用物理约束的神经网络解决重磁异常向下延拓问题
Physics-Trained Neural Network as Inverse Problem Solver for Potential Fields: An Example of Downward Continuation between Arbitrary Surfaces
- 将向上延拓公式硬编码进神经网络，使其自动学习逆解
- 无需真实数据训练，在南极实测与合成数据上均有效
- 适合从事地球物理反演、深度学习结合地质建模的研究者
向下延拓是重力和磁法处理中的关键任务，旨在将观测面的数据转移到更接近源区的另一表面，其效果直接影响地下异常体的探测与凸显。本文将向下延拓视为一个逆问题，依赖于由向上延拓公式定义的正问题求解，并提出一种新型物理训练的深度神经网络（DNN）解决方案。我们将向上延拓过程硬编码至DNN的学习框架中，使DNN自身学习作为逆问题求解器，可在从未见过真实标注数据的情况下完成向下延拓。该方法在合成磁数据及南极西部实测磁数据上进行了测试，初步结果表明其性能优于若干基准方法，为深度神经网络与经典地球物理理论相结合解决更广泛的势场逆问题（如密度与几何建模）开辟了新路径。
原文摘要 · Abstract (English)
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.
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