Physics-Trained Neural Network as Inverse Problem Solver for Potential Fields: An Example of Downward Continuation between Arbitrary Surfaces

We treat downward continuation as an inverse problem that relies on solving a forward problem defined by the formula for upward continuation, and we propose a new physics-trained deep neural network (DNN)-based solution for this task. We hard-code the upward continuation process into the DNN's learning framework, where the DNN itself learns to act as the inverse problem solver and can perform downward continuation without ever being shown any ground truth data. We test the proposed method on both synthetic magnetic data and real-world magnetic data from West Antarctica. The preliminary results demonstrate its effectiveness through comparison with selected benchmarks, opening future avenues for the combined use of DNNs and established geophysical theories to address broader potential field inverse problems, such as density and geometry modelling. Introduction Downward continuation of potential field, including gravity or magnetic field, refers to transferring the data from one observation surface to a lower surface that is closer to the source of the field. The goal is to enhance the resolution of the continued field and amplify the shallow geological signals. Airborne surveys are typically flown at uneven heights, making continuation from these surfaces a common requirement. Downward continuation is a critical task in the processing of potential field data, impacting the success of various downstream analyses, such as revealing the density structure and boundaries of anomalous bodies, especially for detecting and highlighting shallow anomalous sources. Many methods have been developed for the task of downward continuation (e.g.