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

摘要

Seawater intrusion (SWI) is a complex process, where 3D modeling is oftennecessary in order to monitor and manage the affected aquifers. Here, wepresent a synthetic study to test a joint hydrogeophysical inversion approachaimed at solving the inverse problem of estimating initial and currentsaltwater distribution. First, we use a 3D groundwater model for variabledensity flow based on discretized flow and solute mass balance equations. Inaddition to the groundwater model, a 3D geophysical model was developed fordirect current resistivity imaging and inversion. The objective function of thecoupled problem consists of data misfit and regularization terms as well as acoupling term that relates groundwater and geophysical states. We present anovel approach to solve the inverse problem using an Alternating DirectionMethod of Multipliers (ADMM) to minimize this coupled objective function. Thesensitivities are derived analytically for the discretized system of equations,which allows us to efficiently compute the gradients in the minimizationprocedure and reduce the computational complexity of the problem. The methodwas tested on different synthetic scenarios with groundwater and geophysicaldata represented by solute mass fraction data and direct current resistivitydata. With the ADMM approach, we were able to obtain better estimates for thesolute distribution, compared to just considering each data set separately orsolving with a simple coupled approach.