Implicit structural modeling of geological structures with deep learning

Implicit structural modeling by interpolating sparse geological data is typically challenging but of importance to many human activities ranging from natural source exploration to hazard assessments. In the existing methods, this problem is formulated as a least-squares minimization or an interpolation problem, in which one solves a volumetric scalar function that represents all structural features of geology. We consider implicit structural modeling as an image inpainting task and compute the scalar function by recovering a full structural model from the significantly sparse geological data. We use a channel attention and multi-scale fusion convolutional neural network to systematically aggregate features with different spatial resolutions for producing a plausible hypothesis of subsurface conditioned on the known fault and horizon data. Furthermore, we use a hybrid loss function to enhance the structural boundaries and eliminate the blurry geometrical features for yielding a realistic geological model. To train our network, we use a workflow to automatically create numerous synthetic models with varying structural features and apply random masks to simulate partially missing horizon data. Although training with only the synthetic data, our network works well to infer the full structures in regions without any available structural information by learning a general representation of geology. Multiple numerical examples with various structural patterns indicate that our method can reliably and robustly generate geological models that strictly honor the input geological data.