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Refracted

= sin-^/^)

(a) Reflected and refracted wave with a separation of x between transmit and receive antennas

(a) Reflected and refracted wave with a separation of x between transmit and receive antennas

Transmit antenna

Transmit antenna

Refracted

(b) Reflected and refracted wave with a separation of x' between transmit and receive antennas

Refracted

(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 contrasting electrical permittivities. Electrical permittivity of the host media is £j, and the permittivity of the lower layer is £2. Following the law of reflection, the angle of reflection is equal to the angle of incidence >1 = >2, and >1' = (2'. The angle of refraction follows Snell's law and is constant irrespective of the incident angle.

dissipates as part of it is reradiated to the outside of the object. Closed objects are said to have a resonant frequency based on the size of the object, and the electrical properties of the object and the surrounding material. However, the ability of an object to resonate depends on the wavelength (velocity of the object, divided by the frequency of the wave) with respect to dimensions of the object. The length of time that an object resonates is determined by the permittivity contrast between the object and the surrounding material.

Diffraction and resonant scattering are complicated phenomena that depend on the properties of the incident wave (including polarization, amplitude, and frequency content) and the size, shape, and electrical properties of the scattering object. Diffraction scattering can be seen on some GPR records where the boundaries between media are sharp (e.g., engineering investigations of foundations), but resonant scattering is very difficult to discern in all but the most ideal conditions.

7.2.2 gpr Recording

Considering the wave scattered from the object in Figure 7.3, if a receive antenna is switched on at precisely the instant that the pulse is transmitted, then the pulses will be recorded by the receive antenna as a function of time. The first pulse will be the wave that travels directly through the air (because the velocity of air is greater than any other material), and the second pulse that is recorded will be the pulse that travels through the material and is scattered back to the surface, traveling at a velocity determined by the permittivity (e) of the material. The resulting record measured at the receive antenna is similar to one of the time-amplitude plots shown in Figure 7.3b, with the "input" wave consisting of the direct wave that travels through air, and the "output" pulse consisting of the wave reflected from the buried scattering body. The recording of both pulses over a period of time with receive antenna system is called a "trace," which can be thought of as a time-history of the

Trace Amplitude

Direct arrival

Trace Amplitude

Direct arrival

(a) Single location yields a trace of data

3D Block "pseudo image"

(c) Traces combined to form a cross section, and cross sections combined to form a 3D block

FIGURE 7.3 Steps in the GPR process: (a) formation of a single time trace of data, showing the direct arrival and reflection from the object; and (b) multiple traces for a wiggle-trace display, with each trace representing a different position on the earth's surface. Multiple traces can be color coded, with different colors (gray scales) assigned to amplitudes, and the result displayed as a cross section, or as a three-dimensional block view as shown on the right side of the figure.

(a) Single location yields a trace of data

(b) Multiple locations yield a cross section record of time-distances traces

3D Block "pseudo image"

(c) Traces combined to form a cross section, and cross sections combined to form a 3D block

FIGURE 7.3 Steps in the GPR process: (a) formation of a single time trace of data, showing the direct arrival and reflection from the object; and (b) multiple traces for a wiggle-trace display, with each trace representing a different position on the earth's surface. Multiple traces can be color coded, with different colors (gray scales) assigned to amplitudes, and the result displayed as a cross section, or as a three-dimensional block view as shown on the right side of the figure.

travel of a single pulse from the transmit antenna to the receive antenna, and includes all of its different travel paths. The trace is the basic measurement for all time-domain GPR surveys. A scan is a trace where a color scale, or a gray scale, has been applied to the amplitude values.

7.2.3 Polarization

The electromagnetic field at a given point in space, at a specific time, has both a magnitude and a direction, and can be described by a vector. As the electromagnetic wave propagates, the orientation and magnitude of these vectors change as a function of time. Polarization describes the magnitude and direction of the electromagnetic field as a function of time and space. Commercial antenna systems are designed to take advantage of the polarization of waves. However, one must be aware of polarization when interpreting data, because a polarized wave has a preferred orientation to detecting objects, particularly linear objects like pipes.

The importance of polarization can be seen by considering the fact that because a linearly polarized (electrical current oscillates back and forth along a straight line as the wave propagates perpendicular to the direction of oscillation) signal has an electric field component in only one direction, then any linear metallic object oriented perpendicular to the direction of polarization will not scatter the signal, and the object will not be detected. This effect is illustrated in Figure 7.4. The practical solution to this potential problem is to run multiple surveys to cover several potential

Antenna, and

Plastic

Metal

Direct trav

Antenna, and

Plastic

Metal

Direct trav

(a) Antennas parallel to the axis of the pipe

Antenna, and

Antenna, and

(b) Antennas perpendicular to the axis of the pipe

FIGURE 7.4 Three-dimensional block and cross sections over plastic (dielectric) and copper (conductor) cylinders when the antennas are (a) parallel to the long axis and (b) perpendicular to the long axis of the cylinder. Note the buried screwdriver that was located above the plastic cylinder.

(b) Antennas perpendicular to the axis of the pipe

FIGURE 7.4 Three-dimensional block and cross sections over plastic (dielectric) and copper (conductor) cylinders when the antennas are (a) parallel to the long axis and (b) perpendicular to the long axis of the cylinder. Note the buried screwdriver that was located above the plastic cylinder.

orientations of subsurface objects, or to measure more than one component of the transmitted linearly polarized signal. Examples of the effect of polarization are presented in the following section on interpretation of GPR data.

7.2.4 Velocity

Electromagnetic waves travel at a specific velocity determined primarily by the permittivity of the material. The relationship between the velocity of the wave and material properties is the fundamental basis for using GPR to investigate the subsurface. To state this fundamental physical principle in a different way: the velocity is different between materials with different electrical properties, and a signal passed through two materials with different electrical properties over the same distance will arrive at different times. The interval of time that it takes for the wave to travel from the transmit antenna to the receive antenna is simply called the travel time. The basic unit of electromagnetic wave travel time is the nanosecond (ns), where 1 ns = 10-9 s.

The time it takes an electromagnetic wave to travel from one point to another is called the travel time, which is measured as an inverse function of velocity. Because the velocity of an electromagnetic wave in air is 3 x 108 m/s (0.3 m/ns), then the travel time for an electromagnetic wave in air is approximately 3.3333 ns per m traveled. The velocity is proportional to the inverse square root of the permittivity of the material, and because the permittivity of earth materials is always greater than the permittivity of the air, the travel time of a wave in a material other than air is always greater than 3.3333 ns/m.

The permittivity is also commonly referred to as the dielectric permittivity, but for simplicity it will be referred to as the permittivity in this book. The permittivity has been explained as a measure of polarizability of a material, which causes displacement currents to flow, which in turn affects the propagation of an electromagnetic wave. The effect of the permittivity on attenuation was previously discussed.

The permittivity is also directly related to the velocity of propagation of an electromagnetic wave, which is a very important property for analyzing and processing GPR data. The permittivity is related to the velocity by the following relationship:

where vm is the velocity of the wave through any material, v0 is the speed of light in air (3 x 108 m/s), em is the permittivity of the material, and e0 is the permittivity of free space (air in a vacuum), with a value of 8.85 x 10-12 Farads/m.

The ratio of the permittivity of the material to the permittivity of air (er = em /e0) is called the relative permittivity. The range of values of relative permittivity is from 1 for air to ~81 for water. The high permittivity of water is caused by the rotational polarization of the water molecule. Not surprisingly, the quantity of water tends to dominate the relative permittivity of porous rocks and minerals.

7.3 EQUIPMENT 7.3.1 System Overview

GPR equipment consists of antennas, electronics, and a recording device, as shown in Figure 7.5. The transmitter and receiver electronics are always separate, but in a fixed-mode configuration, they are often contained in different boxes, and in some systems designed for moving-mode operation, all v m m

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