In prestack seismic data, outlier errors occur and can negatively influence the outcome of the amplitude-versus-angle (AVA) inversion process. Hence, their effect needs to be minimized during AVA inversion. AVA inversion based on the [ ]-norm-based likelihood function is highly sensitive to outlier errors. In comparison, AVA inversion based on the [ ]-norm-based likelihood function is less affected by outlier errors, and for this reason we have used it with the total variation regularization method used as a constraint to invert discontinuities from geologic bodies. To ensure that the inversion results contain low-frequency components, prior information constraints from model parameters are added to the inverse objective function, which is then solved by the iterative reweighted least-squares method. Results of numerical tests and real-data examples from the application of this method indicate that the algorithm is strongly robust against noise, especially abnormal outlier errors, and that the results of the inversion are reasonable.

Seismic impedance inversion has become a common approach in reservoir prediction. At present, the critical issue in the application of seismic inversion is its low computational efficiency, especially in 3D. To improve the computational efficiency, we have developed an inversion method derived from the proximal objective function optimization algorithm. Our inversion method calculates each unknown parameter in the model vector, one by one during iteration. Compared with routine gradient-dependent inversion algorithms, such as the iteratively reweighted least-squares (IRLS) algorithm, our inversion method has lower computational complexity as well as higher efficiency. In addition, to obtain a sparse reflectivity series, a long-tailed Cauchy distribution is used as the a priori constraint. The weak nonlinear problem owing to the introduction of Cauchy sparse constraint is addressed by taking advantage of reweighting strategy. Results of synthetic and real data tests illustrate that the proposed inversion method has higher computational efficiency than IRLS algorithm, and its inversion accuracy remains the same.

Poststack seismic impedance inversion is an effective approach for reservoir prediction. Due to the sensitivity to noise and the oscillation near the bed boundary, Gaussian distribution constrained seismic inversion is unfavorable to delineate the subtle-reservoir and small-scale geologic features. To overcome this shortcoming, we have developed a new method that incorporates a priori knowledge in the seismic inversion through a preconditioning impedance model using the adaptive edge-preserving smoothing (Ad-EPS) filter. The Ad-EPS filter preconditioned impedance model for a blocky solution makes the formation interfaces and geologic edges more precise and sharper in the inverted impedance results and keeps the inversion procedure robust even if random noise exists in the seismic data. Furthermore, compared with the conventional EPS filter, the Ad-EPS filter is able to resolve thick and thin geologic features through window size scanning, which is used to find the best-fitting window size for each sample to be filtered. The results of numerical examples and real seismic data test indicate that our inversion method can suppress noise to obtain a “blocky” inversion result and preserve small geologic features.

Due to the limitations imposed by acquisition cost, obstacles, and inaccessible regions, the originally acquired seismic data are often sparsely or irregularly sampled in space, which seriously affects the ability of seismic data to image underground structures. Fortunately, compressed sensing provides theoretical support for interpolating and recovering irregularly or undersampled data. Under the framework of compressed sensing, we have adopted a robust interpolation method for high-dimensional seismic data, based on elastic half norm regularization and tensor dictionary learning. Inspired by the elastic net, we first develop the elastic half norm regularization as a sparsity constraint, and we establish a robust high-dimensional interpolation model with this technique. Then, considering the multidimensional structure and spatial correlation of seismic data, we introduce a tensor dictionary learning algorithm to train a high-dimensional adaptive tensor dictionary from the original data. This tensor dictionary is used as the sparse transform for seismic data interpolation because it can capture more detailed seismic features to achieve the optimal and fast sparse representation of high-dimensional seismic data. Finally, we solve the robust interpolation model by an efficient iterative thresholding algorithm in the transform space and perform the space conversion by a modified imputation algorithm to recover the wavefields at the unobserved spatial positions. We conduct high-dimensional interpolation experiments on model and field seismic data on a regular data grid. Experimental results demonstrate that this method has superior performance and higher computational efficiency in noise-free and noisy seismic data interpolation, compared to extensively used dictionary learning-based interpolation methods.

Reliably estimating reservoir parameters is the final target in reservoir characterisation. Conventionally, estimating reservoir characters from seismic inversion is implemented by indirect approaches. The indirect estimation of reservoir parameters from inverted elastic parameters, however, will produce large bias due to the propagation of errors in the procedure of inversion. Therefore, directly obtaining reservoir parameters from prestack seismic data through a rock-physical model and prestack amplitude variation with offset (AVO) inversion is proposed. A generalised AVO equation in terms of oil-porosity (OP), sand indicator (SI) and density is derived by combining a physical rock model and the Aki–Richards equation in a whole system. This makes it possible to perform direct inversion for reservoir parameters. Next, under Bayesian theorem, we develop a robust prestack inversion approach based on the new AVO equation. Tests on synthetic seismic gathers show that it can dramatically reduce the prediction error of reservoir parameters. Furthermore, field data application illustrates that reliable reservoir parameters can be directly obtained from prestack inversion.