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.

The frequency-weighted-exponential (FWE) function was designed to fit various asymmetric amplitude spectra by two parameters: symmetry index and bandwidth factor. A relation can be built between the FWE function and the Q-factor of media. When a source wavelet propagates in attenuating media, the FWE function is used to fit the amplitude spectra of the source and attenuated wavelet to obtain the symmetry indexes and bandwidth factors. After recalculating the bandwidth factors based on the average of the symmetry indexes, the Q-factor can be estimated by the decrease in the bandwidth factor between the source and attenuated wavelet. Compared with the existing commonly used methods, this method applies to various source wavelet types, and it has better tolerance to random noise. On this basis, we further evaluated an approach to invert the interval Q-factor from seismic reflection data. We used the FWE function to fit the local spectral contents of the interval seismic reflection data to obtain the symmetry indexes and bandwidth factors. After recalculating the bandwidth factors with the average of the symmetry indexes, the reciprocal of the bandwidth factor versus traveltime was linearly fit, and then the Q-factor can be calculated from the slope. This approach has high accuracy without having to correct for the tuning effect when the attenuation is high. It is suitable for different types of synthetic seismic traces and also produces good results in a field-data case study.

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.

At an interface separating two viscoelastic media, the variation of the reflection coefficient with the incident angle is associated with the quality factors (Q-factors) of both media; this sets up a theoretical foundation for Q-factor inversion by amplitude variation with incident angle (AVA). The AVA inversion for Q-factors was applied to a field example of a gas reservoir to detect gas. Considering that the AVA inversion is commonly performed to obtain P- and S-wave velocities in the previous interpretation of the field seismic data, a new AVA inversion process for Q-factors was designed. The existing P- and S-wave velocities were used as the reference phase velocities at the dominant frequency of seismic signals in viscoelastic media, and then the Q-factors for P- and S-waves were inverted from the isofrequency components of the partial angle stack gathers with known reference phase velocities. The application in the field example found that this process obtained stable inverted Q-factor results, providing more powerful evidence for reservoir characterization.