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Identifying dispersive GPR signals and inverting for surface wave-guide properties

formerly ETH Zurich

H. Vereecken

Forschungszentrum Juelich

Robert W. Jacob

Bucknell University

View larger version (10K): [in this window] [in a new window]   Figure 1. Diagram of the broadside (TE) source-receiver configuration. The x-axis is oriented parallel to the long axes of the antennas. 0, 1, 2 are the relative permittivities and 1, 2 the conductivities of the respective media. RTEab is the reflection coefficient of the TE mode GPR waves incident at the boundary between the a and b media, where a and b can be 0 and 1 or 1 and 2.

View larger version (61K): [in this window] [in a new window]   Figure 2. Snapshots in the yz-plane of 3D FDTD modeling of the electric field x traveling through a surface wave guide with 1 = 23 and h = 0.35 m present between the two dashed lines overlying a half-space with 2 = 11 at times (a) t = 50 and (b) 100 ns. The TE0 and TE1 modes can be clearly identified within the yellow circles (see also Figure 3). (enhanced image available in the online edition of TLE.)

View larger version (7K): [in this window] [in a new window]   Figure 3. Electric field distributions for TE0, TE1, TE2, and TE3 modes in a dielectric wave guide.

View larger version (73K): [in this window] [in a new window]   Figure 4. Measured CMP data set showing clear dispersion characteristics enclosed between the dotted lines. The data are normalized to the maximum of each trace. The solid arrow is the group velocity and indicates with which velocity the energy is traveling through the wave guide (v=0.061 m/ns). Observed phase velocities are indicated by the dashed arrows (v=0.087 m/ns).

View larger version (94K): [in this window] [in a new window]   Figure 5. Frequency-band analysis of data set shown in Figure 4 for frequency ranges (a) 24<f<44, (b) 44<f<63, (c) 63<f<83, (d) 83<f<103, (e) 103<f<122, (f) 122<f<142, (g) 142<f<161 and (h) 161<f<181 MHz. The data are normalized to the maximum of each trace. The yellow dashed lines indicate the dominant phase velocity for the specified frequency range. The phase velocity is clearly reducing with increasing frequency in (a)-(e), whereas in (f) a sudden increase of phase velocity is observed, This indicates that a higher-order mode is starting to propagate for these frequencies that again shows a reducing phase velocity with increasing frequency (f)–(h).

View larger version (73K): [in this window] [in a new window]   Figure 6. Phase-velocity spectrum for the TE-mode data shown in Figure 4. The thin yellow curves are picked dispersion curves. The yellow dots indicate the phase velocities obtained from analyzing the different frequency ranges in Figure 5. The thin black curves are the dispersion curves for the TE0 inverted model; and the thin blue curves are the dispersion curves for the TE0-TE1 inverted model.