Seismic inversion is the prime method to estimate subsurface properties from seismic data. However, such inversion is a notoriously ill-posed inverse problem due to the band-limited and noisy nature of the data. Consequently, the data misfit term must be augmented with appropriate regularization that incorporates prior information about the sought-after solution. Conventionally, model-based regularization terms are problem-dependent and hand-crafted; this can limit the modeling capability of the inverse problem. Recently, a new framework has emerged under the name of Plug-and-Play (PnP) regularization, which suggests reinterpreting the effect of the regularizer as a denoising problem. Convolutional neural networks-based denoisers are state-of-the-art methods for image denoising: their adoption in the PnP framework has led to algorithms with improved capabilities over classical regularization in computer vision and medical imaging applications. In this work, we present a comparison between standard model-based and data-driven regularization techniques in post-stack seismic inversion and give some insights into the optimization and denoiser-related parameters tuning. The results on synthetic seismic data indicate that PnP regularization using a bias-free CNN-based denoiser with an additional noise map as input can outperform standard model-based methods.

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Seismic inversion is the leading method to map and quantify changes from time-lapse (4D) seismic datasets, with applications ranging from monitoring of hydrocarbon-producing fields to carbon capture and sequestration. Time-lapse seismic inversion is however, a notoriously ill-posed inverse problem: the band-limited nature of seismic data, alongside inaccuracies in the repeatability of consecutive acquisition surveys make it challenging to obtain high-resolution, clean estimates of 4D effects. Adding prior information to the inversion process in the form of properly crafted regularization (or preconditioning) is therefore essential to successfully extract weak signals that are usually buried under strong noise. In this work, we leverage the fact that 4D seismic inversion can be described as a coupled inversion of its baseline and monitor 3D seismic datasets. In existing approaches, the coupling is introduced by penalizing the squared L 2 -norm of difference between the baseline and the monitor acoustic impedances, as this is usually assumed to be small. A major downside of such a regularization is that, whilst reducing the overall level of noise in the estimated acoustic impedance differences, the resulting 4D effects are usually oversmoothed and their strength is underestimated. We instead propose to adapt the joint inversion and segmentation algorithm introduced by Ravasi and Birnie (2021) to the problem of 4D seismic inversion. Our technique produces two acoustic impedance models by inverting the corresponding 3D seismic datasets, regularized by Total-Variation. Moreover, the objective function to optimize is augmented with a segmentation term that renders solutions consistent with the expected 4D effects (obtained, for example, as part of a 4D feasibility study by means of Gassmann fluid substitution). A numerical experiment is presented to validate the effectiveness of the proposed approach and its superiority over state-of-the-art 4D inversion methods.

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