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Measuring the Electrical Properties of Soil Using a Calibrated Ground-Coupled GPR System

^a Earth Science Systems, LLC, Golden, CO 80402
^b U.S. Geological Survey, Denver, CO

View larger version (13K): [in this window] [in a new window]   FIG. 1. Depiction of a ground penetrating radar system as a series of N-port networks. The Pt,t port and the Pr,r port of the antenna system refer to the transmitting antenna feed port and the receiving antenna feed port, respectively. Note that the antenna networks include the soil that lies within the reactive near-field region of the antennas (i.e., the zone up to about a half wavelength in depth beneath the antennas).

View larger version (17K): [in this window] [in a new window]   FIG. 2. Illustration showing various energy coupling mechanisms between antennas in a ground-coupled bistatic array that contribute to early arriving waveforms. Several soil layers with different electromagnetic properties are depicted. TX and RX are the transmitting and receiving antennas, respectively; is relative permittivity; µ0 is the magnetic permeability of free space; and is conductivity.

View larger version (37K): [in this window] [in a new window]   FIG. 3. Example of the inverse model for soil properties (IMSP) forward operator. Plots show the change in Hilbert envelope amplitudes of the early waveforms at 7.5, 15, 22.5, and 30 ns as a function of standoff and conductivity. The relative permittivity is 9 for all plots.

View larger version (32K): [in this window] [in a new window]   FIG. 4. Inverse model for soil properties (IMSP) inversion history for a known standoff. The relative uncertainty is 10% (RDP is the relative dielectric permittivity). Triangles are initial models, squares are acceptable solutions, and circles represent the logarithm of the residual at each iteration. Initial models on the left side of the figure descend to acceptable solutions, while those on the right descend to a local minimum that does not meet the stopping criterion (Eq. [4]).

View larger version (28K): [in this window] [in a new window]   FIG. 5. Solution set statistics vs. relative uncertainty of the data using the Hilbert attributes. Note that the population remains constant for relative uncertainties up to 12% (RDP is the relative dielectric permittivity). This indicates that the solution set is contained in a single basin of attraction.

View larger version (24K): [in this window] [in a new window]   FIG. 6. The mean sensitivities calculated across the 125 initial parameter values for the spectral and Hilbert attribute sets (RDP is the relative dielectric permittivity and Cond. is conductivity).

View larger version (55K): [in this window] [in a new window]   FIG. 7. Left panels show estimates of soil properties from the inverse model for soil properties (IMSP) algorithm from the Mud Lake site. The bars indicate the uncertainty in the parameter estimate (i.e., ± one solution set standard deviation). Triangles indicate laboratory results (RDP is the relative dielectric permittivity). The results are invalid in the shaded regions due to rough surface scattering and equipment problems. Right panels show the actual ground penetrating radar (GPR) data, the waveform attributes, and the predicted attributes.

View larger version (36K): [in this window] [in a new window]   FIG. 8. The upper-left panel shows the reflection coefficient at the surface of the clay lens, and the lower-left panel shows the permittivity of the clay lens (conductivity is included in the imaginary component). The upper-right panel shows the reflection coefficient calculated from low noise survey data (thick lines) and data with a signal/noise ratio of 10:1 (thin lines). The lower-left panel shows the corresponding permittivity determined from the simulated data.

View larger version (14K): [in this window] [in a new window]   FIG. 9. Simulated waveforms for a 2-m-deep perfectly conducting plane (top) and for an 8-m-deep clay lens (bottom). The signal/noise ratio for the lower waveform is 10:1.

View larger version (23K): [in this window] [in a new window]   FIG. 10. Processing outline to estimate the electrical properties of a planar reflector (TX is transmission, RX is receiving, FDTD is finite difference time domain, and Star(z, ) is the target response function).