Unsupervised methods for single 3-D seismic data reconstruction, such as deep image prior (DIP) and Bernoulli sampling (BS) frameworks, have achieved promising results. However, they suffer from expensive computational costs caused by a large number of iterations. Moreover, in the absence of labels, the final reconstructed results often require visual inspection to pick out, which inevitably introduces subjective errors. To address the above problems, we introduce local Pearson correlation coefficient (LPCC) and local mean absolute error (LMAE) to assess the correlation and difference between seismic traces. The mean values of LPCC (MLPCC) and LMAE (MLMAE) for all nonedge traces in the reconstructed result can evaluate the quality of the reconstructed result based on the internal similarity and internal difference of 3-D seismic data without labels. We further develop an MLPCC-MLMAE-based early stopping strategy. The training process will stop once the number of values behind the highest MLPCC has reached the patience value, and the MLMAE is used as one of the indispensable constraints for the highest MLPCC. We apply the proposed early stopping strategy to the DIP and BS frameworks and demonstrate that it has the ability to significantly reduce computational costs through experiments on synthetic and field data, which makes the DIP and BS frameworks a major step toward practical production. Furthermore, the quantitative evaluation metrics allow the network to automatically and intelligently monitor the training process, and the prediction at the end of iteration is used as the final reconstructed result, thus eliminating the need for human intervention.

Fractures play a very important role in hydrocarbon accumulation and migration as well as hydraulic fracturing. Small-scale fractures contain dense sets of fractures that extend from meters to tens of meters in length. They are at risk resulted in drilling loss and fracturing disturbance. It is therefore vital to build a comprehensive fracture system, especially a dedicated description of small-scale fractures is desired. Conventional large-scale fracture identification mostly depends on the post-stack seismic attributes. Ant tracking places ants as seeds on discontinuous anomalies to locate fracture areas. Taking advantage of wide-azimuth pre-stack seismic, we design an azimuthal anisotropy-driven ant-tracking scheme for small-scale fracture detection. First, we fit ellipses to six azimuthal sectors to obtain fracture intensity and strike. Second, we propose an anisotropic Bayes Ant Colony Optimization (ani-Bayes ACO). The novel algorithm is built on an anisotropic transfer mechanism via a Bayesian framework to optimize the detection of small-scale fractures. Specifically, the computed fracture intensity and strike automatically allocate the range of ants’ detection. The anisotropic transfer mechanism strengthens the detection in the fracture-dense zone and constrains ants to track the geometric structure along the fracture. Finally, we combine conventional ant-tracking to construct an across-scale fracture volume. The bandwidth of the resultant fracture system has been enhanced by incorporating the fracture intensity and geometry into tracing. This new theme may accelerate the automated interpretation by simultaneously characterizing the across-scale fractures and fracture zones. The application of field data in the Sichuan Basin, China demonstrated the robustness of our proposed scheme.

A large-scale computation usually hinders the production of the existing 3D anisotropic P/S wave-mode decomposition methods, such as low-rank approximation, LU factorization or local Fourier transformation. To tackle this problem, we develop a fast decoupled operator in 3D vertical transverse isotropic (VTI) media for P/S wave-mode decomposition and apply this operator to elastic reverse time migration (ERTM) and angle-domain common-image gathers (ADCIGs). To start with, we construct the 3D VTI Christoffel equation in the wavenumber-domain and obtain three elliptical solutions that represent the P-, SV- and SH-polarization direction. We project the original elastic wavefields to these polarization vectors and derive the decoupled formulations of P-, SV-, and SH-waves. To improve the efficiency, these decoupled formulations are then converted to the space domain and depend on the model parameters and phase angles. Further removing the phase angle term from such space-domain decoupled formulations, the approximate P-, SV- and SH-wavefield components are finally obtained. These approximate wave components are proved to compute an accurate phase angle as that of exact P-, SV-, and SH-waves and can be used for ERTM imaging and ADCIGs extraction. A fast decoupled operator is thusly developed and only requires gradient operations and once Fast Fourier transformation (for SV-waves). Both simple and complex synthetic examples demonstrate the effectiveness and feasibility of our approaches.

Most existing traditional and deep learning (DL)-based methods used for random noise attenuation or reconstruction of seismic data typically only process two-dimensional (2-D) data. Very few methods are able to perform both denoising and reconstruction tasks for three-dimensional (3-D) seismic data. We develop a framework based on a self-supervised 3-D partial convolutional neural network (3-DPCNN) for multi-task processing of single 3-D seismic data volume, including random noise attenuation, reconstruction, and simultaneous denoising and reconstruction. The proposed method utilizes 3-D spatial structure information via 3-D convolution kernels and exploits Bernoulli sampling to generate training data pairs and test data. Attributed to Bernoulli sampling, the 3-DPCNN can be trained with only one noisy and/or corrupted seismic data volume; therefore, all supervised information is derived from the original data, and no external supervised information is required. The data augmentation strategy does not always boost the performance of the 3-DPCNN. Therefore, whether it is used and which transform is randomly employed are determined by the task type and the data. In addition, a double ensemble learning strategy is employed to boost 3-DPCNN performance and avoid randomness in the predictions. We evaluate the proposed method using multiple synthetic and field data. The experiments show that the proposed method has remarkable denoising and reconstruction abilities and is competitive with and even superior to a variety of traditional and DL-based benchmark algorithms.

As oil and gas exploration moves towards complicated geological environments, high-resolution and true-amplitude seismic imaging becomes increasingly important for detecting and evaluating hydrocarbon reservoirs. Traditional ray-based and wave-equation imaging methods can be considered as the adjoint operator of seismic forward modeling, which are difficult to produce high-quality images in complicated structures because of limited frequency band, unbalanced illumination and irregular acquisition. Least-squares migration (LSM) generates an inverse solution for subsurface reflectivity model with high image resolution and balanced amplitudes. Previous studies on LSM mainly focused on the developments of theoretical and practical strategies, but few on error and uncertainty analysis. We present a quantitative analysis method to evaluate the errors of LSM results. The ϕdataand ψdatafunctions are first computed based on the local similarity andL2-norm misfit between observed and synthetic data. They are used as data-domain kinematic and dynamic errors, respectively. Then, these local functions are mapped to the subsurface using a Kirchhoff-integral relation to calculate image-domain errors. Numerical examples for synthetic and field data demonstrate that as the iteration of LSM increases, the total kinematic and dynamic errors are reduced, and they vary in different locations. For low signal-to-noise-ratio field data, LSM might enlarge image errors at large iterations because of the overfitting issue, and proper regularization is very important to facilitate the convergence of LSM to a good solution.