Seismic data frequently exhibit missing traces, substantially affecting subsequent seismic processing and interpretation. Deep learning-based approaches have demonstrated significant advancements in reconstructing irregularly missing seismic data through supervised and unsupervised methods. Nonetheless, substantial challenges remain, such as generalization capacity and computation time cost during the inference. This work introduces a reconstruction method that uses a pretrained generative diffusion model for image synthesis and incorporates deep image prior (DIP) to enforce data consistency when reconstructing missing traces in seismic data. The proposed method has demonstrated strong robustness and high reconstruction capability of poststack and prestack data with different levels of structural complexity, even in field and synthetic scenarios where test data were outside the training domain. This indicates that our method can handle the high geological variability of different exploration targets. Additionally, compared to other state-of-the-art seismic reconstruction methods using diffusion models, during inference, our approach reduces the number of sampling timesteps by up to$4\times $. Our implementation is available athttps://github.com/PAULGOYES/CDDIP.git.

The global demand for unconventional energy sources such as geothermal energy and white hydrogen requires new exploration techniques for precise subsurface structure characterization and potential reservoir identification. The magnetotelluric (MT) method is crucial for these tasks, providing critical information on the distribution of subsurface electrical resistivity at depths ranging from hundreds to thousands of meters. However, traditional iterative algorithm-based inversion methods require the adjustment of multiple parameters, demanding time-consuming and exhaustive tuning processes to achieve proper cost function minimization. Recent advances have incorporated deep learning algorithms for MT inversion, primarily based on supervised learning, and large labeled datasets are needed for training. This work utilizes TensorFlow operations to create a differentiable forward MT operator, leveraging its automatic differentiation capability. Moreover, instead of solving for the subsurface model directly, as classical algorithms perform, this letter presents a new deep unsupervised inversion algorithm guided by physics to estimate 1-D MT models. Instead of using datasets with the observed data and their respective model as labels during training, our method employs a differentiable modeling operator that physically guides the cost function minimization, making the proposed method solely dependent on observed data. Therefore, the optimization algorithm updates the network weights to minimize the data misfit. We test the proposed method with field and synthetic data at different acquisition frequencies, demonstrating that the resistivity models obtained are more accurate than those calculated using other techniques. Our implementation is available athttps://github.com/PAULGOYES/MT_guided1DInversion.git.

Seismic data interpolation of irregularly missing traces plays a crucial role in subsurface imaging, enabling accurate analysis and interpretation throughout the seismic processing workflow. Despite the widespread exploration of deep supervised learning methods for seismic data reconstruction, several challenges remain. Particularly, the requirement for extensive training data and poor domain generalization due to the seismic survey’s variability pose significant issues. To overcome these limitations, this article introduces a deep-learning-based seismic data reconstruction approach that leverages data redundancy. This method involves a two-stage training process. First, an adversarial generative network is trained using synthetic seismic data, enabling the extraction and learning of their primary and local seismic characteristics. Second, a reconstruction network is trained with synthetic data generated by the generative adversarial network (GAN), which dynamically adjusts the distortion level at each epoch to promote feature diversity. This approach enhances the generalization capabilities of the reconstruction network by allowing control over the generation of seismic patterns from the latent space of the GAN, thereby reducing the dependency on large seismic databases. Experimental results on field and synthetic seismic datasets, both pre-stack and post-stack, show that the proposed method outperforms the baseline supervised learning and unsupervised approaches, such as deep seismic prior (DSP) and internal learning (IL), by up to 8 dB of PSNR.

Due to environmental and economic constraints inherent to seismic exploration, there are often missing shotpoints and receivers that degrade the resolution of the final seismic image. Hence sophisticated interpolation techniques are required for the recovery of dense and uniform spatial sampling. Recent approaches improve the interpolation by adopting robust models through denoisers. We introduce a 3D shot gather interpolation method that jointly considers a sparse prior and a regularization induced by a multichannel volumetric denoiser. The proposed volumetric regularization uses collaborative filters that perform denoising through transform-domain shrinkage of a group of similar seismic cubes extracted from a land seismic acquisition. This grouping and collaborative filtering paradigm exploit the local correlation present in each cube and the non-local correlation between different cubes. Experiments on theStratton 3D surveyshow that the proposed method can interpolate 3D shot gathers in an orthogonal seismic recording from a swath geometry, outperforming methods based on 2D denoisers and 5D seismic data reconstruction in terms of root mean square error and in the recovery of seismic reflections.

Physical and budget constraints often result in irregular sampling, which complicates accurate subsurface imaging. Pre-processing approaches, such as missing trace or shot interpolation, are typically employed to enhance seismic data in such cases. Recently, deep learning has been used to address the trace interpolation problem at the expense of large amounts of training data to adequately represent typical seismic events. Nonetheless, most research in this area has focused on trace reconstruction, with little attention having been devoted to shot interpolation. Furthermore, existing methods assume regularly spaced receivers/sources failing in approximating seismic data from real (irregular) surveys. This work presents a novel shot gather interpolation approach which uses a continuous coordinate-based representation of the acquired seismic wavefield parameterized by a neural network. The proposed unsupervised approach, which we call coordinate-based seismic interpolation (CoBSI), enables the prediction of specific seismic characteristics in irregular land surveys without using external data during neural network training. Experimental results on real and synthetic 3D data validate the ability of the proposed method to estimate continuous smooth seismic events in the time-space and frequency-wavenumber domains, improving sparsity or low-rank-based interpolation methods.

Physical and budget constraints often result in inadequate sampling for accurate subsurface imaging. Preprocessing approaches, such as missing trace interpolation, are typically employed to enhance seismic data in such cases. The compressed sensing (CS) framework has been applied for modeling missing seismic data, which is estimated by sparsity-based computational algorithms. While existing work mainly focuses on recovering missing traces resulting from receiver subsampling, source subsampling has greater economical advantages, as sources are more expensive than receivers. Moreover, stronger image models different from sparsity have not been explored for source recovery. This work presents a consensus equilibrium (CE) approach to recover missing seismic shots, which enables to incorporate various regularization operators modeling different data priors. Simulation results from a real 3-D land seismic dataset demonstrate that the CE approach provides more accurate estimations of the linear and hyperbolic events in the recovered shots, compared with pure sparsity-based reconstructions.