frequency wavefields and easy to accelerate computation with parallelization. For the frequency-domain algorithm feature, we can solve multiple shots at the same time. The implementation of frequency-domain EFM is shown for the full scalar wave equation. Based on this theory, numerical examples of seismic process and time acceleration are presented.

A frequency-domain element-free method for seismic modeling and reverse-time migration