Introduction and History Electromagnetic Wave Propagation
Velocity Wavelength Attenuation Dispersion
"Among the more profound questions of
geologic science are several whose solution requires a knowledge of the chemical and
physical properties of rocks...
...and the subject calls urgently for special experimentation."
-John Wesley Powell
Report of the Director
U.S. Geological Survey
1882
Electrical Properties of Rocks, Soils and Fluids
![[Under Construction]](images/undercon.gif){kind=small}
The electrical and magnetic properties of rocks, soils and fluids (natural materials) control the speed of propagation of radar waves and their amplitudes. In most cases, the electrical properties are much more important than the magnetic properties. At radar frequencies, electrical properties are dominantly controlled by rock or soil density, and by the chemistry, state (liquid/gas/solid), distribution (pore space connectivity) and content of water.
Electrical properties (Robert, 1988) come
in two basic types: one that describes energy dissipation and one that describes energy
storage. Electrical dissipation comes as the result of charge motion (or transport)
called conduction. Electrical conductivity is the ability of a material to transport
charge through the process of conduction, normalized by geometry to describe a material
property. Dissipation (or energy loss) results from the conversion of electrical
energy to thermal energy (Joule heating) through momentum transfer during collisions as
the charges move. Electrical storage is the result of charge storing energy
when the application of an external force moves the charge from some equilibrium position
and there is a restoring force trying to move the charge back. This process is
dielectric polarization, normalized by geometry to be the material property called
dielectric permittivity. As polarization occurs, causing charges to move, the charge
motion is also dissipative. (See the animation in the CHARGE.EXE
program.)
In either case, charge motion is described by the diffusion
equation. Charges moving with finite velocity result in frequency dependent
properties described by overdamped harmonic oscillators and the Debye single relaxation
equation (Pellat, 1897; Debye, 1929) at frequencies below tens of
gigahertz. Adding the storage force balance in the acceleration term to the
diffusion equation results in a wave propagation equation. The combined electrical
and magnetic storage (polarization) terms through the properties of dielectric
permittivity and magnetic permeability control the velocity of electromagnetic wave propagation.
Electrical polarization is the result of a wide variety of
processes, including polarization of electrons in orbits around atoms, distortion of
molecules, reorientation of polar moelcules (like water molecules), accumulation of charge
at interfaces, and electrochemical reactions. Nearly all polarization of importance
in earth materials is the result of some interaction involving water (Franks,
1970). The dominant mechanisms of electrical conduction are ionic charge
transport through water filling pore spaces in rocks and soils.
The electrical mechanisms of importance to ground penetrating
radar are (Olhoeft, 1984, 1987, 1994, 1998, 2000):
1) electrical conduction losses, mostly from metals, salt water, and other good conductors
which dissipate the energy as heat: these are good reflectors, easy to see with
radar, but impossible to see through or past (radar can see through fresh water).
2) dielectric polarization relaxation by rotational orientation of the water molecule: a
>10 GHz process in free water, but in the 10 kHz range in ice, 10 MHz range in
clathrate hydrates, and at frequencies from 100 Hz to 100 MHz caused by interactions
inside pore structures. These losses are proportional to the amount of free or
mobile water present.
3) electrochemical polarization at the interface between water and clay minerals like
montmorillonite, caused by the active surface chemistry and high surface areas. This
is important below 100 MHz. This is not an important process in finely ground
"rock flour" engineering size fraction clays which have high surface areas but
low chemical reactivity.
4) scattering as the wavelength of propagating energy is sent
in random directions by scales of geological heterogeneity
comparable to the wavelength. Pea gravel becomes important above 1 GHz. This
is akin to the difference between an ice cube and a snowball to visible light. They
are both made of the same material (ice), but the grain size distribution in the snow is
comparable to the wavelength of light, causing scattering, and making the snow look white
and opaque compared to the transparent ice cube. Scattering is both good and bad.
If there is no scattering, then there is nothing for the radar to see. If
there is too much scattering, then the radar can't see anything through the scatter.
Desirable scattering is called a target or a reflector and undesirable scattering
is called clutter.
These electrical mechanisms create frequency dependence resulting in dispersion (frequency dependent velocity and attenuation that
change pulse shape with distance of propagation), contrast resulting in scattering, and they cause energy losses which limit depth of investigation. Energy is also lost in magnetic relaxation and by geometric spreading losses (see radar equation). Geometric spreading losses result as the
propagating wavefront expands away from the source (transmitter) antenna,
and the power is spread over the surface of the antenna pattern (much like being spread
over the surface area of a balloon expanding about the antenna).
(Shivola, 1999)
(BHS mixing formula)
(properties of water equations)
(figures showing frequency dependence with water content)
(Cole-Cole equation)
Dielectric Properties of Body Tissues at RF and Microwave Frequencies
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
Data Acquisition Data Processing Modeling Interpretation Uncertainty
Applications: Noninvasive Surface Borehole Airborne Satellite and Space