Seismic acoustic impedance inversion (SAII) aims at recovering the subsurface impedance to achieve lithology interpretation. However, its ill-posedness and nonlinearity pose a great challenge to find an optimal solution. Regularization is an effective method to solve SAII by imposing prior information, but it suffers from high computational complexity and limited inversion performance. To mitigate the above limitations, we propose an optimization-inspired semisupervised deep learning SAII approach that incorporates the advantages between the model-driven optimization algorithm and the data-driven deep learning method. Specifically, it is implemented by parameterizing the alternating iterative method (AIM) by splitting it into two parts where the convolutional neural networks are adopted to learn the regularization terms and a nonlinear mapping and thus called the proposed network as AIM-SAIINet. The proposed method can not only simultaneously invert the seismic wavelet and impedance but also obtain high-resolution data as an intermediate product to facilitate the training of AIM-SAIINet and enhance the inversion accuracy. In addition, we introduce a joint semisupervised training scheme in which the network is first jointly pretrained in a supervised manner using the synthetic training data to provide good initial values, and then, a semisupervised training scheme is adopted to fine-tune it using few labeled data pairs to achieve high inversion accuracy. The synthetic and field data examples are conducted to validate the effectiveness of AIM-SAIINet, which achieves higher inversion accuracy at a fast computational speed compared with the traditional methods.

Seismic blind high-resolution inversion (BHRI) aims at retrieving the high-resolution data to characterize the stratigraphic structures in the case of an unknown seismic wavelet. However, the unknown wavelet and ill-posedness pose a great challenge to the high-resolution inversion. Regularization-based BHRI is an effective approach. However, it is sensitive to the sets of initial values, regularization terms, and regularization parameters and suffers from computational burden problems. To address these issues, we propose a sequential iterative deep learning method (SIDLM) to implement a BHRI in a fast computational speed, which incorporates three learned components to sequentially invert initial high-resolution data, seismic wavelet, and final high-resolution data in an end-to-end fashion. Specifically, to mitigate the influence of initial values, a data-driven network U-Net is adopted to learn an initial high-resolution data. Furthermore, the architecture makes use of prior information encoded in the forward operator to build a new general alternating direction method of multipliers (ADMM)-like iterative deep neural network, instead of the traditional alternating iterative inversion. The proposed ADMM-like network utilizes the convolutional neural networks to learn the proximal operators to solve each subproblems in alternating iterative inversion. Therefore, all parameters of BHRI, such as the regularization parameters and transform operator, can be implicitly learned from the training datasets in an end-to-end fashion, not limited to the form of the penalty function. Finally, the synthetic and field data examples are conducted to demonstrate the effectiveness of the proposed SIDLM.

The time-varying seismic super-resolution inversion technique becomes more and more attractive in seismic exploration. However, most existing inversion methods suffer from amplitude loss and manual adjustment parameters. In this letter, we present an adaptive time-varying seismic super-resolution inversion method based on the Lp (0<p<1) regularization to address these issues. First, the Lp-norm with 0<p<1 is applied to constrain the reflectivity to obtain a sparser and more robust solution than the L1 regularization. To solve the nonconvex inversion problem adaptively, second, we provide a new algorithm called singular value decomposition (SVD)-Hadamard product parametrization (HPP). The idea of the new algorithm is to apply an HPP to express the Lp (0<p≤1) regularization into a sum of the L2 regularizations that are easy to be programed and solved. Then, the SVD is adopted to solve each L2 regularization. It is convenient to apply the L-curve method or its variants to determine the regularization parameters at each iteration for finishing the inversion adaptively. Finally, synthetic and field data examples are tested to validate the effectiveness of the proposed method.

Seismic high-resolution processing plays a critical role in reservoir target detection. As one of the most common approaches, regularization can achieve a high-resolution inversion result. However, the performance of regularization depends on the settings of the associated parameters and constraint functions. Further, it is difficult to solve an objective function with complex constraints, and it requires designing an optimization algorithm. In addition, existing algorithms have high computational complexity, which impedes the inversion of the large data volume. To address these problems, an optimization-inspired deep learning inversion solver is proposed to solve the blind high-resolution inverse (BHRI) problems of various seismic wavelets rapidly, called BHRI-Net. The method builds on ideas from classic regularization theory and recent advances in deep learning, and it makes full use of prior information encoded in the forward operator and noise model to learn an accurate mapping relationship. It unrolls the alternating iterative BHRI algorithm into a deep neural network, and it applies the convolutional neural network to learn proximal mappings, in which all parameters of the BHRI algorithm are learned from training data. Further, the proposed network can be split into two parts and incorporate the transfer learning strategy to invert field data, which increases the flexibility of the proposed network and reduces training time. Finally, the tests on synthetic and field data show that the proposed method can effectively invert the high-resolution data and seismic wavelet from observation data with improved accuracy and high computational efficiency.

We proposed a multitrace semiblind nonstationary deconvolution method. The proposed method estimates reflectivity and source wavelet simultaneously for pursuing high-resolution seismic processing. The mathematical framework is derived based on convolution exchange law and Fourier transform property. In this framework, seismic records are treated as the convolution of a time-varying wavelet and nonattenuated reflectivity or the convolution of a constant wavelet and attenuated reflectivity. Using these two equivalence relations, we devise an objective function containing two variables, the reflectivity and wavelet. In addition, we add the 2-D total variation constraint to the cost function, which preserves lateral and vertical continuity of the estimated reflectivity. The cost function is solved by alternating iteration and proximal splitting methods, under the assumptions of a known attenuation model and sparse reflectivity. In addition, the mathematical framework is extended to implement semiblind deconvolution in an approximate layered earth model. To demonstrate the effectiveness of the proposed method, we apply the proposed method to synthetic data and field data and confirm that the proposed method can achieve better reflectivity and source wavelet.