Correntropy-based least-squares reverse time migration

We propose a robust least-squares reverse-time migration (LSRTM) approach based on correntropy that effectively mitigates the impact of non-Gaussian data residuals commonly encountered in seismic inversion. The proposed approach, termed σ -LSRTM, introduces a tunable hyperparameter — the kernel bandwidth σ — which balances robustness to outliers and sensitivity to small errors. In the limit of a large bandwidth, σ -LSRTM recovers conventional LSRTM as a special case, preserving its optimality under ideal Gaussian assumptions. We formulate σ -LSRTM as a constrained optimization problem and derive its gradient efficiently using the adjoint-state method. Numerical experiments on a complex deep-water reservoir model demonstrate that σ -LSRTM improves image quality and robustness in scenarios where data residuals deviate from ideal Gaussian statistics. Under Gaussian measurement noise, modest improvements arise from the presence of modeling inaccuracies — including background velocity errors and Born approximation limitations — that introduce non-Gaussian components into the residuals even when the data noise itself is Gaussian. Under non-Gaussian noise conditions, the improvements are substantially more pronounced. These results establish σ -LSRTM as a robust generalization of conventional LSRTM that maintains statistical consistency in Gaussian regimes while providing substantially increased robustness when these assumptions are violated.