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Post-stack seismic inversion is a widely used technique to retrievehigh-resolution acoustic impedance models from migrated seismic data. Itsmodelling operator assumes that a migrated seismic data can be generated fromthe convolution of a source wavelet and the time derivative of the acousticimpedance model. Given the band-limited nature of the seismic wavelet, theconvolutional model acts as a filtering operator on the acoustic impedancemodel, thereby making the problem of retrieving acoustic impedances fromseismic data ambiguous. In order to compensate for missing frequencies,post-stack seismic inversion is often regularized, meaning that priorinformation about the structure of the subsurface is included in the inversionprocess. Recently, the Plug-and-Play methodology has gained wide interest inthe inverse problem community as a new form of implicit regularization, oftenoutperforming state-of-the-art regularization. Plug-and-Play can be applied toany proximal algorithm by simply replacing the proximal operator of theregularizer with any denoiser of choice. We propose to use Plug-and-Playregularization with a 2D pre-trained, deep denoiser for 2D post-stack seismicinversion. Additionally, we show that a generalization of Plug-and-Play, calledMulti-Agent Consensus Equilibrium, can be adopted to solve 3D post-stackinversion whilst leveraging the same 2D pre-trained denoiser used in the 2Dcase. More precisely, Multi-Agent Consensus Equilibrium combines the results ofapplying such 2D denoiser in the inline, crossline, and time directions in anoptimal manner. We verify the proposed methods on a portion of the SEAM Phase 1velocity model and the Sleipner field dataset. 1

Plug-and-Play regularized 3D seismic inversion with 2D pre-trained denoisers