Deep learning (DL) is a powerful tool for mining features from data, which can theoretically avoid assumptions (e.g., linear events) constraining conventional interpolation methods. Motivated by this and inspired by image-to-image translation, we applied DL to irregularly and regularly missing data reconstruction with the aim of transforming incomplete data into corresponding complete data. To accomplish this, we established a model architecture with randomly sampled data as input and corresponding complete data as output, which was based on an encoder-decoder-style U-Net convolutional neural network. We carefully prepared the training data using synthetic and field seismic data. We used a mean-squared-error loss function and an Adam optimizer to train the network. We displayed the feature maps for a randomly sampled data set going through the trained model with the aim of explaining how the missing data are reconstructed. We benchmarked the method on several typical datasets for irregularly missing data reconstruction, which achieved better performances compared with a peer-reviewed Fourier transform interpolation method, verifying the effectiveness, superiority, and generalization capability of our approach. Because regularly missing is a special case of irregularly missing, we successfully applied the model to regularly missing data reconstruction, although it was trained with irregularly sampled data only.

The normal-to-shear fracture compliance ratio is commonly used as a fluid indicator. In the seismic frequency range, the fluid indicator lies between the values for isolated fluid-filled fractures and dry fractures, and it is not easy to discriminate the fluid content. Assuming that the fracture surfaces are smooth, we use $1-{\mathrm{\Delta }}_N/{\mathrm{\Delta }}_N^{\mathrm{dry}}$, with ${\mathrm{\Delta }}_N$ and ${\mathrm{\Delta }}_N^{\mathrm{dry}}$ representing the normal fracture weakness of the saturated and dry rock, to indicate fluid types, and to define a fluid influencing factor. The fluid influencing factor is sensitive to the fluid properties, the aspect ratio of the fractures, and the frequency. Conventionally, the amplitude versus offset and azimuth (AVOA) inversion is formulated in terms of the contrasts of the fracture weaknesses across the interface, assuming that the fractures are vertical with the same symmetry axis. We consider fractures with arbitrary azimuths, and develop a method to estimate fracture parameters from wide-azimuth seismic data. The proposed AVOA inversion algorithm is tested on real 3D prestack seismic data from the Tarim Basin, China, and the inverted fracture density show good agreement with well log data, except that there are some discrepancies for one of the fractured reservoir sections. The discrepancies can be ascribed to neglect of the dip angle for the tilted fractures and the conjugate fracture sets, and to the validity of the linear-slip model. The fractured reservoirs are expected to be liquid saturated, under the assumption of smooth fractures. Overall, the inverted fracture density and fluid influencing factor can be potentially used for better well planning in fractured reservoirs and quantitatively estimating the fluid effects.

Sparse-spike deconvolution (SSD) is an important method for seismic resolution enhancement. With the wavelet given, many trace-by-trace SSD methods have been proposed for extracting an estimate of the reflection-coefficient series from stacked traces. The main drawbacks of trace-by-trace methods are that they neither use the information from the adjacent seismograms nor do they take full advantage of the inherent spatial continuity of the seismic data. Although several multitrace methods have been consequently proposed, these methods generally rely on different assumptions and theories and require different parameter settings for different data applications. Therefore, traditional methods demand intensive human-computer interaction. This requirement undoubtedly does not fit the current dominant trend of intelligent seismic exploration. Therefore, we have developed a deep learning (DL)-based multitrace SSD approach. The approach transforms the input 2D/3D seismic data into the corresponding SSD result by training end-to-end encoder-decoder-style 2D/3D convolutional neural networks (CNN). Our key motivations are that DL is effective for mining complicated relations from data, the 2D/3D CNN can take multitrace information into account naturally, the additional information contributes to the SSD result with better spatial continuity, and parameter tuning is not necessary for CNN predictions. We determine the significance of the learning rate for the training process’s convergence. Benchmarking tests on the field 2D/3D seismic data confirm that the approach yields accurate high-resolution results that are mostly in agreement with the well logs, the DL-based multitrace SSD results generated by the 2D/3D CNNs are better than the trace-by-trace SSD results, and the 3D CNN outperforms the 2D CNN for 3D data application.

Elastic reverse time migration (ERTM) is developed for better characterization of complex structures by imaging multicomponent seismic data. However, conventional ERTM is subject to limitations such as finite recording aperture, limited bandwidth, and imperfect illumination. Elastic least-squares reverse time migration (ELSRTM) can improve imaging accuracy gradually with iterations by minimizing the residuals between the observed and calculated multicomponent data. Conventional ELSRTM suffers from crosstalk artifacts caused by coupled elastic wavefields with different wave modes. Decomposing the coupled elastic wavefields into pure P- and S-waves is an effective method to suppress these crosstalk artifacts. Considering the trade-off between calculation accuracy and efficiency, we have developed a new ELSRTM scheme for isotropic media based on decoupled wave equations to suppress these wave mode-related crosstalk artifacts in the images of conventional ELSRTM. Pure wavefields are obtained by solving the decoupled wave equations using the finite-difference method in our new ELSRTM method. We also derive new decoupled adjoint-state wave equations that are suitable for the elastic velocity-stress equations in isotropic media. Furthermore, we use the gradient equations based on pure wavefields to update the reflectivity images. Synthetic examples demonstrate that our new ELSRTM method can generate images that better represent the subsurface when compared with conventional ERTM and conventional ELSRTM.

Automatic fault detection in seismic images using deep learning-based methods has attracted great interest in recent years. Detecting faults by deep learning methods is generally considered a supervised learning task, which requires numerous diverse training samples and corresponding accurate labels. Because field data with faults labeled by experienced interpreters are difficult to acquire, training samples are usually generated synthetically, in which the 1D seismic wavelets are convolved with reflectivity models. However, the 1D-convolution-based synthetic seismic images still differ from the real seismic images. Therefore, the network trained by such samples may fail to detect some faults in the field data. Full-wavefield approaches are the optimal seismic modeling methods, but they cannot be widely used at present due to the high cost. In this paper, we present an efficient approach to generate realistic synthetic seismic images by using a point-spread function (PSF)-based convolution. Because the size of a seismic sample used for deep learning training is a small range relative to the field seismic data, assuming the background velocity is close to homogeneous in such a small range, we can efficiently construct the PSF using the analytical Green’s function. With an Intel Core i9-10900K CPU, the PSF approach takes approximately 15 min to generate a seismic image of size 128 × 128 × 128, whereas it takes approximately 20 h to generate a seismic image of the same size using reverse time migration. The examples of one synthetic image and two field seismic images demonstrate that the network trained with the PSF convolution samples can predict more accurate and continuous faults than that trained with the 1D convolution samples.

SUMMARY: Deep learning (DL) has achieved remarkable progress in geophysics. The most commonly used supervised learning (SL) framework requires massive labelled representative data to train artificial neural networks (ANNs) for good generalization. However, the labels are limited or unavailable for field seismic data applications. In addition, SL generally cannot take advantage of well-known physical laws and thus fails to generate physically consistent results. The weaknesses of standard SL are non-negligible. Therefore, we provide an open-source package for geophysics-steered self-supervised learning (SSL; taking application to seismic deconvolution as an example). With the wavelet given, we incorporate the convolution model into the loss function to measure the error between the synthetic trace generated by the ANN deconvolution result and the observed data, steering the ANN’s learning process toward yielding accurate and physically consistent results. We utilize an enhanced U-Net as the ANN. We determine a hard threshold operator to impose a sparse constraint on the ANN deconvolution result, which is challenging for current DL platforms because no layer is available. 2-D/3-D ANNs can naturally introduce spatial regularization to the ANN deconvolution results. Tests on synthetic data and 3-D field data with available well logs verify the effectiveness of the proposed approach. The approach outperforms the traditional trace-by-trace method in terms of accuracy and spatial continuity. Experiments on synthetic data validate that sparsity promotion matters for sparse recovery problems. Field data results of the proposed approach precisely identify the layer interfaces and mostly match well with the log. All codes and data are publicly available at https://doi.org/10.5281/zenodo.7233751 (Xintao Chai).