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

In complex geological settings and in the presence of sparse acquisition systems, seismic migration images manifest as non-stationary 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 or by a migration-demigration process. In this work, we adopt a novel deep learning 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 point-spread functions in our case): the proposed 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/regularise output models in a training-data-driven fashion. As such, the resulting deblurred images show 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 show 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 towards future Deep-Learning-based quantitative reservoir characterization and monitoring.