Joint inversion of GPR and ER data

Electrical methods are proven tools for successfully imaging the subsurface (Jol, 2008; Knight, 2001). Ground penetrating radar (GPR) is sensitive to electrical permittivity through reflectivity and electrical conductivity through attenuation. Electrical resistivity tomography (ER) is directly sensitive to electrical conductivity. GPR and ER data hold high and low spacial-frequency information respectively of the media of interest. We propose a joint inversion of GPR and ER data to image electrical permittivity and conductivity. The two types of data are inherently linked through Maxwell's equations and work cooperatively to regularize each other while honoring the physics. We first compute sensitivity updates separately for both the GPR and ER data using the adjoint method, and then we sum these updates to account for both types of sensitivities. Our algorithm makes no assumption of the subsurface geometry with the caveat of needing a good initial model. In this work, we test our method with a numerical experiment.