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Application of Microwave Tomography in Hydrogeophysics: Some Examples

^a Istituto per il Rilevamento Elettromagnetico dell'Ambiente (IREA-CNR), Via Diocleziano 328, I-80124 Napoli, Italy
^b Istituto per i Beni Archeologici e Monumentali (IBAM-CNR), Via per Monteroni, Campus Universitario, 73100 Lecce, Italy

View larger version (24K): [in this window] [in a new window]   FIG. 1. Geometry of the problem of reconstruction of the location of a buried object from GPR measurements at the air–soil interface (a is the semi-extent along the x axis of the investigation domain; zmin is the minimum depth of the investigation domain; b is the semi-extent of the investigation domain along the depth; xM is the semi-extent of the measurement (observation) domain; b and b are the relative dielectric permittivity and the electrical conductivity of the soil; and µ0 is the magnetic permeability of the free space).

View larger version (10K): [in this window] [in a new window]   FIG. 2. The meaning of the (a) incident field and (b) the total field as the sum of the incident field and the field scattered by object (pipes) for a half-space geometry (Einc is the incident field; Escat is the field scattered by the buried objects; TX is the transmitting antenna; and RX are the receiving antennas).

View larger version (13K): [in this window] [in a new window]   FIG. 3. Born approximation assuming that no mutual interaction arises between the objects (Einc is the incident field; Escat is the field scattered by the buried objects; TX is the transmitting antenna; and RX are the receiving antennas).

View larger version (24K): [in this window] [in a new window]   FIG. 4. Reconstruction of a point-like target by backpropagation in a homogeneous medium. Actual permittivity = 4. Model permittivities are (a) 1, (b) 2, (c) 3, and (d) 4. The gray scale is normalized to the maximum reconstructed level of (d).

View larger version (19K): [in this window] [in a new window]   FIG. 5. Reconstruction of a point-like target by backpropagation in a homogeneous medium. Actual permittivity = 4. Model permittivities are (a) 5, (b) 6, (c) 7, and (d) 8. The gray scale is normalized to the maximum reconstructed level of (d).

View larger version (16K): [in this window] [in a new window]   FIG. 6. Normalized graph of the maximum level of contrast vs. the model permittivity for the cases of Fig. 4 and 5. The actual relative dielectric permittivity is 4.

View larger version (18K): [in this window] [in a new window]   FIG. 7. Normalized graph of the maximum level of contrast vs. the model permittivity; relative dielectric permittivity ranges from 3.5 to 4.5 with a step of 0.1. The actual relative dielectric permittivity is 4.

View larger version (13K): [in this window] [in a new window]   FIG. 8. A single pipe buried in a homogeneous half-space (p.e.c. = perfectly electric conducting).

View larger version (17K): [in this window] [in a new window]   FIG. 9. Reconstruction of a single target in a half-space. Actual permittivity = 10. Model permittivity equals (a) 4, (b) 10, and (c) 20. The gray scale is normalized to the maximum reconstructed level of (b).

View larger version (63K): [in this window] [in a new window]   FIG. 10. Radar traces of a single target: (a) noiseless data, (b) noisy data, (c) noisy data filtered between 450 and 1350 MHz.

View larger version (41K): [in this window] [in a new window]   FIG. 11. Tomographic reconstruction from the data of Fig. 10b. Actual permittivity = 10. Model permittivity equals (a) 10 and (b) 12. The gray scale is normalized to the maximum reconstructed level of (a).

View larger version (10K): [in this window] [in a new window]   FIG. 12. A stratified scenario with three target in a two layered soil with flat buried interface. The permittivity is 9 in the shallower layer and 20 in the deeper one (p.e.c. = perfectly electric conducting).

View larger version (26K): [in this window] [in a new window]   FIG. 13. Radar traces in the stratified scenario with three target in a two layered soil with flat buried interface.

View larger version (52K): [in this window] [in a new window]   FIG. 14. Tomographic reconstruction obtained from the traces of Fig. 13. Model permittivity = 10. The gray scale is normalized to the maximum reconstructed level.

View larger version (29K): [in this window] [in a new window]   FIG. 15. A stratified scenario with three targets in a two layer soil with an irregular buried interface. The permittivity is 9 in the shallower layer and 20 in the deeper one (p.e.c. = perfectly electric conducting).

View larger version (33K): [in this window] [in a new window]   FIG. 16. Radar traces in the stratified scenario with three targets in a two-layer soil with an irregular buried interface.

View larger version (28K): [in this window] [in a new window]   FIG. 17. Tomographic reconstruction obtained from the traces of Fig. 16. Model permittivity = 10. The gray scale is normalized to the maximum reconstructed level.