Negation Invariant Representations of 3-D Vectors for Deep Learning Models Applied to Fault Geometry Mapping in 3-D Seismic Reflection Data

We can represent the orientation of a plane in 3-D by its normal vector. However, every plane has two normal vectors that are negatives of each other. We propose four novel representations of vectors in 3-D that are negation invariant and can be used by a neural network to predict orientation. Our proposed solution is the first to introduce representations that are negation invariant, continuous, and easily parallelizable on the graphics processing unit (GPU). We evaluate the representations by predicting the orientation of a plane on a toy task, and by applying them to synthetic seismic tomographic data where we predict the presence and orientation of faults for every voxel in the volume. We further make use of the orientation of the faults in a post-processing algorithm on the GPU that separates the faults into segments (i.e., instances) that do not intersect, which allows us to selectively visualize faults in 3-D. We demonstrate the utility of the representations by deploying the model on the Laminaria 3-D seismic volume as a case study. We quantitatively compare the model's prediction against human interpretations of slices through the volume as well as existing interpretations in literature. Our analysis shows good agreement (F1 score of 88%) of the model with human interpretation in the shallow levels, where the ambient noise is lower, but this agreement degrades at deeper levels (F1 score of 68%). We explore possible reasons for this degradation.