Geoscience Reference
In-Depth Information
When a wave encounters a material with a different permittivity, then the electromagnetic energy
will change direction and character. This transformation at a boundary is called scattering. When
a wave impinges on interface, it scatters the energy according to the shape and roughness of the
interface and the contrast of electrical properties between the host material and the object. Part of
the energy is scattered back into the host material, and the other portion of the energy may travel
into, and through, the object. Scattering at the interface between an object and the host material is of
four main types: (1) specular reflection scattering, (2) diffraction scattering, (3) resonant scattering,
and (4) refraction scattering.
A vector line drawn from the transmit antenna to the reflection point on a layer (Figure 7.1b) or
object (Figure 7.1c) is called a ray. Because the reflected energy follows the Law of Relection , as
illustrated by the rays in Figure 7.2, where the angle of reflection is equal to the angle of incidence,
then the reflection point for any given transmit-receive antenna pair over a flat layer (Figure 7.1b,
Figure 7.2) is at a point in the subsurface that is halfway between the transmit and receive antennas.
The wave energy that propagates into the object, or layer, enters at an angle determined by contrast
in electrical properties and is called the refracted energy. The angle that the wave enters into the
second (lower) object or layer is called the angle of refraction and is determined by Snell's law,
as shown in Figure 7.2. Refraction scattering is not generally an important consideration for GPR
measurements over the surface of the earth, because GPR waves attenuate very rapidly in most near-
surface earth materials, and velocities decrease with increasing depth. However, refraction may be
important for determining layer thicknesses in building materials and roadbeds, where the velocity
of an overlying layer is sometimes less than the velocity of a lower layer.
Diffraction scattering occurs when a wave is partially blocked by a sharp boundary. The wave
scatters off of a point, and the wave spreads out in different directions, as first noted by Fresnel
(1788-1827). The nature of the diffracted energy depends upon the sharpness of the boundary and
the shape of the object relative to the wavelength of the incident wave. Diffractions commonly can
be seen on GPR and seismic data as semicoherent energy patterns that splay out in several direc-
tions from a point or along a line. Geologically, they often are measured in the vicinity of a vertical
fault, or a discontinuity in a geologic layer (abrupt horizontal change in the geology).
Resonant scattering occurs when a wave impinges on a closed object (e.g., a cylinder), and the
wave bounces back and forth between different points of the boundary of the object. Every time
the wave hits a boundary, part of the energy is refracted back into the host material, and part of the
energy is reflected back into the object. This causes the electromagnetic energy to resonate (some-
times called ringing) within the object. The resonant energy trapped inside of the object quickly
Transmit
antenna x
Receive
antenna
Transmit
antenna
Receive
antenna
x
φ 1
φ 2
φ 2 = φ 1
φ 1
φ 2
φ 2 = φ 1
Reflected
Incident
Incident
Reflected
ε 1
ε 1
ε 2
ε 2
Refracted
Refracted
φ r = sin -1 2 1 )
φ r = sin -1 2 1 )
(a) Reflected and refracted wave with a
separation of x between transmit and
receive antennas
(b) Reflected and refracted wave with a
separation of x between transmit and
receive antennas
fIGURe 7.2 Transmitted electromagnetic wavefront reflected and refracted from a buried layer with con-
trasting electrical permittivities. Electrical permittivity of the host media is ε 1 , and the permittivity of the lower
layer is ε 2 . Following the law of reflection, the angle of reflection is equal to the angle of incidence ϕ1 = ϕ2, and
ϕ1′ = ϕ2′. The angle of refraction follows Snell's law and is constant irrespective of the incident angle.
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