Robust elastic frequency-domain full-waveform inversion using the L1 norm

Elastic frequency-domain full-waveform inversion is here applied to a realistic synthetic offshore model to study the behavior of the least-squares and least-absolute-value norms, in the presence of noisy multi-component seismic data. As expected, the inversion results show that the L-2 norm is highly sensitive to non-Gaussian errors in the data and gives rise to high amplitude artifacts in the reconstructed models. The L-1 norm shows more robust behavior, whatever the noise characteristics, and allows convergence towards acceptable models, for both the compressional-wave and shear-wave velocity models. This study highlights the sensitivity of the full-waveform inversion results for the chosen norm in the case of noisy data. The marginally used L-1 norm reveals a robust alternative to the L-2 norm for frequency-domain full-waveform inversion of weakly redundant data. Citation: Brossier, R., S. Operto, and J. Virieux (2009), Robust elastic frequency-domain full-waveform inversion using the L1 norm, Geophys. Res. Lett., 36, L20310, doi: 10.1029/2009GL039458.