Filling the Gap: Enhancing Borehole Imaging with Tensor Neural Network

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Borehole imaging is crucial in geological 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. While existing methods, such as pattern filling and CNN-based techniques, show some efficacy, they often require a large amount 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 geological images by leveraging the structural characteristics of images. In particular, tensor representations based on Tucker decomposition have shown strong capabilities in data completion. Inspired by this, we propose a novel self-supervised Tensor Neural Network (TNN) utilizing Tucker decomposition as our backbone. Since borehole images are wraped to 2D data, converting them into tensor representations is a critical step in leveraging the proposed 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 the proposed tensor network, we employ Adaptive Slice Concatenation with Replacement to restore the complete images from the enhanced tensors, ensuring that the tensor representation of 3D data is accurately depicted in the 2D images. The proposed TNN can be further enhanced by incorporating a structural regularizer. Actual data experiments demonstrate that our method effectively fills gaps in borehole images with higher clarity and detail. The completed images retain crucial geological features and textures, surpassing some of the existing self-supervised learning methods.