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

TL;DR

This paper introduces a physics-trained neural network that effectively performs downward continuation in potential field data, leveraging physical laws to solve inverse problems without ground truth data, demonstrated on synthetic and real-world magnetic data.

Contribution

The paper presents a novel DNN framework that incorporates physical laws for inverse potential field problems, enabling downward continuation without training on ground truth data.

Findings

Effective in synthetic magnetic data tests

Successful application to real-world Antarctic data

Outperforms selected benchmark methods

Abstract

Downward continuation is a critical task in potential field processing, including gravity and magnetic fields, which aims to transfer data from one observation surface to another that is closer to the source of the field. Its effectiveness directly impacts the success of detecting and highlighting subsurface anomalous sources. 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.