Traveltimes of direct arrivals in vertical radar profiles (VRPs) are tomographically inverted to estimate the earth’s electromagnetic (EM) velocity between a surface transmitter and a downhole receiver. We determine the 1D interval velocity model that best fits the first-arrival traveltimes by using a weighted, damped, least-squares inversion scheme. We assess the accuracy of the velocity model using synthetic traveltimes from a known velocity-distribution model simulating an unconfined aquifer. The inverted velocity profile closely matched the velocity profile of the input model in the synthetic examples. Using vertical radar profile data from an unconfined aquifer near Boise, Idaho, we inverted traveltimes to obtain velocity estimates at the well location. The velocity change at a depth of 2.0 m corresponds well with the measured depth to the water table of 1.95 m, and at depths between 2 and 18 m, the velocities ranged between 0.06 and 0.1 m/ns. Our estimates approximately match the velocity distribution determined from neutron-derived porosity logs at depths greater than about 2 m. An important function of inverse methods is to assess (quantitatively and qualitatively) the uncertainty of inverted velocity estimates. We note that the velocity values in the upper and lower parts of the inverted model are not as well constrained compared to those between the depths of 4 and 13 m. From the model resolution and model covariance matrices of the real-data inversion,we determine the uncertainty in our velocity model, leading to more reliable interpretations of the subsurface.
Clement, William P. and Knoll, Michael D.. (2006). "Traveltime Inversion of Vertical Radar Profiles". Geophysics, 71(3), K67-K76. http://dx.doi.org/10.1190/1.2194527