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Introduction and History
Electromagnetic Wave Propagation
To many people, ground penetrating radar is a
black box that makes images like cross-sections through the ground. Few people go
beyond the image stage even though the raw images are considerably distorted by the data acquisition process. However, understanding the
interactions between the electric and magnetic fields and the properties of matter can provide
quantitative information to help characterize the material and to correct the images into
true cross-sections of the earth. Nearly everything experienced in daily life is a
consequence of the interactions between fields and electrons, including electromagnetism and wave
propagation (Balanis,
1989, Smith, 1997).
Electrical
properties come from the interaction between electrical fields and charged particles,
particularly the electron.
Electrical conduction (transport) is the result of charge motion and results in energy
dissipation (energy loss or conversion to heat). Electrical polarization (dielectric
permittivity) is the result of charge separation over a distance, storing energy.
This energy loss and storage by charge and consequences in frequency
dependence are illustrated in the program CHARGE.EXE.
Magnetic polarization (permeability or susceptibility) is the result of electron
spin and motion in atomic orbits, and also results in energy loss and storage.
Electrical and magnetic processes
are also coupled, so accelerating electrons generate electromagnetic radiation (Smith, 1997), moving
charges (currents) generate a magnetic field, and time varying magnetic fields cause
charges to move. The velocity of electromagnetic wave
propagation (speed of light) is the reciprocal of the square-root of the product of
permittivity times permeability. The velocity in low
loss, non-magnetic materials is (to a good aproximation) the speed of light in vacuum
divided by the square root of the relative dielectric permittivity (relative to that in
free space).
Maxwell's equations (Maxwell, 1864, 1991) describe the
propagation of an electromagnetic field. It is a coupled process, propagating as a
three-dimensional, polarized, vector wave field. At low frequencies and high losses,
the equations reduce to the diffusion equation and are called electromagnetic induction.
At the high frequencies of radar, the energy storage in dielectric and magnetic
polarization creates wave propagation. In the ideal, lossless case (vacuum), the
electric and magnetic fields are in phase, orthogonal polarized vector fields, propagating
at the speed of light (Balanis, 1989, Smith, 1997).
In real materials, they are out of phase, not completely polarized, propagating with a
velocity lower than the speed of light in vacuum, scattered by changes in electric and
magnetic properties, and with all of the preceding varying as functions of frequency.
The polarized vector field propagates in a straight line
(neglecting relativistic gravitational effects) until it encounters a change in electrical or magnetic
properties. At the change, the wave is scattered
(reflected, refracted or diffracted) with amplitudes determined by the Fresnel reflection coefficient, angles determined by Snell's Law, and a polarization change described by the Stokes-Mueller matrices. Amplitudes are also varying with
direction from the antenna (controlled by the antenna pattern),
and with distance from the antenna (geometric spreading losses and material property
dissipation losses) as described by the radar equation.
Part of what determines whether or not significant scattering occurs is the spatial scale
over which the change in properties occurs. This is both a detectability and a
resolution issue. Resolution is determined by the spatial
geometry of change versus the size of the wavelength of the
propagating field.
(picture of 3D polarized vector propagating wave, with and without loss)
Velocity Wavelength
Attenuation Dispersion
Rocks, Soils and Fluids: Electrical
Properties Magnetic Properties
Environmental Influences
Heterogeneity, Anisotropy and
Scale Radar Equation
Scattering Polarization Fresnel
Reflection Snell Angle
Stokes-Mueller Matrices
Poincare Sphere
Antennas Coupling Near / Far
Fields Waveguides Multipathing Resonance
Survey Design Contrast Geometry
Resolution Depth of Investigation Orientation
Noise Interference Logistics
Data Acquisition Data Processing Modeling
Interpretation Uncertainty
Applications: Noninvasive Surface Borehole
Airborne Satellite and Space
GPR Bibliography
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