多物理量的极弱监督反演
Extremely Weak Supervision Inversion of Multi-physical Properties
摘要：
多物理场反演在地球物理学中占有重要地位。它已被广泛用于推断各种物理性质（如速度和电导率）。在这些反演问题中，有些是显式地由偏微分方程控制的，而另一些则不是。没有显式的控制方程，传统的多物理反演技术将是不可行的，数据驱动的反演需要昂贵的全标签。为了克服这个问题，我们开发了一种新的数据驱动的多物理场反演技术，具有极弱的监督。我们的主要发现是，伪标签可以通过学习非常稀疏的测井位置的地球物理属性之间的局部关系来构建。我们探讨了从两个不同的测量~（地震和EM数据）到三个地球物理属性~（速度，电导率和CO $_2$饱和度）的多物理场反演问题。我们的结果表明，我们能够反演的属性没有明确的控制方程。此外，三个地球物理属性的标签数据可以显著减少50倍~（从100个减少到只有2个位置）。
英文摘要：
Multi-physical inversion plays a critical role in geophysics. It has been widely used to infer various physical properties~(such as velocity and conductivity). Among those inversion problems, some are explicitly governed by partial differential equations~(PDEs), while others are not. Without explicit governing equations, conventional multi-physical inversion techniques will not be feasible and data-driven inversion requires expensive full labels. To overcome this issue, we develop a new data-driven multi-physics inversion technique with extremely weak supervision. Our key finding is that the pseudo labels can be constructed by learning the local relationship among geophysical properties at very sparse well-logging locations. We explore a multi-physics inversion problem from two distinct measurements~(seismic and EM data) to three geophysical properties~(velocity, conductivity, and CO$_2$ saturation). Our results show that we are able to invert for properties without explicit governing equations. Moreover, the label data on three geophysical properties can be significantly reduced by 50 times~(from 100 down to only 2 locations).
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