Joint Hydrogeophysical Inversion: State Estimation for Seawater Intrusion Models in 3D

TL;DR

This paper introduces a novel joint hydrogeophysical inversion method using ADMM to improve 3D seawater intrusion modeling by integrating groundwater and geophysical data, demonstrating enhanced saltwater distribution estimates in synthetic scenarios.

Contribution

The paper presents a new ADMM-based approach for coupled hydrogeophysical inversion that efficiently combines groundwater and geophysical data for seawater intrusion modeling.

Findings

Improved saltwater distribution estimates with joint inversion.

Analytical sensitivities enable efficient gradient computation.

Synthetic tests show superiority over separate or simple coupled methods.

Abstract

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.