FREQUENCY-DOMAIN REVERSE TIME MIGRATION USING THE L1-NORM

Waveform inversion algorithms generally use the L-2-norm. However, previous work indicates that the L-1-norm objective function can produce better results than the L-2-norm objective function because the L-1-norm is more robust against outliers. Moreover, because field data always contain some outliers, adopting the L-1-norm objective function for waveform inversion would therefore be beneficial. Thus, we consider adopting the L-1-norm for reverse time migration, since the algorithm structure of reverse time migration is identical to that of waveform inversion. Thus, we propose introducing the L-1-norm into frequency domain reverse time migration for 2D acoustic media. To verify the effectiveness of our algorithm, we compare the results with those from the conventional algorithm. First, we apply both algorithms to synthetic data drawn from the Marmousi model. We also apply both algorithms to synthetic data on which we add artificial random outliers. Considering the data without outliers, both algorithms yield similar results regardless of the norm used. However, when we consider the data containing outliers, our algorithm using the L-1-norm yields better results. We then apply the same algorithm to field data obtained from an area in the Gulf of Mexico. As expected from the synthetic test, our algorithm yields superior results. Through these experiments, we conclude that the newly proposed algorithm would be useful for performing reverse time migration on data containing considerable outliers, thus eliminating some preprocessing steps through the use of the L-1-norm.