The magnetic inversion method is one of the non-destructive geophysical methods, which aims to estimate the subsurface susceptibility distribution from surface magnetic anomaly data. Recently, supervised deep learning methods have been widely utilized in lots of geophysical fields including magnetic inversion. However, these methods rely heavily on synthetic training data, whose performance is limited since the synthetic data is not independently and identically distributed with the field data. Thus, we proposed to realize magnetic inversion by self-supervised deep learning. The proposed self-supervised knowledge-driven 3D magnetic inversion method (SSKMI) learns on the target field data by a closed loop of the inversion and forward models. Given that the parameters of the forward model are preset, SSKMI can optimize the inversion model by minimizing the mean absolute error between observed and re-estimated surface magnetic anomalies. Besides, there is a knowledge-driven module in the proposed inversion model, which makes the deep learning method more explicable. Meanwhile, comparative experiments demonstrate that the knowledge-driven module can accelerate the training of the proposed method and achieve better results. Since magnetic inversion is an ill-pose task, SSKMI proposed to constrain the inversion model by a guideline in the auxiliary loop. The experimental results demonstrate that the proposed method is a reliable magnetic inversion method with outstanding performance.

翻译：磁反演方法是一种非破坏性地球物理方法，旨在根据地表磁异常数据估计地下磁化率分布。近年来，有监督深度学习方法已被广泛应用于包括磁反演在内的众多地球物理领域。然而，这些方法严重依赖合成训练数据，由于合成数据与实测数据并非独立同分布，其性能受到限制。因此，我们提出通过自监督深度学习实现磁反演。所提出的自监督知识驱动三维磁反演方法（SSKMI）通过反演与正演模型的闭环在目标实测数据上进行学习。鉴于正演模型参数预设，SSKMI可通过最小化观测与重估计地表磁异常之间的平均绝对误差来优化反演模型。此外，所提反演模型中包含知识驱动模块，使深度学习方法更具可解释性。同时，对比实验表明，知识驱动模块可加速所提方法的训练并取得更优效果。由于磁反演是一个不适定问题，SSKMI提出在辅助环路中通过引导准则约束反演模型。实验结果表明，所提方法是一种性能卓越的可靠磁反演方法。