Crosshole Radar Velocity Tomography with Finite-Frequency Fresnel Volume Sensitivities

Document Type


Publication Date



Crosshole-radar velocity tomography is increasingly being used to characterize the electrical and hydrologic properties of the Earth's near-surface. Because radar methods are sensitive to the water content of geologic materials, velocity tomography is a good proxy for imaging soil water retention in the vadose zone and porosity in the saturated zone. In many near-surface environments, radar velocity varies over a few orders of magnitude. Common velocity tomography applies ray theory that assumes infinite frequency propagation. The ray approximation may induce velocity modelling artefacts and loss of localization. We propose an alternative method for computing velocity tomogram sensitivities using Fresnel volumes based on first-order scattering. The Fresnel volume sensitivities account for the finite-frequency of the crosshole radar signal and model the physics of radar propagation more accurately than the ray theory approximation.

We demonstrate that applying finite-frequency Fresnel volume sensitivities provides improved radar velocity tomograms in low contrast environments. Analysis of the singular value decomposition of the sensitivity matrix demonstrates how the finite-frequency inversion recovers and localizes velocity heterogeneities better than ray theory. The singular value spectrum obtained from the full waveform sensitivities matches well with the Fresnel volume results. Furthermore, these basis functions are smooth and localized because the kernels capture the first order wave propagation effect compared to ray based sensitivity, which is a high frequency approximation. Through forward modelling experiments, we validate the finite-frequency sensitivity for crosshole radar velocity. In the Fresnel volume approach, the traveltime picking is more efficient because the datum is the peak of the first pulse rather than the first arrival, and therefore, data pre-processing is simpler and may be easily automated. The synthetic Fresnel volume inversion results show improvements in the final model and the data fits are better when compared to the ray theoretical inversions.


Authors formerly at Center for Geophysical Investigation of the Shallow Subsurface, Department of Geosciences, Boise State University.