Reconstructing an accurate and high-resolution subsurface model is attractive in the fields of both geology and seismology. However, due to the band-limited characteristics of seismic data, the inversion greatly depends on the reliability of the initial model. A fairly acceptable initial model could lay a good foundation for seismic inversion. In this article, we first introduce a well-log interpolation method with the local slope as a constraint for building a high-fidelity starting model in prestack amplitude versus offset/angle (AVO/AVA) inversion. First, we briefly review the basic theory of general seismic inversion. Then, instead of using the conventional preconditioned least-squares method, we introduce shaping regularization theory into the geological structure-guided well-log interpolation to accelerate the convergence. We use the plane-wave destruction (PWD) algorithm to extract the slope attribute from seismic data, images, or velocity models. The slope is used as the constraint to solve the inverse problem based on the shaping regularization method. Numerical examples demonstrate that the proposed initial model building method performs better than the conventional ones. It greatly improves the accuracy of inversion results. Furthermore, we apply the proposed model building method to the inverse problems of AVO/AVA inversion and reservoir parameter estimation of several field data sets for the first time, which demonstrate encouraging performance.

Seismic waveform inversion has been one of the most studied topics in recent years, which can be implemented both in common shot gather and prestack common midpoint gather. However, there are still several intractable issues to be addressed urgently, such as high-computational complexity, nonuniqueness, and robustness. In this paper, we have developed a model-based prestack waveform inversion (PWI) with a generalized propagation matrix scheme as forward operator, where a regularized function is minimized with the limited memory-Broyden-Fletcher-Goldfarb-Shanno technique to determine a model update corresponding to an adaptively determined regularization weight in each iterative step. To avoid falling into local extrema in the process of solving the objective function, we introduce an optimal transport method into the objective function to improve its convexity and use L-curve method to acquire the optimal regularization weight adaptively. The model tests show that the proposed scheme performs better than the conventional method significantly both on convergence and on accuracy. Furthermore, we apply the PWI with the proposed inversion scheme to the well-logging data and real seismic data. The results demonstrate that the proposed inversion scheme is not only capable of obtaining an accurate description of subsurface properties but also has a good convergence and robustness.

Since most information on S-wave velocity and density exists in the middle to large angle range of seismic data, traditional inversion methods based on the Zoeppritz approximation have difficulty in obtaining satisfactory results. Therefore, as a high-accuracy amplitude varied with angle (AVA) inversion, exact Zoeppritz (EZ) equation inversion has aroused a lot of attention in recent years. As for any other nonlinear inversion, iterative convergence and error are the important problems. In this letter, based on a Bayesian framework, we introduce optimal transport into EZ equation AVA inversion. Then, the limited-memory Broyden-Fletcher-Goldfarb-Shanno method is adopted to solve the regularization-constrained least-square argument function to obtain the inversion results, including P-wave velocity, S-wave velocity, and density. We compare this method with a conventional method, which is based on an L2 norm or weighted L2 norm as a residual method in the model test. The results show that the proposed method not only reduces the error of the results to be smaller than L2 norm, but it also improves the convergence rate.

Prestack seismic inversion has emerged as a powerful technique for reconstructing parameters attribute to the subsurface properties and building the geophysical parameter models. However, the inversion algorithms always suffer from spatial blur and low resolution. Total variation (TV) regularization preserves the spatial variation boundary of data by highlighting the sparsity of the first-order difference, which is regarded as an important technical means for image restoration. However, when the data do not change along the spatial grid direction, TV regularization is prone to a staircase effect. In this article, a directional TV (DTV) method is proposed to conduct the prestack amplitude variation with offset/angle (AVO/AVA) inversion. The method consists of three essential steps: estimating the seismic slope attribute from the seismic data, introducing seismic slope attribute to the TV regularization to establish the objective function, and optimizing the objective function by the split-Bregman algorithm. Finally, the conventional and proposed methods are applied to the synthetic and the real seismic data. The comparison of different methods demonstrates that the proposed method is applicable to reveal the detailed subsurface models, alleviate the staircase effect or artifact substantially, and further upgrade the quality of prestack inversion results.

Coherent seismic noise is usually difficult to attenuate due to the similar morphological patterns between noise and useful signals. To attenuate coherent noise, special preknowledge should be utilized in a state-of-the-art approach, which causes significant inconvenience. Here, we develop an automatic method to attenuate coherent noise based on the adaptive dictionary learning algorithm. The adaptive dictionary algorithm can learn the features of both signals and coherent noise and leave obvious morphological differences in the dictionary atoms. These differences in the dictionary atoms can be transformed into statistical differences, which can be measured and then used to distinguish between signal and noise atoms. We evaluate several statistical metrics in characterizing the dictionary atoms and their feasibilities in distinguishing between signal and noise atoms. We find that the kurtosis metric can best represent the differences between signal and noise atoms, and then we design a kurtosis-based filter to reject those high-kurtosis atoms and their corresponding coefficient vectors for suppressing the coherent noise. Synthetic and real data examples demonstrate the performance of the proposed algorithm.