Joint Inversion of Full-Waveform Ground-Penetrating Radar and Electrical Resistivity Data — Part 2: Enhancing Low Frequencies with the Envelope Transform and Cross Gradients

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Recovering material properties of the subsurface using ground-penetrating radar (GPR) data of finite bandwidth with missing low frequencies and in the presence of strong attenuation is a challenging problem. We have adopted three nonlinear inverse methods for recovering electrical conductivity and permittivity of the subsurface by joining GPR multioffset and electrical resistivity (ER) data acquired at the surface. All of the methods use ER data to constrain the low spatial frequency of the conductivity solution. The first method uses the envelope of the GPR data to exploit low-frequency content in full-waveform inversion and does not assume structural similarities of the material properties. The second method uses cross gradients to manage weak amplitudes in the GPR data by assuming structural similarities between permittivity and conductivity. The third method uses the envelope of the GPR data and the cross gradient of the model parameters. By joining ER and GPR data, exploiting low-frequency content in the GPR data, and assuming structural similarities between the electrical permittivity and conductivity, we are able to recover subsurface parameters in regions where the GPR data have a signal-to-noise ratio close to one.