Implicit neural representation for potential field geophysics

The recent use of spatial coordinate features in multilayer perceptron (MLP) neural networks provides opportunities for novel applications in potential field geophysics. So-called coordinate MLP networks allow for learning a representative function of potential fields from their surveyed samples. We present a novel method for implicit neural representation of potential fields, demonstrate the quality of the learned implicit function by encoding synthetic and real airborne geophysical survey line data, and compare the result to grid data processed with traditional gridding methods. We further demonstrate the analytical calculation of gradients directly in the continuous domain of the neural network using automatic differentiation, with the same framework used to train the neural network representation. A regular grid created with the proposed method closely matches the ground truth reference synthetic forward model, with a root mean-square error of 10.3 nT, compared to 18.75 nT for minimum curvature. Horizontal gradients calculated with this method are accurate against numerically derived gradients, while the vertical gradient is poor for these case study data. The training process is rapid, and only requires recorded samples from a single survey extent.