用物理引导的生成模型联合反演重力磁力数据，提升深部矿藏探测精度
Joint 3D Gravity and Magnetic Inversion via Rectified Flow and Ginzburg-Landau Guidance
- 将三维重磁联合反演重构为修正流生成过程，基于物理仿真数据训练
- 引入广义伊辛模型正则项，有效识别矿体分布并约束解空间唯一性
- 提供可复用的密度变分自编码器，支持后续地质建模与推理任务
随着浅层矿产资源日益枯竭，地下矿藏探测变得尤为重要。传统地质方法存在局限，而地表可获取的重力与磁力数据为联合反演提供了新途径——在已知地表观测值的情况下，联合重建产生这些信号的地下密度分布。然而该问题病态且解不唯一。传统确定性方法依赖人工先验，仅收敛于单一解，难以刻画解的分布特性。本文提出一种新框架，将三维重磁联合反演重构为在 Noddyverse 数据集（目前最大的物理基反演数据集）上的修正流过程，并引入广义吉尔伯格-朗道（GL）正则项，作为改进的伊辛模型，增强矿体识别能力，实现物理感知训练。同时提出基于GL理论的引导机制，可作为即插即用模块集成至现有无条件去噪器中。最后，我们训练并发布了3D密度的变分自编码器（VAE），为该领域下游研究提供基础工具。
原文摘要 · Abstract (English)
Subsurface ore detection is of paramount importance given the rising depletion of shallow mineral resources in recent years. It is crucial to explore approaches that go beyond the limitations of traditional geological exploration methods. Due to readily available surface readings, joint magnetic and gravitational inversion is a promising new method - given magnetic and gravitational data on a surface, jointly reconstructing the underlying densities that generate them. However, this is ill-posed and has non-unique solutions. Deterministic methods often require handcrafted priors and converge to a single solution and do not capture the distribution, which is often of interest. We introduce a novel framework that reframes 3D gravity and magnetic joint inversion as a rectified flow on the Noddyverse dataset, the largest physics-based dataset for inversion. We introduce a Ginzburg-Landau (GL) regularizer, a generalized version of the Ising model that aids in ore identification, enabling physics-aware training. We also propose a guidance methodology based on GL theory that can be used as a plug-and-play module with existing unconditional denoisers. Lastly, we also train and release a VAE for the 3D densities, which facilitates downstream work in the field.
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