Weakly Supervised Inversion of Multi-physics Data for Geophysical Properties

Multi-physics inversion plays a critical role in geophysics. It has been widely used to simultaneously infer various geophysical 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 physical-based inversion techniques are not feasible and data-driven inversion requires expensive full labels. To overcome this issue, we proposed 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 locations. We explore the multi-physics inversion problem from two distinct measurements~(seismic and electromagnetic data) to three geophysical properties~(velocity, conductivity, and CO$_2$ saturation) with synthetic data based on the Kimberlina storage reservoir in California. Our results show that we are able to invert for properties without explicit governing equations. Moreover, the labeled data on three geophysical properties can be significantly reduced by 50 times~(from 100 down to only 2 locations).