Potential Wavefield Inversion (PWI): quasi-acoustic surrogates for elastic media

Ivan Sanchez, Anton Ziegon, Daniel O. Trad

Potential Wavefield Inversion (PWI) is introduced as an alternative formulation for elastic parameter estimation based on the inversion of dilatation-rate and vorticity fields. These quantities represent the local compressional and shear components of particle motion and are obtained from spatial derivatives of the velocity field. We derive the complete forward formulation using quasi-acoustic surrogate equations and the corresponding inverse formulation using the adjoint-state method. The surrogate equations preserve sensitivity to P- and S-wave velocity structure while avoiding the full elastic system, which reduces parameter coupling and simplifies the numerical implementation. We evaluate the approach using transmission and reflection tests in a Camembert model and a Syncline model with near-surface complexity. The results show that PWI recovers the location and magnitude of P- and S-wave anomalies with reduced cross-talk compared to elastic FWI. The method is effective in transmission and produces interpretable updates in reflection settings, although converted waves in the observed data can introduce artifacts. When these conversions are mitigated, PWI recovers cleaner and more focused anomalies. The experiments demonstrate that PWI provides a computationally efficient and interpretable framework for elastic model building, and they highlight the importance of data conditioning and multi-component acquisition for reliable derivative-based inversions.