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We describe a novel framework for estimating subsurface properties, such asrock permeability and porosity, from time-lapse observed seismic data bycoupling full-waveform inversion, subsurface flow processes, and rock physicsmodels. For the inverse modeling, we handle the back-propagation of gradientsby an intrusive automatic differentiation strategy that offers three levels ofuser control: (1) at the wave physics level, we adopted the discrete adjointmethod in order to use our existing high-performance FWI code; (2) at the rockphysics level, we used built-in operators from the $\texttt{TensorFlow}$backend; (3) at the flow physics level, we implemented customized PDE operatorsfor the potential and nonlinear saturation equations. These three levels ofgradient computation strike a good balance between computational efficiency andprogramming efficiency, and when chained together, constitute a coupled inversesystem. We use numerical experiments to demonstrate that (1) the three-levelcoupled inverse problem is superior in terms of accuracy to a traditionaldecoupled inversion strategy; (2) it is able to simultaneously invert forparameters in empirical relationships such as the rock physics models; and (3)the inverted model can be used for reservoir performance prediction andreservoir management/optimization purposes.

Coupled Time-lapse Full Waveform Inversion for Subsurface Flow Problems using Intrusive Automatic Differentiation