## Basic Principles

GPR uses the principle of scattering electromagnetic energy in the form of an electromagnetic wave to locate buried objects. The basic principles and theory of operation for GPR have evolved through the disciplines of electrical engineering and seismic exploration, and GPR specialists tend to have backgrounds either in geophysical exploration or electrical engineering. The fundamental principle of operation is the same as that used to detect aircraft overhead, but with GPR, antennas are moved over the surface, similar to a sonic fish-finder, rather than rotating about a fixed point. This has led to the application of field operational principles that are analogous to the seismic reflection method.

It is not necessary to understand electromagnetic theory to use and interpret GPR data, but it is important to know a few basic principles and have an empirical understanding of how electromagnetic energy travels (propagates) in the subsurface. We begin with the most basic description of a wave: a propagating wave is described by a frequency, a velocity, and a wavelength, as shown in Figure 7.1a. If we have two waves and add them together, then we also have to consider the phase, or time offset, of the wave, as shown in Figure 7.1b. We also know from basic physics that we can add waves with different frequencies and different phases together, then we can form any wave shape that we want; and, this wave will still propagate. A wave composed of multiple frequencies, with a resulting finite time duration (e.g., a pulse of electromagnetic energy), is called a time-domain wave. A time-domain wave, similar to the waveform commonly applied to GPR systems, is shown in Figure 7.1c. The most fundamental underpinning principle of GPR is as follows: (a) a pulse of time-domain electromagnetic energy can be formed by a transmit antenna, propagate into the earth with a particular velocity and amplitude, and be recorded by a receive antenna, and (b) the energy of pulse recorded over time provides a time-history of the pulse traveling through the subsurface (Figure 7.1c).

The theory of GPR is based on Maxwell's equations and the vector form of the wave equation, which is the same fundamental theory as the seismic method, with a major difference being that the seismic method is based on the scalar wave equation, and GPR is based on the vector wave equation. In a practical sense, this means that the propagating GPR wave has both a magnitude and an orientation.

### 7.2.1 Propagation and Scattering

The practical result of the radiation of electromagnetic waves into the subsurface for GPR measurements is shown by the basic operating principle illustrated in Figure 7.1. The electromagnetic wave is radiated from a transmitting antenna, spreads out over time in the form of a spherical wavefront (Figure 7.1a), and travels through the material at a velocity determined, primarily, by the permittivity (sometimes called the dielectric constant or electric permittivity) of the material. FIGURE 7.1 Simple wave reflection scattering in the subsurface: (a) simplified view of the process of a wave spreading from an antenna, (b) rays demonstrating by the ray method of a transmitted electromagnetic wave scattered from a buried layer with a contrasting permittivity, and (c) reflection scattering from a buried pipe. Permittivity of the host media is £j, and the permittivity of the reflecting target is £2. FIGURE 7.1 Simple wave reflection scattering in the subsurface: (a) simplified view of the process of a wave spreading from an antenna, (b) rays demonstrating by the ray method of a transmitted electromagnetic wave scattered from a buried layer with a contrasting permittivity, and (c) reflection scattering from a buried pipe. Permittivity of the host media is £j, and the permittivity of the reflecting target is £2.

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 Reflection, 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 directions 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 (sometimes called ringing) within the object. The resonant energy trapped inside of the object quickly

Transmit antenna

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