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.