Image-domain seismic inversion by deblurring with invertible Recurrent Inference Machines

In complex geologic settings and in the presence of sparse acquisition systems, seismic migration images manifest as nonstationary blurred versions of the unknown subsurface model. Thus, image-domain deblurring is an important step to produce interpretable and high-resolution models of the subsurface. Most deblurring methods focus on inverting seismic images for their underlying reflectivity by iterative least-squares inversion of a local Hessian approximation; this is obtained by either direct modeling of the so-called point-spread functions (PSFs) or by a migration-demigration process. In this work, we adopt a novel deep-learning (DL) framework, based on invertible recurrent inference machines (i-RIMs), which allows approaching any inverse problem as a supervised learning task informed by the known modeling operator (convolution with PSFs in our case): our algorithm can directly invert migrated images for impedance perturbation models, assisted with the prior information of a smooth velocity model and the modeling operator. Because i-RIMs are constrained by the forward operator, they implicitly learn to shape/regularize output models in a training-data-driven fashion. As such, the resulting deblurred images indicate great robustness to noise in the data and spectral deficiencies (e.g., due to limited acquisition). The key role played by the i-RIM network design and the inclusion of the forward operator in the training process is supported by several synthetic examples. Finally, using field data, we find that i-RIM-based deblurring has great potential in yielding robust, high-quality relative impedance estimates from migrated seismic images. Our approach could be of importance toward future DL-based quantitative reservoir characterization and monitoring.