  Post-stack seismic inversion is a widely used technique to retrieve
high-resolution acoustic impedance models from migrated seismic data. Its
modelling operator assumes that a migrated seismic data can be generated from
the convolution of a source wavelet and the time derivative of the acoustic
impedance model. Given the band-limited nature of the seismic wavelet, the
convolutional model acts as a filtering operator on the acoustic impedance
model, thereby making the problem of retrieving acoustic impedances from
seismic data ambiguous. In order to compensate for missing frequencies,
post-stack seismic inversion is often regularized, meaning that prior
information about the structure of the subsurface is included in the inversion
process. Recently, the Plug-and-Play methodology has gained wide interest in
the inverse problem community as a new form of implicit regularization, often
outperforming state-of-the-art regularization. Plug-and-Play can be applied to
any proximal algorithm by simply replacing the proximal operator of the
regularizer with any denoiser of choice. We propose to use Plug-and-Play
regularization with a 2D pre-trained, deep denoiser for 2D post-stack seismic
inversion. Additionally, we show that a generalization of Plug-and-Play, called
Multi-Agent Consensus Equilibrium, can be adopted to solve 3D post-stack
inversion whilst leveraging the same 2D pre-trained denoiser used in the 2D
case. More precisely, Multi-Agent Consensus Equilibrium combines the results of
applying such 2D denoiser in the inline, crossline, and time directions in an
optimal manner. We verify the proposed methods on a portion of the SEAM Phase 1
velocity model and the Sleipner field dataset. 1
