Filling the gap: Enhancing borehole imaging with a tensor neural network

Borehole imaging is crucial in geologic research as it offers insights into subsurface formations and supports reservoir assessment, mineral exploration, and hydrocarbon extraction. However, the effectiveness of borehole imaging is limited by the incompleteness of data due to the design constraints of borehole imaging tools. Missing areas in borehole images pose challenges to geologists. Although existing methods, such as pattern filling and convolutional neural network-based techniques, show some efficacy, they often require a large number of complete images for training. In recent years, unsupervised deep-learning and tensor-based methods have gained attention for their ability to reconstruct missing or degraded geologic images by leveraging the structural characteristics of these images. In particular, tensor representations based on Tucker decomposition have shown strong capabilities in data completion. Inspired by this, we develop a novel self-supervised tensor neural network (TNN) using Tucker decomposition as our backbone. Because borehole images are originally in two dimensions, converting them into tensor representations is a critical step in leveraging our tensor representation. To achieve this, we introduce the adaptive boundary-detection cropping with augmentation algorithm, which adapts 2D images into 3D tensors. After interpolating the tensors using our tensor network, we use adaptive slice concatenation with replacement to restore complete images from the enhanced tensors, ensuring that the tensor representation of the 3D data is accurately shown in 2D images. Our TNN can be further enhanced by incorporating a structural regularizer. Actual data experiments demonstrate that our method effectively fills gaps in borehole images with greater clarity and detail. The completed images retain the crucial geologic features and textures, surpassing some of the existing self-supervised learning methods.