We describe the optimal choice of the temporal frequency in the sequence of frequency domain seismic waveform inversion. The formulations in the time domain and the frequency domain are mathematically equivalent; however, frequency-domain approach is superior in computational efficiency. One of the reasons of the efficiency is that the temporal frequency can be selected arbitrarily in the inversion process. If one selected highly coarse sampling, computation time would be minimized because the less number of iterative calculations are required. Nevertheless, there arises a significant question how to select the frequencies adequately for the input of the inversion processes. The insufficient number of data inputs would decrease the inversion stability and might lead to the local minimum. A method to select an optimal temporal frequency sequence is developed on the basis of the wavenumber continuity. A numerical experiment assures that the optimal set of frequency components determined by the proposed method is sufficient to image the anomalies and extract the information from the velocity models. Owing to the its high resolution results, the waveform inversion with the optimal processing procedure is applicable to the precise subsurface imaging and monitoring.
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