High-fidelity fault detection on seismic images is one of the most important and challenging topics in the field of automatic seismic interpretation. Conventional hand-picking-based and semi-human-intervened fault-detection approaches are being replaced by fully automatic methods thanks to the development of machine learning. We have developed a novel multiscale attention convolutional neural network (MACNN) to improve machine-learning-based automatic end-to-end fault detection on seismic images. The most important characteristics of our MACNN fault-detection method are that it uses a multiscale spatial-channel attention mechanism to merge and refine encoder feature maps of different spatial resolutions. The new architecture enables our MACNN to more effectively learn and exploit contextual information embedded in the encoder feature maps. We determine through several synthetic data and field data examples that our MACNN tends to produce higher resolution, higher fidelity fault maps from complex seismic images compared to those of the conventional fault-detection convolutional neural network, thus leading to improved geologic fidelity and interpretability of detected faults.

Automatic identification of faults on seismic structural images is a challenging yet crucial task in quantitative seismic interpretation. Human picking or attribute-based fault detection methods may misidentify faults on noisy, complex seismic images. We develop a new automatic fault detection method using a nested residual U-shaped convolutional neural network. Each of the encoders and decoders in this neural network is a residual U-Net, leading to a nested architecture. The final fault map results from the fusion of three fault maps with low, medium, and high fault resolutions. We demonstrate the excellent fault-detection capability of our nested neural network using a series of synthetic and field seismic images. We find that our approach produces clearer and more interpretable fault maps than the current state-of-the-art U-Net fault detection method, particularly on noisy seismic images. Our new automatic fault detection method can facilitate reliable quantitative seismic interpretation on field seismic images.

Conventional finite-element methods for solving the acoustic-wave Helmholtz equation in highly heterogeneous media usually require finely discretized mesh to represent the medium property variations with sufficient accuracy. Computational costs for solving the Helmholtz equation can therefore be considerably expensive for complicated and large geological models. Based on the generalized multiscale finite-element theory, we develop a novel continuous Galerkin method to solve the Helmholtz equation in acoustic media with spatially variable velocity and mass density. Instead of using conventional polynomial basis functions, we use multiscale basis functions to form the approximation space on the coarse mesh. The multiscale basis functions are obtained from multiplying the eigenfunctions of a carefully designed local spectral problem with an appropriate multiscale partition of unity. These multiscale basis functions can effectively incorporate the characteristics of heterogeneous media's fine-scale variations, thus enable us to obtain accurate solution to the Helmholtz equation without directly solving the large discrete system formed on the fine mesh. Numerical results show that our new solver can significantly reduce the dimension of the discrete Helmholtz equation system, and can also obviously reduce the computational time.