  Solving multiphysics-based inverse problems for geological carbon storage
monitoring can be challenging when multimodal time-lapse data are expensive to
collect and costly to simulate numerically. We overcome these challenges by
combining computationally cheap learned surrogates with learned constraints.
Not only does this combination lead to vastly improved inversions for the
important fluid-flow property, permeability, it also provides a natural
platform for inverting multimodal data including well measurements and
active-source time-lapse seismic data. By adding a learned constraint, we
arrive at a computationally feasible inversion approach that remains accurate.
This is accomplished by including a trained deep neural network, known as a
normalizing flow, which forces the model iterates to remain in-distribution,
thereby safeguarding the accuracy of trained Fourier neural operators that act
as surrogates for the computationally expensive multiphase flow simulations
involving partial differential equation solves. By means of carefully selected
experiments, centered around the problem of geological carbon storage, we
demonstrate the efficacy of the proposed constrained optimization method on two
different data modalities, namely time-lapse well and time-lapse seismic data.
While permeability inversions from both these two modalities have their pluses
and minuses, their joint inversion benefits from either, yielding valuable
superior permeability inversions and CO2 plume predictions near, and far away,
from the monitoring wells.
