In this paper, we develop a novel reconstruction method that uses sophisticated denoising priors to recover the missing seismic data. First, we construct a regularization item defined by a denoising convolutional neural network (DCNN) and combine it with back-projection fidelity to formulate a novel model for reconstructing missing seismic data. This model incorporates the advantages of regularization by DCNN and back-projection fidelity, which can employ the deep denoising priors learned by the integrated DCNN to obtain excellent reconstruction results with less iterative optimization. Next, we design and deduce an efficient iterative algorithm to minimize the formulated reconstruction model. Concretely, we separate the fidelity and regularization items in the formulated model by employing a generalized approximate message passing strategy, forming a bipartite graph consisting of output and input nodes. Following the first-order necessary condition, we then derive the closed-form solution of each message variable subordinated to the output and input nodes in the bipartite graph, thus resulting in an iterative procedure with multi-message nested passing. Finally, we conduct tests on the feasibility and effectiveness of the proposed algorithm using three datasets. All results prove that the developed method has faster reconstruction efficiency while obtaining higher reconstruction quality in comparison with the conventional sparsity-promoting reconstruction methods.

The problem of recovering the complete seismic data from undersampled field-observed data is a long-term challenge. Many recent efforts to address this problem develop model-based recovery methods. However, current model-based methods cannot accurately capture inherent priors of seismic data to obtain optimal recovery results. For this issue, we have developed a novel model-based seismic data recovery method, which integrates a deep learning (DL)-based targeted denoiser into the seismic data recovery model and leverages the deep targeted denoising priors learned by this denoiser to implement high accuracy data recovery. Specifically, we first use operator-splitting technology to decouple the data-consistency term and prior constraint term in a seismic data recovery model, resulting in an alternating optimization scheme composed of a least-squares inversion subtask and a proximal minimization subtask. The DL-based targeted denoiser, a dual-channel deep denoising network (DcDDNet), is then plugged into the alternating optimization scheme as a modular component, according to the mathematical equivalence between the proximal operator and the targeted denoiser. This modular component replaces the formalized proximal minimization subtask and plays the role of an implicit prior in the recovery optimization problem. Finally, the least-squares inversion and deep denoising subtasks in the alternating optimization scheme are iteratively executed to achieve seismic data recovery. Due to the integration of the powerful DcDDNet, this method not only enjoys high flexibility and impressive generalization capability but also has high computational efficiency and excellent performance. Synthetic and field data with regular and irregular undersampling are used to evaluate the recovery capability of this method. The results demonstrate that, compared with the f-x adaptive interpolation and curvelet-based recovery methods, our method has advantages in visual and quality metrics. In addition, this method also is more practical in seismic applications because it works in the time-space domain and can handle spatial aliasing and spectral leakage.

Recently, multi-trace impedance inversion has attracted great interest in seismic exploration because it improves the horizontal continuity and fidelity of the inversion results by exploiting the lateral structure information of the strata. However, computational inefficiency affects its practical application. Furthermore, in terms of vertical constraints on the model parameters, it only considers smooth features while ignoring sharp discontinuity features. This leads to yielding an over-smooth solution that does not accurately reflect the distribution of underground rock. To deal with the above situations, we first develop a low-dimensional multi-trace impedance inversion (LMII) framework. Inspired by compressed sensing, this framework utilizes low-dimensional measurements in sparse space containing the maximum information of the signal to construct the objective function for multi-trace inversion, which can significantly reduce the size of the inversion problem and improve the inverse efficiency. Then, we introduce the elastic half (EH) norm as a vertical constraint on the model parameters in the LMII framework and formulate a novel constrained LMII model for impedance inversion. Because the introduced EH norm takes into account both the smoothness and blockiness of rock impedance, the constrained LMII model can effectively raise the inversion accuracy of complex strata. Finally, an efficient alternating multiplier iteration algorithm is derived based on the variable splitting technique to optimize the constrained LMII model. The performance of the developed approaches is tested using synthetic and practical data, and the results prove their feasibility and superiority.

Multi-trace amplitude variation with angle inversion (MAVAI) is a vital tool for estimating the physical parameters of subsurface media, and it plays an important role in oil and gas exploration. However, the existing MAVAI method relies on the Kronecker product to construct an extremely large-scale inverse problem, and its computational inefficiency limits its widespread application. Furthermore, regarding regularization constraints, the existing MAVAI method only considers the smoothness of the inversion parameters, which leads to ambiguous formation boundaries and hinders accurate identification for complex reservoirs. To address these issues, a compressed MAVAI method with elastic half-norm regularization is proposed. Specifically, we first developed a compressed MAVAI (CMAVAI) framework that uses compressed measurements of seismic data and reference models in a sparse domain to construct the CMAVAI objective function, thereby reducing the scale of the inversion problem and improving inversion efficiency. Subsequently, the elastic half-norm is introduced into the CMAVAI framework as a regularization constraint for reservoir parameter estimation. Since the elastic half-norm can simultaneously characterize both the smoothness and blocky features of the subsurface medium, it effectively improves inversion accuracy compared to the MAVAI method. Finally, the performance of the proposed method is evaluated using a theoretical model and field data. The results demonstrate that, compared with the traditional MAVAI algorithm, the CMAVAI framework can effectively improve inversion efficiency while maintaining inversion accuracy. Moreover, the CMAVAI method regularized by the elastic half-norm can improve the accuracy of inversion parameters while retaining the high prediction efficiency of the CMAVAI framework.