Seismic data reconstruction is a crucial step in seismic data processing. Traditional methods and deep learning approaches have both been widely used in this field. However, they ignored the interactive learning of inter-channel information, especially in the case of high missing rate where feature extraction became more difficult. To address this issue, we propose an adaptive feature fusion network for the reconstruction of both random and consecutive missing seismic data. The information interaction block is designed into this model to improve the efficiency and adaptability of feature selection. It adaptively emphasizes important feature channels and enables inter-channel information exchange learning. To enhance the ability to capture global and local details, a cross-dimensional feature fusion module is designed at the bottleneck, integrating information from both the channel and spatial dimensions. Additionally, the strategy loss is designed to enable the network to learn the correlations among missing parts of the seismic traces, thereby boosting the reconstruction performance of our model. Compared with other state-of-the-art seismic data reconstruction methods, the proposed algorithm achieves improvements in both qualitative and quantitative evaluations: the reconstruction quality has improved by 20% on both synthetic and field datasets with random missing data. The reconstruction quality has improved by 30% on both synthetic and field datasets with consecutive missing data. At the end of the paper, we conducted ablation experiments, hyperparameter analysis and discussion.

In seismic data interpretation, accurate delineation of faults is crucial for subsurface hydrocarbon resource exploration and production. Traditional manual interpretation is time-consuming, labor-intensive and subjective. Deep learning has been widely studied for automatic fault detection in recent years. U-Net and its variants dominate the network structures for the excellent performance in terms of accuracy and generalizability, however, often require significant computational resources and memory usage. For conventional U-Nets, they usually need large channel number at each layer for diverse feature extraction. As multiple channels may capture similar features, this may lead to feature redundancy and a waste for memory and computing resource. To mitigate this problem, we propose a lightweight 3D fault detection neural network, LightUNetFault3D, which contains Global Spatial Convolution Module (GSCM) and Semantic Difference Module (SDM), which dramatically decreases channel number at both encoding and decoding side of U-Net. In the encoding stage, GSCM is used to improve the ability to capture long-range features by introducing additional global spatial information. In the decoding stage, SDM containing difference and fusion operations is used instead of original skip connection. Difference is conducive to extracting boundary features in seismic data, which are closely related to fault detection. Fusion performs weighted summation of differential features from encoder and decoder instead of concatenation. These two modules greatly improve the efficacy of feature extraction for the task of fault detection and a small number of channels is used in LightUNetFault3D. Consequently, the capacity and Floating-Point Operations Per Second (FLOPs) of LightUNetFault3D are only 15% and 9% of the baseline FaultSeg3D model. Meanwhile, LightUNetFault3D still achieves continuous fine fault structures on field dataset tests.

Seismic wavefield simulation is crucial for acquisition design, inversion, and interpretation in seismic exploration. The essence of seismic wavefield simulation is to solve wave equations. A physics-informed neural network (PINN) provides an alternative approach to solving partial differential equations and shows great potential for various geophysical problems. However, the accuracy of PINN-based seismic wavefield simulation is unsatisfactory due to spectral bias. Multiscale Fourier feature mapping (MFFM) has been shown to be effective in enhancing the accuracy of simulation results. This letter proposes a modified MFFM PINN for solving the Helmholtz wave equation to further improve the accuracy of seismic wavefield simulation. An auxiliary network is used to determine the initial hyperparameter value for the multiscale feature range in MFFM using the velocity model as input. The hyperparameter is fine-tuned by allowing it to be learnable during the subsequent training process of the neural network. In addition, activation functions with learnable frequencies are proposed for use in all hidden layers. Experiment results demonstrate that the proposed method automatically determines the optimal hyperparameter for accurate wavefield simulation efficiently.

To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have been developed to construct dimension-independent algorithms. However, there are three challenges for these infinite-dimensional Bayesian methods: prior measures usually act as regularizers and are not able to incorporate prior information efficiently; complex noises, such as more practical non-i.i.d. distributed noises, are rarely considered; and time-consuming forward PDE solvers are needed to estimate posterior statistical quantities. To address these issues, an infinite-dimensional inference framework has been proposed based on the infinite-dimensional variational inference method and deep generative models. Specifically, by introducing some measure equivalence assumptions, we derive the evidence lower bound in the infinite-dimensional setting and provide possible parametric strategies that yield a general inference framework called the Variational Inverting Network (VINet). This inference framework can encode prior and noise information from learning examples. In addition, relying on the power of deep neural networks, the posterior mean and variance can be efficiently and explicitly generated in the inference stage. In numerical experiments, we design specific network structures that yield a computable VINet from the general inference framework. Numerical examples of linear inverse problems of an elliptic equation and the Helmholtz equation are presented to illustrate the effectiveness of the proposed inference framework.

Landslide susceptibility mapping is a practical approach for identifying landslide-prone areas. In this letter, we apply a semisupervised learning method, positive unlabeled-bagging (PU-bagging) to generate a landslide susceptibility map over a study area from the Loess Plateau in North-Central China. PU-bagging deals with the lack of negative samples in a training set and uses only positive and unlabeled samples. We prove the effectiveness of our approach by comparing the PU-bagging decision tree (DT) generated landslide susceptibility map with the ground truth (known landslide locations), as well as by comparing its performance with three widely used models (logistic regression, support vector machine, and artificial neural network). The promising results and the fact that the method is general urge us to believe that the PU-bagging should be able to perform in other landslide-prone areas where only positive samples are provided.