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Inverse analysis has been utilized to understand unknown undergroundgeological properties by matching the observational data with simulators. Toovercome the underconstrained nature of inverse problems and achieve goodperformance, an approach is presented with embedded physics and a techniqueknown as automatic differentiation. We use a physics-embedded generative model,which takes statistically simple parameters as input and outputs subsurfaceproperties (e.g., permeability or P-wave velocity), that embeds physicalknowledge of the subsurface properties into inverse analysis and improves itsperformance. We tested the application of this approach on four geologicproblems: two heterogeneous hydraulic conductivity fields, a hydraulic fracturenetwork, and a seismic inversion for P-wave velocity. This physics-embeddedinverse analysis approach consistently characterizes these geological problemsaccurately. Furthermore, the excellent performance in matching theobservational data demonstrates the reliability of the proposed method.Moreover, the application of automatic differentiation makes this an easy andfast approach to inverse analysis when dealing with complicated geologicalstructures.

Physics-embedded inverse analysis with automatic differentiation for the earth's subsurface