Application of Borehole Radar and Fresnel Volume Tomography to Characterize a Heterogeneous Alluvial Aquifer

Publication Date


Type of Culminating Activity


Degree Title

Doctor of Philosophy in Geophysics



Major Advisor

Partha S. Routh, Ph.D.


Environmental and engineering investigations of the subsurface benefit from minimally invasive and nearly continuous characterization through the application of the appropriate geophysical methods. Consequently, borehole radar surveys, and particularly crosshole tomography, are well suited for imaging hydrogeophysical property distributions, such as radar velocity or porosity, in the shallow subsurface. The focus of this dissertation is the application of borehole radar and Fresnel volume tomography to characterize a heterogeneous alluvial aquifer. Confidence bounds of borehole radar surveys are assessed by examining uncertainties in field data and collocated results. A unified workflow is developed to generate consistent radar propagation velocity tomograms with finite-frequency Fresnel volumes assuming first order scattering as an improvement over ray based methods.

As a precursor to applying Fresnel volume velocity tomography at the Boise Hydrogeophysical Research Site (BHRS), an assessment and mitigation of borehole radar field data errors is completed. The investigation concerns eight sources in an error budget and confirms that certain systematic errors, such as time zero, sampling frequency mismatch, and borehole deviation can be mitigated. Other experimental errors more difficult to mitigate, such as instrument timing and cable stretch, are quantified so that this uncertainty can be incorporated as data weighting into the velocity inversion. Furthermore, simulations incorporating budgeted random errors provide estimates of velocity uncertainty on the order of 2.7 % . Simulations also demonstrate the value of quality control diagrams for processing field data before generating velocity tomograms.

To reconnoiter the BHRS subsurface, a three-dimensional (3-D) velocity distribution is synthesized using results from 27 level-run (LR) surveys and 13 vertical-radar profiles (VRP). The surveys are combined to enhance the strengths of each method and are then interpolated using a 3-D grid. This efficient physical property characterization precedes the Fresnel volume tomography because it provides an image of subsurface heterogeneity at the site; velocity estimates for computing the tomogram sensitivities; and a 0.003 m/ns velocity uncertainty derived using adjacent surveys. Although the LR and VRP methods do not yield dense data coverage, this approach to subsurface characterization is relatively fast when compared to radar tomography.

The analytical derivation of the Fresnel volume sensitivity for crosshole-radar is presented starting from the Helmholtz equation for electromagnetic wave propagation and assuming first order scattering through the Born approximation. This velocity tomography approach is validated through comparison of singular values and basis functions with the full waveform sensitivity, and through forward and inverse modeling of synthetic data. The finite-frequency model more closely approximates the full waveform sensitivity and overcomes some regularization requirements of ray theory tomograms. Fresnel volume tomography is an improvement over current methods because (1) robust traveltimes are picked based on first peaks of recorded waveforms, (2) regularization trade-off is determined using an L-curve for linear inversions, and (3) meter-sized velocity heterogeneities in a synthetic velocity model are recovered and localized, a resolution enhancement over ray theory.

Application of Fresnel volume tomography at the BHRS includes an assessment and interpretation of three adjacent and four intersecting tomograms. This analysis of repeat measurements provides an uncertainty on velocity estimates of about 2.5 %. In the BHRS subsurface, two primary pairs of alternating slow and fast velocity zones are imaged. Fast velocity zones are located between about 832 and 834 meters (m), and between 839 and 843 m; whereas slow velocity zones are located between 834 and 839 m, and between about 843 and 845 m. Using a published petrophysical relation and a BHRS-specific relation, the slow velocity zones of 0.077 to 0.082 meters per nanosecond (m/ns), are interpreted as high porosity zones of around 0.27, and the fast velocity zones of 0.088 to 0.092 m/ns, are interpreted as low porosity zones of around 0.18. The bottom slow velocity or high porosity zone is laterally continuous and may be important for ground water flow at the BHRS. Furthermore, velocity tomograms are compared to four collocated neutron porosity logs transformed by means of empirical petrophysical transforms. High porosity zones interpreted from the radar tomograms correlate with collocated neutron logs, whereas low porosity zones do not correlate well due to measurement differences.

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