Joint Inversion in Hydrogeophysics: A Synthetic Case of Seawater Intrusion

Abstract:

Geophysics has become a common tool in the last two decades to supplement the lack of groundwater (GW) data for GW models calibration. One of the common applications is investigating the solute transport processes such as seawater intrusion, which, under certain geological conditions, is a good target for electromagnetic methods. Combining these two different sources of data, however, is still subject of ongoing investigation. One of the caveats is the different scales of geophysical and GW models, as well as the empirical petrophysical relationships that relate geophysical and groundwater states. Solving the parameter estimation problem in this field adds even more complexity, and careful analysis of the potential and the limitations of such an inverse problem should therefore precede the collection of field data.

We developed a 3D groundwater model for variable density flow in Matlab based on discretized flow and solute mass balance equations. In conjunction with the GW model, a geophysical model was developed for 3D electromagnetic modeling and inversion in the time domain. Having both models in the same environment makes the implementation of coupling easier. In our inverse problem, we assume we can collect data for both geophysical and groundwater processes and that we have some information about groundwater model parameters. The unknown parameter can be initial or current solute content depending on the available data.

In the joint inversion framework the data misfit error was minimized for both models at the same time. To achieve this we derived the sensitivities of collected data w.r.t to the solute content (and soil bulk conductivity) based on discretized system of equations. This helps to reduce the computational burden of the problem but also gives insights about experiment setup. The objective function then consists of data misfit and regularization terms but also coupling term that relates groundwater and geophysical states. The coupling term can be represented by Archie's law, if known, or just by some similarity measure (e.g. cross gradient field product). Due to the synthetic character of our example we can compare the results with other coupled inversion frameworks and also just separate inversion by either groundwater or geophysical model.