Crosstalk Reduction in L1-norm-based Simultaneous-source Full Waveform Inversion

Simultaneous-source technique has been mainly employed for the l2-norm-based full waveform inversion. Considering that real field data are noisy, however, it would be preferable to use robust objective function such as the l1-norm objective function. When we combine the simultaneous-source technique and the l1-norm objective function, there are several problems to be resolved. In case of the l2-norm-based full waveform inversion, the gradient direction of the simultaneous-source inversion has an identical form with that of the individual-source inversion if the crosstalk terms are excluded. In case of the l1-norm-based simultaneous-source inversion, however, the gradient direction is not coincident with that of the individual-source inversion. For this reason, the meaning and the crosstalk reduction of the l1-norm-based simultaneous-source inversion are questionable. In this study, we investigate the gradient direction of the l1-norm-based simultaneous-source inversion and verify the way how the crosstalk noise is suppressed through the statistical approach. Numerical example shows that the l1-norm-based simultaneous-source efficiently reduces the crosstalk and can give reasonable inversion results for noisy data.