Preconditioning Full Wave Inversion Using Geological Structure-Oriented Gradient Filtering

Full waveform inversion (FWI) is inherently an ill-posed inverse problem. Gradient preconditioning in FWI is crucial for improving the convergence and stability of the inversion process, as it helps refine the gradient and mitigate the ill-posed nature of FWI. Conventional strategies involve applying smoothing operators, such as Gaussian or Laplacian filters, directly at each FWI iteration. While these operators are easy to implement, they can compromise the structural information embedded in the gradient. To address this drawback, we propose a structure-oriented filter that enhances the gradient’s structure while smoothing the gradient along known geological slopes. This preconditioning method effectively preserves the geological structures. We applied the proposed approach to 3-D field data from the Brazilian presalt region and compared the inversion results with those obtained using conventional strategies. The enhancement in resolution and structural coherence is striking, with most of the velocity model’s details being preserved. In addition, the reverse time migrated (RTM) image computed using the FWI velocity model obtained with the proposed preconditioning strategy revealed more detailed geological features associated with complex salt layers, with more focused and sharper edges compared with the RTM image derived from the velocity model using conventional preconditioning methods. To further validate the FWI velocity model obtained with our method, we performed quality control tests, including observed and predicted data comparison and phase residual analysis, which confirmed the reliability of the results. We believe this technique has the potential to be applied to a wide range of field data in the future.