Elements of Electromagnetic Theory for GPR Applications José M. Carcione OGS, Trieste, Italy and Marco A. B. Botelho UFBA, Salvador, Brasil

The Hanai-Bruggeman model. Water is the starting host material (2) into which infinitesimal amounts of grains are gradually included. The model agrees with Archie's law, i.e., it preserves the continuity of the water phase. W=1/3 for spherical grains. Lichtenecker-Rother (LR) equation c=2 (CRIM)

Experimental data.

The Hanai-Bruggeman model.

Perpendicular broadside AVO theory Parallel endfire Perpendicular broadside

AVO theory

AVO theory

AVO theory. TM Brewster angle Model 1: Air --------------- fresh water Model 2: Air ---------------- seawater

AVO. Brewster and critical angles Model 5: fresh water ----------------------- seawater/DNAPL NAPL-2: bio-degraded (higher conductivity) TM case

AVO inversion. Brewster and critical angles TM case: Fresh Water -------------------------------------- Seawater (50 %)/DNAPL (%) f-k inversion

The exploding reflector experiment

The exploding-reflector experiment

Plane-wave and exploding reflector PW ER

Fine layering. Backus averaging

EM theory in anisotropic media

EM theory. Anisotropy Complex slowness

Conclusions Permittivity and conductivity (Hanai-Bruggeman, CRIM, etc.). Reflection and refraction coefficients (AVO, Brewster, critical angles). 3. Full-wave synthetic radargrams (single emission, plane wave, exploding reflector, etc.). 4. Anisotropic media (fine layering, fractures, cracks, etc.)

Notes