Comparison of Frequency-Selection Strategies for 2D Frequency-Domain Acoustic Waveform Inversion

Several frequency-selection strategies have been used to obtain global minimum solutions in waveform inversion. One strategy, called the discretization method, is to discretize frequencies with a large sampling interval to minimize redundancy in wavenumber information. Another method, the grouping method, groups frequencies with redundancy in wavenumber information. The grouping method can be carried out in two ways. With the first method, the minimum frequency is fixed and the maximum frequency is gradually extended upward (i.e., the overlap-grouping method). Under the second method, frequencies are not overlapped across the groups and waveform inversion proceeds from lower to higher frequency groups (i.e., the individual-grouping method). In this study, we compare these three frequency-selection strategies using both synthetic and real data examples based on logarithmic waveform inversion. Numerical examples for synthetic and real field data demonstrate that the three frequency-selection methods provide solutions closer to the global minimum compared to solutions resulting from simultaneously performed waveform inversion, and that the individual-grouping method yields slightly better resolution for the velocity models than the other methods, particularly for the deeper part. These results may imply that using either too small or too large data sets at every stage slightly deteriorates inversion results, and that grouping data in appropriately sized aggregations improves inversion results.