Waveform inversion of Vertical Radar Profile data: Inversion of VRP data

We have applied Bayesian inversion to full waveform bore-hole radar data. Our goal is to quantify the possible range of subsurface electric permittivity and conductivity. First we have analyzed the uncertainties, both random and systematic, in a typical vertical radar profile (VRP). This analysis is essential in being able to say whether a subsurface model actually fits the data. Then we have written a ray-theoretic VRP modeling algorithm. In order to reduce the range of possible models, we have incorporated data-independent prior information from bore-hole porosity and induction logs. We have done this by simulating the fluctuations around the mean of the logs by an ARMA model. We generated pseudo-random models of subsurface electric permittivity and conductivity simulated from the ARMA process. Those models have the same statistical properties as the bore-hole measurements, but not the exact values. Then we selected from these models those that fit the data. This allows us to quantitatively estimate the range of models that fit the data and are consistent with the logs.