Cross‐correlation reflection waveform inversion based on a weighted norm of the time‐shift obtained by dynamic image warping

The computational efficiency of cross‐correlation reflection waveform inversion can be improved by utilizing the outcomes of reverse time migration instead of the least‐squares reverse time migration results in each iteration. However, the inversion effect of cross‐correlation reflection waveform inversion needs to be optimized as the inversion results may not be optimal. The conventional cross‐correlation operator tends to produce interference values that can compromise the precision of time‐shift estimations. Moreover, the time shift obtained through dynamic image warping can exhibit spiky disturbances, making it difficult to determine accurate time‐shift values. These challenges can cause the inversion process to converge to a local minimum, thereby affecting the quality of the inversion results. To address these limitations, this paper proposes a new approach called cross‐correlation reflection waveform inversion based on dynamic image warping. The proposed method integrates a weighted norm derived from dynamic image warping to effectively regulate the time‐shift values throughout the inversion process. The effectiveness of the proposed cross‐correlation reflection waveform inversion based on the dynamic image warping method is validated through simulations using a simple two‐layer model and a resampled Sigsbee 2A model. A comparative analysis is performed to evaluate the performance of cross‐correlation reflection waveform inversion based on dynamic image warping in mitigating cross‐correlation interference, demonstrating its superior capability compared to the conventional cross‐correlation reflection waveform inversion method.