  Seawater intrusion (SWI) is a complex process, where 3D modeling is often
necessary in order to monitor and manage the affected aquifers. Here, we
present a synthetic study to test a joint hydrogeophysical inversion approach
aimed at solving the inverse problem of estimating initial and current
saltwater distribution. First, we use a 3D groundwater model for variable
density flow based on discretized flow and solute mass balance equations. In
addition to the groundwater model, a 3D geophysical model was developed for
direct current resistivity imaging and inversion. The objective function of the
coupled problem consists of data misfit and regularization terms as well as a
coupling term that relates groundwater and geophysical states. We present a
novel approach to solve the inverse problem using an Alternating Direction
Method of Multipliers (ADMM) to minimize this coupled objective function. The
sensitivities are derived analytically for the discretized system of equations,
which allows us to efficiently compute the gradients in the minimization
procedure and reduce the computational complexity of the problem. The method
was tested on different synthetic scenarios with groundwater and geophysical
data represented by solute mass fraction data and direct current resistivity
data. With the ADMM approach, we were able to obtain better estimates for the
solute distribution, compared to just considering each data set separately or
solving with a simple coupled approach.
