Handbook of Geophysics and Archaeology

Some basic concepts of waves were introduced in Chapter 6 and some of these concepts were used in the presentation of electromagnetic induction (Chapter 7). In particular, the oscillatory character of timevarying magnetic fields was considered wave-like because, as generated by electromagnetic induction tools, these fields exhibit a periodicity over time that is characteristic of wave motion (Sect. 6.1).

There is one distinguishing characteristic that makes EMI signals not completely wave-like, and this is that they do not propagate. Wave energy travels (propagates) at some characteristic wave speed (Sect. 6.1) that depends on the material through which it travels and the nature of the wave. In contrast, a change in the magnetic field at the source was considered to manifest an instantaneous change in the magnetic field at all points surrounding the source in EMI. Ground Penetrating Radar (GPR) is a true wave-based method in that this method must iuclude the effects of wave propagation, and this one difference between GPR and EMI totally changes the nature of the instrumentation, the data acquisition, and the interpretation.

The concepts associated with GPR are simpler than those of EMI and 'map' subsurface features by exploiting the fact that, for waves, the distance from the wave source to a buried object is equal to the wave speed times the travel time. The implementation of GPR is no more complicated than the use of a digital tape measure (Fig. 6.2). The interpretation of GPR data does require, however, more skill and insight than the interpretation of EMI data. This is a consequence of the time dependence being implicit in EMI and explicit in GPR. Without any knowledge of the time or frequency effects in EMI it is possible to identify buried objects from EMI data simply by measured changes in response as a result of moving the measurement on or above the ground surface (Fig. 7.40). This is not the case for GPR where wave travel time introduces an additional dimension to the acquired data. The interpretation complication associated with time dependence in GPR sets it apart from the other methods considered thus far, and allows object depth to be determined almost exactly with very little effort. In contrast, target depths must be estimated for gravity, magnetometry, and EMI and these estimates must be based on some assumption about the target's shape.

9.1 Reflection and Refraction

In Chapter 6, waves were characterized in different ways. Similarly, there are various ways to characterize methods for exploiting waves. For example, the problem of determining the distance between two cities by driving at a constant speed and measuring the elapsed time (Sect. 6.1) can be characterized as a transmission technique because it involves travel in one direction only. Determining the distance to a wall by using a digital tape measure (Fig. 6.2) is referred to as a reflection technique since it involves bouncing a sound pulse off the wall. Transmission methods will not be considered here but will be developed in a later chapter on 'geotomography.' The concept of transmission is only introduced here so that another effect, known as refraction, that can play a role in both reflection and transmission methods can be explored. Reflection and refraction are the only wave effects not considered in Chapter 6 which are necessary to understand GPR.

9.1.1 Refraction

Refraction means the bending of wave propagation paths (such paths are called rays), and an obvious example in refraction is the view of objects below the surface of the water. It is well known that objects below the water surface appear closer, an illusion resulting from the refraction of light and the way the human brain interprets signals received through the eyes. The mechanisms for this illusion are illustrated in Fig. 9.1.

$Figure 9.1. Illustration of how refraction causes objects below the water surface to appear closer.$

Figure 9.1. Illustration of how refraction causes objects below the water surface to appear closer.

Visual depth perception results from using two eyes. The brain integrates the signal from each eye by comparing images from both and determining how much one image is shifted laterally with respect to the other. If an object is far away, the images from both eyes are nearly identical. As an object becomes closer, the images received from each eye become more skewed and, based on this skewness, the object can appear closer. This is the effect that is exploited in three-dimensional movies. These movies actually consist of two different movies superimposed. More properly, these are the same movie but one is shifted with respect to the other on the screen. Special glasses are worn such that one eye sees only one movie and the other eye sees only the other movie. Viewing a three-dimensional movie without the special glasses, the two individual movies would be evident. By repeatedly wearing and removing the glasses, it would be apparent that, for objects that appear close, the two movies appear more skewed on the screen. Since movie screens are two-dimensional, this is the only way to create a three-dimensional effect. In a three-dimensional world, images from both eyes are directly used for the same effect. Figure 9.1 shows a coin at the bottom of a glass of water. Rays are also shown extending from either side of the coin to the nearest eye. These rays (Sect. 6.4) define particular directions of propagation of the waves of light from the edges of the coin to the eyes. As these rays pass from the water into the air, they are refracted (bent). Eyes and brains have no way of accounting for refraction, and they interpret the signals received by the eyes by extending the received rays backward down to the plane of the coin along the straight rays that pass from each eye to the water surface. These ray paths are illustrated by the dashed lines in Fig. 9.1. It is recognized that these rays are further apart at the plane of the coin than the actual rays and, hence, the coin appears either closer or larger.

Refraction can occur whenever a wave passes from a material having a certain wave speed into a material having a different wave speed. The definition of the speed of light in relation to material properties is presented in Sect. 9.3. The speed of light in air is 300 million meters per second and the speed of light in water is about 33 million meters per second. This wave speed difference causes refraction and the illusion is illustrated in Fig. 9.1. The amount of ray bending that occurs when a wave passes from one medium to another is proportional to the ratio of the wave speeds in the two mediums. The relationship between the amount of ray bending that occurs and the ratio of wave speeds is known as Snell's Law. This ratio is known as the index of refraction. Figure 9.2 illustrates the ray bending between the two mediums.

$Figure 9.2. Illustration of the effect of the index of refraction on ray bending.$

Figure 9.2. Illustration of the effect of the index of refraction on ray bending.

A ray passing from a medium having a wave speed & into a medium having a wave Speed c₂, greater than c₁, is shown Fig. 9.2a. Because c₂ is greater than c₁, the ray bends towards the horizontal interface between the two mediums. Had the ray passed from a region of higher wave speed c₂ into a material of lower wave speed c₁, the ray would have bent away from the horizontal interface (Fig. 9.2b). The ray bending shown in Fig. 9.2c is similar to that shown in Fig. 9.2a except that the ray passes from a medium with a wave speed c₁ into a medium of wave speed c₃, where c₃ is greater than c₂ and, hence, there is a greater refraction.

9.1.2 Reflection

Wave speeds also play a key role in reflection. In the digital tape measure experiment (Fig. 6.2), the sound bounced (reflected) off the wall because there was a difference in sound speed between the air and the wall. The amount of energy that bounces off the wall, relative to the energy incident on the wall, is proportional to the coefficient of reflection. If the speed of sound in air is and the speed of sound in the wall is c₂, the reflection coefficient is defined to be

Figure 9.3. Illustration of the reflection and transmission of energy at an interface between materials of differing wave speeds.

In this figure, a digital tape measure is used to illustrate the reflection and transmission of an incident ray upon encountering a change in wave speed between two materials. The proportion of energy that is reflected is determined by the reflection coefficient and the amount transmitted is proportional to the coefficient of transmission, which is defined as

T r a n s m i s s i o n C o e f f i c i e n t = 1 - R e f l e c t i o n C o e f f i c i r n t = \frac{2 c_{1}}{c_{2} + c_{1}}

and it is evident from this relationship that, for c₂ = c₁, the transmission coefficient is equal to one and the reflection coefficient is equal to zero so that all the energy is transmitted and none is reflected.

In the above discussion of reflection, the incident ray that is shown is perpendicular to the interface. This is a special case known as normal incidence that will be discussed in Sect. 9.1.3. The case when a planar interface is not perpendicular to the incident ray is shown in Fig. 9.4.

Figure 9.4. Illustration of a reflected ray from a tilted planar interface.

Here again, there is a planar interface between materials of wave speed c₁ and c₂, however, the planar interface is tilted with respect to the horizontal. The dashed line in Fig. 9.3 is for reference and along a direction perpendicular to the planar interface. The angle between the incident ray and the dashed line is known as the angle of incidence, denoted by θ_i, on Fig. 9.4, and the angle between the dashed line and the reflected ray is known as the angle of reflection, denoted by θ_r on Fig. 9,4. These angles are both measured from the perpendicular to the interface, the dashed line on Fig. 9.4, and these two angles are simply related by

Equation 9.3:

Angle of Incidence = Angle of Reflection

The reflection cases examined thus far are relatively simple because only a single reflection has been considered. For a ray from a digital tape measure that is incident perpendicular to a wall of finite thickness with air on either side (Fig. 9.5), both reflection and transmission must be considered.

Figure 9.5. Illustration of multiple reflections resulting from normal incidence and two changes in wave speed.

The situation depicted in Fig. 9.4 becomes more complicated when transmission and finite wall thickness are considered. Figure 9.6 displays the same finite wall thickness as shown in Fig. 9.5 but for a tilted wall.

$Figure 9.6. Illustration of multiple reflection and refraction resulting from two changes in wave speed and non-normal incidence.$

Figure 9.6. Illustration of multiple reflection and refraction resulting from two changes in wave speed and non-normal incidence.

The conditions shown in this figure are quite similar to those in Fig. 9.5 except that the rays are refracted (Fig. 9.2) at all transmissions across both interfaces. As a result of the refractions, the rays do not simply bounce up and down within the wall, but move (propagate) within the wall's interior. This effect is called wave guiding since refraction results in trapped waves being guided down the wall. Wave guiding is the reason why sound can be heard loudly and clearly when speaking to someone through a long pipe or tube.

9.1.3 Normal Incidence

Normal incidence is a special case of reflection and refraction. Specifically, it is the case when the incident ray is along a direction perpendicular to an interface separating materials having two different wave speeds. Normally incident rays are illustrated in Figs. 9.3 and 9.5 and, as shown in these figures, a normally incident ray is reflected backwards directly towards the ray source. This follows directly from Equation 9.3 where the angle of incidence is zero, which implies that the incident ray is perpendicular to the interface (the direction defined by the dashed line in Fig. 9.4), and the angle of reflection is also zero. It should be recognized from this relationship and Fig. 9.4 that the digital tape measure does not work unless there is normal incidence because the reflected ray does not return to the digital tape measure and, consequently, cannot be detected. Ground penetrating radar exploits reflected normally incident rays and, while GPR interpretation (Sect. 9.2) is not simple, normal incidence makes interpretation far more simple than measurements where normal incidence does not occur.

Normal incidence also simplifies the character of refraction. As established in Sect. 9.1.1, the amount of ray bending that occurs when a ray passes across an interface separating materials of differing wave speed depends on the change in wave speed across the interface. When the ray is normally incident on the interface, there is no refraction (Fig. 9.7), no matter how great the change in wave speed across the interface, the ray direction does not change.

$Figure 9.7. There is no refraction of a normally incident ray across an interface.$

Figure 9.7. There is no refraction of a normally incident ray across an interface.

The transmitted rays in Figs. 9.3 and 9.5 are normally incident and there is no refraction. In contrast, the transmitted rays illustrated in Fig. 9.6 are not normally incident and, as shown, there is refraction across all interfaces.

9.2 GPR Measurements and Simple Interpretations

The major components of a digital tape measure are a high frequency acoustic transmitter and receiver, a clock, a simple computer chip to implement Equation 9.4, and a display to present the measured distance.

Figure 9.8. Illustration of the use of a digital tape measure to determine the distance to two offset, parallel walls.

In this figure, many digital tape measures have been placed along a line that is parallel to both walls. The near wall and far wall are 10 and 15 m from the measurement line, respectively. Each digital tape measure provides a distance to the wall that is directly opposite the particular digital tape measure because, as depicted in Fig. 9.8, all rays exhibit normal incidence. From the elapsed time measured at each digital tape measure, it is possible to plot the measured round trip travel time as a function of the position along the measurement line of each digital tape measure. This is shown in the lower portion of Fig. 9.8. The scale on the left is the measured elapsed time and note that, for all the digital tape measures opposite the near wall, the round trip travel time is about 0.06 seconds. Similarly, all the digital tape measures opposite the far wall provide identical travel times of about 0.09 seconds. The most important aspect of the measured travel times displayed in Fig. 9.8 is that the pattern of measured travel times replicates the shape of the actual wall structure. From the measured travel times and the sound speed in air (335 meters per second), Equation 9.4 can be used to convert from travel time to distance. This conversion is shown as the scale on the right side of the lower portion of Fig. 9.8. After this conversion, the plotted distance accurately displays the wall geometry and dimensions.

Digital tape measures are relatively expensive so that the use of many such tools could be cost prohibitive. An alternate means to conduct the experiment shown in Fig. 9.8 is to use only one digital tape measure but move it along the line making measurements at fixed intervals along the measurement line. Clearly, this procedure will yield results identical to those shown in Fig. 9.8.

9.2.1 Simple Concepts of GPR

Ground penetrating radar functions much like the digital tape measure example presented in Fig. 9.8 with two exceptions. First, the digital tape measure uses high frequency sound waves while GPR uses electromagnetic (radio) waves. There are a number of distinctions between acoustic and electromagnetic waves that will be discussed in subsequent sections. However, for the moment, the most important is that the speed of light (the propagation speed of electromagnetic waves) is about one million times greater than the speed of sound. This does not change the fact that the digital tape measure is a good analogy for GPR, but it should be recognized that measurements must be made at a much higher rate for GPR because of the substantially higher wave speed. A second and important difference between GPR and a digital tape measure is that the digital tape measure is designed to determine only the distance to the nearest reflecting surface. For this reason, the digital tape measure does record data but only 'counts' clock ticks until the first reflection is received. In subsurface investigations, there are often layers of different geologic material at different depths alongwith isolated objects embedded within particular geologic strata. A feature of interest may be deeper than the shallowest reflecting object or layer so that data acquisition must continue beyond the arrival time of this first reflection. This requires that received signals be recorded as a function of time for some user-specified time duration. Digital tape measure operation, as depicted in Figs. 9.3-6, and 9.8, employs a single emitted ray. This is an oversimplification and, in fact, these devices emit many rays. A single ray is shown in the above-cited figures to represent the fact that digital tape measures emit rays over a very limited range of directions. In GPR systems, the wave source emits rays over a very broad range of directions and this difference is important in that it allows features of varying shapes to be detected.

Figure 9.9. Illustration of the GPR instrumentation system (a) consisting of a transmitting T and receiving R antenna that move in unison along the ground surface. The transmitting antenna behaves as a point source (b) sending out rays in many different directions. When rays encounter a change in wave speed, (c) these rays will be reflected but only one will be directed (black) such that it will be captured by the receiving antenna.

For simplicity, assume that the GPR transmitting antenna emits a pulse (Fig. 6.25) which, as described in Sect. 6.4, is a short 'burst' of energy. In general, the transmitting and receiving antennas are sufficiently close together that it can be assumed that the transmitted and received rays comprise a normally incident ray pair (Fig. 9.10). Furthermore, given a horizontal interface at a depth d, where the wave pulse travels in the upper layer at wave speed n, the round trip distance traveled from the transmitting antenna to the interface and from the interface to the receiving antenna is 2d and related to the wave speed and round trip travel time t by

or the travel time is related to the round trip distance and the wave speed through the relationship

A digital tape measure simply counts clock ticks until a reflection is detected and then, based on the time elapsed between the initiation of the pulse and the received reflection, uses Equation 9.4 to compute and display the distance to the reflecting surface. A GPR instrument is somewhat more complicated in that it records the received signal as a function of time over some prescribed time duration. Until a reflection is received it records zeros, then records the arrival time of the reflected pulse as a non-zero value (a 'blip') and zeros for later times. For the interface shown in Fig. 9.10, a blip appears at time t = 2d/c₁ and zeros are recorded at all other times. The measured response over time is plotted on the right side of Fig. 9.10 and this is shown with a vertical time axis because, as illustrated, increasing time can be associated with increasing depth.

Figure 9.10. Because the two antennas are much closer together than the depth, d, to a reflecting interface, the incident and reflected ray can be considered as a normally incident and reflected ray pair. The line plot on the right depicts the reflected pulse arriving at a time t = 2d/c₁.

9.2.2 Interpretation of GPR Data

With these simple concepts of GPR operation, it is now possible to consider the interpretation of GPR data. Typically, GPR data is acquired by moving the antenna pair along a line on the ground surface. At predetermined intervals along this line, the transmitting antenna emits a burst of wave energy and, at the same time, the recording of the signal arriving at the receiving antenna begins. The received signal as a function of elapsed time is plotted with the time axis vertical and increasing time downward as shown on the right side of Fig. 9.10. This single line plot is called a trace. The antenna pair is moved a short distance along the ground surface and the data acquisition is repeated with the recorded trace associated with this measurement location plotted parallel to but shifted slightly to the right of the first trace. This procedure is repeated until the entire line is surveyed. The resulting pattern of traces is referred to as a radargram. Figure 9.11a displays a synthetic radargram for the horizontal layered structure illustrated in Fig. 9.10.

Figure 9.11. Example of a radargram for a single horizontal interface. The original radargram (a) is converted from time to depth (b) and superimposed on the geologic structure.

The radargram, after the conversion from travel time to travel distance, is shown superimposed over the layered structure in Fig. 9.11b where it becomes clear that the GPR data has accurately replicated the layer structure. This figure also shows three locations of the antenna pair with the traces associated with these measurement positions drawn in black while all other traces are drawn in gray. The purpose of this presentation is to illustrate how the position of a trace within a radargram shifts with antenna position.

Another simple shape is a sloping interface and, as illustrated in Fig. 9.12a, the only ray emitted by the transmitting antenna that can be 'captured' by the receiving antenna is the ray that strikes perpendicular to the interface (normal incidence) and, in this case, the transmitted and reflected ray pair are not vertical.

Figure 9.12. Example of a radargram for a single sloping interface (a). The original radargram (b) is converted from time to depth (c) and superimposed on the geologic structure.

As the antenna pair is moved from left to right, the travel distance perpendicular (normal) to the interface increases and, consequently, the travel time increases. The synthetic radargram is shown ill Fig. 9.12b where it is clear that, once again, the shape of the reflecting surface is approximately mimicked in the GPR data. Using Equation 9.6 (Fig. 9.12c) to convert from travel time to travel distance, it is noted that the slope of the blips replicates the slope of the interface—however, this linear pattern of blips is shifted upward as compared to the actual position of the sloping interface. This is because the conversion is from travel time to travel distance and not depth. Since the interface is inclined, the reflected ray that is detected by the receiving antenna does not originate directly below the antenna pair (Fig. 9.12a). This situation is different from the horizontal interface (Fig. 9.10) where the reflected ray originates from a point directly below the antenna pair and the travel distance is equal to the depth.

A subsurface structure consisting of three layers of different materials characterized by wave speeds c₁, c₂, and c₃ separated by two horizontal interfaces is shown in Fig. 9.13. This situation is much like the single horizontal interface presented in Fig. 9.11 except that, while some of the energy incident on the interface between c₁ and c₂ is reflected, there is also some wave energy transmitted into layer c₂ (Sect. 9.1.2).

Figure 9.13. Illustration of (a) two horizontal interfaces separating materials having three different wave speeds and (b) a synthetic radargram for this structure.

This transmitted wave energy will be reflected from the interface between c₂ and c₃ and, ultimately, detected by the receiving antenna. The synthetic radargram for this two-layered structure is shown in Fig. 9.13b where the horizontal rows of blips are evident. The stronger row of blips appears at a shorter time and is associated with the shallower horizontal interface. The later arriving row of blips is associated with the deeper interface and these blips are weaker because some energy from the incident wave has already been lost to the reflection at the shallower interface. This situation could be reversed, in other words, the shallower interface could yield a weaker line of blips than the deeper interface. This will depend on the relative reflection coefficients (Equation 9.1), across each of the interfaces. The radargram shown in Fig. 9.13a correctly reveals the presence of two horizontal interfaces. A conversion from travel time to travel distance using Equation 9,6 and the wave speed in the upper layer, c₁, will yield a correct depth for the shallow interface and an erroneous depth to the deeper interface. The depth to the shallow interface is correct because the rays reflected from this interface all travel through a material having a wave speed of c₁. For the deeper interface, the downward and upward traveling rays pass through materials having wave speed of and ft- Therefore, using a wave speed of c₁ only yields an incorrect conversion from time to distance and this distance is overestimated if c₂ is greater than c₁, and underestimated when c₂ is less than c₁.

Figure 9.14a depicts a subsurface structure consisting of two interfaces. This structure is similar to that shown in Fig. 9.13 but with the deeper interface being inclined rather than horizontal.

The analysis of this structure is almost identical to that presented for the two horizontal interfaces with only one notable difference. As illustrated in Fig. 9.14a, a ray normally incident on the deeper inclined interface (the transition from c₂ to c₃) can only be realized when there is refraction (Sect. 9.1.1) of this ray through the shallow horizontal interface. Similarly, the reflected ray from the inclined interface must undergo a refraction when passing upward through the horizontal interface. In spite of these refractions, the radargram (Fig. 9.14b) still shows a pattern of blips that clearly reveals the presence of a shallow horizontal interface and a deeper sloping interface.

The examples considered above are all associated with subsurface structures of infinite horizontal extent that are most often shallow geologic structures. One example of a buried feature of finite horizontal extent is a rectangular object characterized by a wave speed c₂ embedded in a homogeneous host material having a wave speed c₁ (Fig. 9.15a). When the antenna pair is positioned to the left of the buried rectangle (Fig. 9.15b), rays emitted by the transmitting antenna can reflect off of the vertical sidewall or the top of the rectangle. However, none of the rays are normally incident on a reflecting surface so no signal will be detected at the receiving antenna. This pattern of no measured response will persist until the antenna pair is directly above the buried rectangle (Fig. 9.15b). For all antenna positions that occur directly above the rectangle, there will be reflections from the upper surface of the rectangle and a later arriving reflection from the lower horizontal surface of the rectangle. Further movement of the antenna pair from left to right will ultimately take the antennas to positions where they are no longer above the buried rectangle and, at these positions, there will be no measured response. The synthetic radargram for this structure is provided in Fig. 9.15c where it can be noted that there are two horizontally truncated patterns of blips associated with the two horizontal surfaces of the rectangle and no evidence of its sidewalls. This pattern is typical of buried features with vertical sidewalls and the absence of the sidewalls in the radargrams arises from the fact that no rays emitted at the ground surface can be reflected from these sidewalls in directions that will lead back to the ground surface.

Figure 9.14. Illustration of (a) a horizontal interface and a deeper inclined interface separating materials having three different wave speeds and (b) a synthetic radargram for this structure.

Figure 9.15. Illustration of a buried rectangle when the antenna pair is (a) not over the top of the rectangle, (b) over the top of the rectangle, and (c) a synthetic radargram for this structure.

It should be noted that, in Fig. 9.15c, the blips associated with the reflection from the lower surface of the rectangle point in the opposite direction of those from the upper surface of the rectangle. This indicates that the responses from the lower surface are negative while those from the upper surface are positive. This change in sign from positive to negative follows directly from the definition of the reflection coefficient (Equation 9.1), and to better understand the origin of the sign change, more precise definitions of parameters in this equation must be introduced. Specifically, the wave speeds c₁ and c₂ should be defined as the wave speed of the material through which the incident wave travels and the wave speed of the material from which the wave is reflected, respectively. Redefining c₁ and c₂ as c₁, for wave speed in the incident material, and c_r for the wave speed of the material from which the wave is reflected, a more proper definition of the reflection coefficient is

For the reflection from the upper surface of the rectangle, the wave is traveling through a material having a wave speed of c₁ and is incident upon a material having a wave speed c₂ so that c_i = c₁ and c_r = c₂. Using the reflection coefficient defined by Equation 9.7 and calling this coefficient C_U to denote that this reflection coefficient is associated with the reflection from the upper surface,

If c₂ is greater than this reflection coefficient is positive. For the reflection from the lower surface of the rectangle, the wave is incident in a material having a wave speed c₂ and reflected from a material having a wave speed c₁. For this reflection, c_i — c₂ and c_r = c₁ making the reflection coefficient, C_L, from the lower horizontal surface

C_{L} = \frac{c_{1} - c_{2}}{c_{1} + c_{2}}; \frac{c_{2} - c_{1}}{c_{2} + c_{1}} = - C_{U}

The above equation states that the sign of the reflection from the lower surface is always opposite that of the upper surface. When the reflection from the upper surface is positive, the reflection from the lower surface is negative, and vice versa.

The sign of the reflection, as presented here, extends to all the previous examples. In these, every reflection was assumed to be associated with a transition from a material with a low wave speed to a deeper material with a higher wave speed. For example, consider the simple horizontal interface (Fig. 9.11). The radargram shown in this figure is based on c₁ being less than c₂ and this relative change in wave speed yields a positive reflection coefficient. Had it been assumed that c₂ was less than c₁, the reflection coefficient would have been negative and the associated radargram would have exhibited negative, rather than positive, responses.

Another simple shape of limited horizontal extent is a circle. Thus far, all reflections considered have been from flat surfaces and, with the introduction of a circular reflector, the meaning of normal incidence to this shape must be defined. A line perpendicular to a curved surface is not necessarily easy to define. However, for a circle, a line normal to its surface will pass directly through the center of the circle. Figure 9.16a presents a circle composed of material having a wave speed c₂ buried in a background material having a wave speed c₁. The normally incident and associated reflected rays are also shown for the illustrated antenna position. As shown, the normally incident ray is directed from the transmitting antenna directly towards the center of the circle and the reflected ray is directly away from the center of the circle. Some of the energy incident on the upper surface of the circle is reflected and the remainder of the energy is transmitted into the circle. Since this ray is normally incident, there is no refraction of the ray when it passes to the interior of the circle. The transmitted ray passes directly through the center of the circle and impinges on the far lower surface of the circle.

Figure 9.16. Illustration of a buried circle when the antenna pair is (a) not over the top of the circle, (b) over the top of the circle, and (c) a synthetic radargram for this structure.

This ray is also normally incident on this surface and, consequently, is reflected back through the center of the circle, continuing on in this direction until reaching the receiving antenna. The rays shown in Fig. 9.16 will yield two reflections, one from the upper surface and the later arriving reflection from the lower surface. Because the ray that is reflected from the lower surface travels the same distance through the background material (c₁) as the first reflection plus a distance twice the diameter of the circle at a wave speed of c₂, the second reflection will be time delayed relative to the first by an amount that is proportional to both the diameter of the circle and the wave speed, % within the circle.

The ray paths associated with the antenna pair directly over the top of the buried circle are shown in Fig. 9.16b. For this measurement position, the normally incident rays on both the upper and lower surfaces of the circle are straight down. In comparing the ray geometry in Figs. 9.16a and 9.16b, it is clear that the travel distance to the upper surface of the circle is shorter when the measurement location is directly over the top of the circle. In fact, this is the shortest travel distance that can be realized for measurements made by moving the antenna pair along a line. Furthermore, moving the antennas towards a position that is directly over the top of the buried circle will result in progressively shorter travel distances and moving the antennas progressively further away from a position directly over the top of the circle will yield an increasing travel time for this reflection. It is also clear from Fig. 9.16b that the transmitted ray and its reflection both travel directly through the center of the circle so that the relative time delay between the reflection from the upper surface and lower surface is identical to that when the measurement location is as shown in Fig. 9.16a. The synthetic radargram for the buried circle is given in Fig. 9.16c and this object is manifested in the GPR data as two parallel downward curved arcs. The earlier arriving arc is the reflection from the upper surface and the later arriving arc is from the lower surface of the circle. These 'frown'-like shapes are referred to as hyperbolas. The sign of the lower hyperbola is reversed relative to the upper hyperbola for reasons presented in the discussion of the buried rectangle. A fundamental difference between the GPR response for a circle and all other shapes considered thus far is that the shape of the circle is not replicated in the radargram. For the common measurement procedure of GPR where an antenna pair is moved in unison along a line on the ground, reasonably accurate shape replication in the data will only occur for reflecting surfaces that are flat. However, these flat surfaces do not have to be horizontal.

A vertical cross-section through a buried wall built on bedrock or firm soil can be approximated by a rectangle resting on a horizontal interface. As shown in Fig. 9.17a, a horizontal interface separates materials having wave speeds c₁ above and c₃ below. The wall is represented by a rectangle composed of a material characterized by a wave speed c₂ resting on the c₃ layer. For the measurement position shown in Fig. 9.17a, there can be reflections from the horizontal interface as well as the top and side of the rectangle. The ray incident on the horizontal interface (the black ray) is normally incident so it is the reflection of this ray only that can be detected by the receiving antenna. For all measurement locations either to the left or right of the rectangle, the only recorded reflection will be from the horizontal interface. These reflections will arrive at the same time and this time will depend on the depth to the horizontal interface and the wave speed, c₁. When the antennas are positioned over the rectangle (wall) (Fig. 9.17b), there can be reflections from the top and bottom of the wall and the horizontal interface. It is only the rays striking the top and bottom of the rectangle that are normally incident and, therefore, only the reflections of these rays (drawn in black) can be detected.

Figure 9.17. Illustration of a buried wall resting on a dense material when the antenna pair is (a) not over the top of the wall, (b) over the top of the wall, and (c) a synthetic radargram for this structure.

For all measurement positions over the wall, there will be two detected reflections, one from the top of the wall and, later, one from the bottom of the wall. The synthetic radargram for this structure is presented in Fig. 9.17c. The two traces in the center of the radargram each show two reflected arrivals. The earliest arriving reflection in each trace is from the upper surface of the rectangle and the later arrival is from the bottom of the rectangle. As illustrated in Fig. 9.17c, the reflection from the interface between the bottom of the wall and the o layer arrives earlier than the reflection between the horizontal interface between c₁ and c₃ even though both reflecting surfaces are at the same depth. This occurs because rays that do not travel through the wall propagate at a single wave speed a while rays that travel through the wall to reach the c₃ layer must first travel through material having a wave speed c₁ and then through a material having a wave speed c₂.

A vertical structure that is sometimes encountered in geophysical exploration is a relic channel. This structure was once an active river or stream cut into the host soil or rock by flowing water. Climatic changes and depositional forces over a long time have resulted in the stream drying up and being buried. The identification of such a structure may be relevant in archaeological studies but, more importantly, it is a relatively simple shape that yields a quite complex radargram. A relic channel can be represented simply as an interface between materials having wave speeds of c₁ and c₂ (Fig. 9.18a). The channel is cut into a material having a wave speed c₂ and has a horizontal bottom and sloping sidewalls. The more recent material deposited on top of the channel has a wave speed of c₁.

Figure 9.18. Illustration of a vertical cross-section through a relic channel when the antenna pair is (a) far to the left of the channel, (b) slightly to the left of the channel, (c) over the left sidewall of the channel, (d) over the top of the center of the channel, and (e) a synthetic radargram for this structure.

There can be reflections from any of the surfaces that define the interface between c₁ and ix However, when the measurement location is far to the left of the channel (Fig. 9.18a) the only normally incident ray is the one shown in black in this figure and it is only the reflection of this ray that can be detected by the receiving antenna. This will be the case for all measurement locations that are either far to the left or far to the right of the channel so that measurements made in this area will produce a horizontal linear pattern of blips. Moving the antenna pair to the right such that it is closer to the channel yet not over the bottom or left sidewall (Fig. 9.18b), there will still be a detected reflection from the horizontal interface to the left of the channel (black) and there can also be a detected reflection from the far sidewall of the channel (black). For this measurement position there will be two recorded reflections, one from the horizontal interface to the left of the channel and a later arriving reflection from the right sidewall of the channel. This is not the first case where multiple reflections have been recorded. These are evident in Figs. 9.13b, 9.14b, 9.15c, 9.16c, and 9.17c. However, in these cases, multiple reflections have originated from a single transmitted ray. The multiple reflection that occurs in Fig. 9.18b arises from two different transmitted rays. This type of situation is sometimes referred to as multipathing since the different reflections result from rays following different paths. Continuing to move the measurement position to the right, an area will be reached where the antenna pair is over the left sidewall of the channel (Fig. 9.18c). There can no longer be a reflection from the horizontal interface to the left of the channel and only a single reflection is detected and this reflection is from the right sidewall of the channel. Because the antenna pair is now closer to this sidewall than for the measurement position shown in Fig. 9.18b, the reflection from this surface will arrive earlier. For measurement locations within a horizontal interval that is over the bottom of the channel (Fig. 9.18d), multipathing will again occur with three reflections arising from three different ray paths. These are from the channel bottom as well as both its left and right sidewall. Continuing a rightward movement of the antenna will first produce a region of single reflections from the left sidewall, followed by reflections from the left sidewall and the horizontal interface to right of the channel, and finally, a horizontal line of single reflections from only the horizontal interface to the right of the channel. The synthetic radargram for the channel is shown in Fig. 9.18e with the channel boundary indicated by the superimposed gray line. In this synthetic data, the shallow horizontal interface to the left and right of the channel as well as the horizontal channel bottom appears as patterns of horizontal blips at two different times. The earlier arriving signals are associated with the horizontal interfaces to the left and right of the channel and, in the center of the radargram, the later arriving horizontal pattern is from channel bottom reflections. The sidewalls of the channels are manifested as an X pattern in the center.

9.2.3 More on Multiples

In the presentation of GPR measurements over a relic channel, it was shown that multipathing can occur. This effect is caused by reflections from different surfaces, where each of these reflections originates with different rays from the transmitting antenna. There is a difference between multipathing and multiples introduced in Sect. 9.1.2. Specifically, multiples originate with a single emitted ray from the transmitting antenna that reflects off of the same interface multiple times (Fig. 9.5).

The GPR interpretations considered in Sect, 9.2.2 are oversimplified in the sense that multiples are not considered. The simplest example of multiples in GPR measurements is the case of a single horizontal interface. The synthetic radargram for this situation is shown without the effects of multiples in Fig. 9,11. Multiples can occur when there is a single horizontal interface because there is a difference in wave speed between air, C_air, and near-surface soil. Figure 9.19a illustrates how multiples can occur for this situation. The ray emitted by the transmitting antenna is reflected from the horizontal interface, returning to the receiving antenna after a time t = 2d/c₁ where these rays are shown in black in Fig. 9,19a. The upwardly moving reflected ray strikes the interface between the soil (c₁) and the air where some of the energy is transmitted to the air and the remaining wave energy is downwardly reflected from the ground surface. The wave energy reflected from the ground surface strikes the horizontal interface between c₁ and c₂ where, again, some energy is transmitted downward through the interface and the remainder is reflected upward through layer c₁ where it is detected by the receiving antenna. This is the first multiple and it makes two round trips to a depth of d (the second round trip ray path is depicted as the dark gray dashed arrows) so that its travel time is t = 4d/c₁. Since some energy is lost from the reflection at the ground surface, the first multiple will be weaker than the original reflection. A second multiple will occur when the first multiple strikes the ground surface. The ray paths for this multiple are shown as the medium gray dashed arrows in Fig. 9.19a. This multiple makes three round trips to a depth of d so its total travel time is t = 6d/c₁. The energy in this reflection is less than that for the first multiple because some energy is lost as a result of the reflection at the horizontal interface between c₁ and a and the reflection at the ground surface. This means that this reflection will be weaker than that associated with the first multiple. The processes will continue with many multiples, each following the same ray path as the preceding multiple with an additional round trip to a depth d. These many multiples are represented by the double-headed dashed black arrow shown in Fig. 9.19a. The synthetic radargram for the horizontal interface including the first two multiples is shown in Fig. 9.19b. In comparing this radargram to the one without multiples (Fig. 9.11), it is clear that both represent the original reflection arriving at a time t = 2d/c₁ directly associated with the interface between c₁ and c₂. However, Fig. 9.19b has the added horizontal structure associated with multiples, where each successive reflection is time delayed by an amount t = 2d/c₁ with respect to the previous reflection and is also weaker than the previous reflection. Multiples, such as those shown in Fig. 9.19b can easily be misinterpreted as multiple horizontal interfaces (Fig. 9.13).

Figure 9.19. Illustration of (a) multiples occurring for a single horizontal interface, (b) a radargram showing the original reflection and the first two multiples, and (c) the ray paths for multiples in a vertical structure with two horizontal interfaces.

When multiple horizontal interfaces do actually exist, there can be many sources of multiples. As shown in Fig. 9.19c as the double-headed dashed arrows, multiples can arise from reflections trapped in layer c₁, as was the case for the single horizontal interface (Fig. 9.19a), and in layer c₂ as well as multiples associated with the composite c₁-c₂ layer. This will produce a far more complicated radargram than that for a single horizontal interface (Fig. 9.19b).

Multiples will not occur for a sloping interface (Fig. 9.12) because, as shown by the gray ray in Fig. 9.20a, the upwrardly moving reflected ray does strike the ground surface at normal incidence. Although there will be a downward reflection at this air-soil interface, this ray cannot strike the sloping surface and be reflected back to the receiving antenna.

Figure 9.20. Illustration of (a) the downwardly reflected ray at the ground surface associated with the upward reflection from a sloping interface and the possible multiple ray paths for a buried circle when the antenna pair is (b) not over the top of the circle and (c) directly over the top of the circle.

For a circle (Fig. 9.16), there can be two sources of multiple reflections. When the antenna pair is not directly over the top of the circle (Fig. 9.20b), the ray reflected from the upper surface of the circle does not strike ground surface at normal incidence. This is the same situation as the sloping interface (Fig. 9.20a) and, for the same reason, this cannot lead to multiples. As illustrated by the double-headed dashed arrows on Fig. 9.20b, multiples can arise from reflections within the circle. Here, there is normal incidence at both the upper and lower surfaces of the circle and this will support multiples, Multiples of this type originating within the circle will occur for all measurement locations; however, when the measurement is made directly over the top of the circle (Fig. 9.20c), the reflection from the upper surface of the circle is normally incident on the ground surface and, for only this particular measurement location, there will be an additional source of multiples.

9.3 Ground Penetrating Radar and Electromagnetic Induction

A considerable amount of information has been presented on GPR without consideration given to the basic nature of electromagnetic (radio) waves and the fundamental material properties that define electromagnetic wave speed. A convenient means to introduce these basics is through the relationship between ground penetrating radar and electromagnetic induction (EMI).

In the presentation of EMI (Chapter 7), the concept of time-varying magnetic fields was introduced and the manner that materials having different electrical conductivities respond to time-varying magnetic fields was exhaustively discussed. The presentation of the simplified concepts of EMI (Sect. 7.6) used an antenna exposed to radio waves as an analogy to EMI and, in this analogy, reference was made to the electric field. Radio waves are a time-varying electric field, much like a time-varying magnetic field and the fact that time-varying magnetic and electric fields are frequently inseparable creates an intimate relationship between GPR and EMI.

Figure 9.21. Illustration showing the amplitude of a time-varying electric field (solid line) and a time-varying magnetic field (dashed line) as a function of propagation distance. The time-varying magnetic field is perpendicular to the electric field and both are perpendicular to the direction of propagation.

The basic material property that is exploited in electromagnetic induction is the electrical conductivity, σ. As the electrical conductivity of a material exposed to a time-varying magnetic field increases, more of the energy of this field is lost to the formation of induced currents. For radio waves, changes in wave speed can result in reflection and refraction of these waves; however, wave speed is not a basic material property. Electrical conductivity will influence wave speed but this influence is secondary to the dielectric constant, ε (the Greek letter epsilon), which is also a basic material property. The dielectric constant is a measure of the energy required to cause a radio wave to propagate through a material relative to some reference material, usually air or a vacuum. Wave speed is inversely proportional to dielectric constant so that increasing the dielectric constant decreases the wave Speed. Taking the dielectric constant to be relative to air and representing the wave speed in air as c_air, the wave speed, c, of a material having dielectric constant, ε, is defined to be

where the √ symbol means the square root. The electromagnetic wave speed in air is 300 million meters per second and a typical value of the dielectric constant of soil is nine so that a representative radar wave speed in soil is

c_{s o i l} = \frac{300 m i l l i o n m / s}{\sqrt{9}} = \frac{300 m i l l i o n m / s}{3} = 100 m i l l i o n m / s

Table 9.1 provides values of dielectric constant and electromagnetic wave speed for a variety of materials.¹

Table 9.1. Typical values of dielectric constant and electromagnetic waves speed of commonly encountered materials in GPR.

material	dielectric constant	wave speed (billion m/s)
air	1	0.3
fresh water	80	0.033
dry sand	4	0.15
saturated sand	25	0.06
limestone	6	0.12
clay	25	0.06

Waves can be characterized by several numbers, including wavelength, λ, and period, r, or frequency, f (Sect. 6.1). Wavelength and frequency are related through the wave speed c by

and, from Equation 9.8, the dielectric constant can be introduced into the definition of wavelength as

This equation can be used to assess the relationship between GPR and EMI. For GPR effects, the wavelength represents a length scale and a similar length. The skin depth δ, was introduced (Sect. 7.7.1), where the skin depth characterized the distance a time-varying magnetic field extends from its source before most of its energy is consumed by the creation of induced currents. Time-varying magnetic and electric fields exist together and, for this reason, it possible for there to be both wave-like effects (reflection and refraction) and induction effects. While both effects can occur simultaneously, usually only one will dominate and the magnitude of the wave effects relative to the induction effects are characterized by the ratio of the skin depth to wavelength. Using Equations 7.6 and 9.9, this ratio can be expressed as

where σ_b and ε are the electrical conductivity and dielectric constant, respectively, of the host material. When the wavelength is small compared to the skin depth, the ratio is greater than one and wave effects will dominate, and, when the wavelength is much greater than the skin depth, the ratio is much less than one and induction will dominate.

If the skin depth and wavelength are comparable, both wave effects and induction will be of similar magnitude. It clear from Equation 9.10 that the ratio of wave to induction effects depends on the ratio of dielectric constant to electrical conductivity and, as this ratio increases, wave effects can become dominant. The wave frequency, f, also appears in this equation and, with increasing frequency, wave-like effects will become more important. A practical distinction between GPR and EMI is their operating frequencies. Electromagnetic induction instruments are typically limited to frequencies not much greater than 20 kHz (20,000 cycles per second, Sect. 7.10.1). More will be presented about GPR operating frequencies in Sects. 9.4, 9.5, and 9.6 but, for comparative purposes, assume that a typical value for GPR operation is 100 MHz (megahertz, millions of cycles per second, or 1000 kHz) and a typical operating frequency for EMI is 10 kHz. Table 9.2 presents the dielectric constant and electrical conductivity for the materials given in Table 9.1 along with the ratio defined by Equation 9.10 at both 10 kHz and 100 MHz, the assumed operating frequencies for EMI and GPR, respectively.

Table 9.2. Typical values of dielectric constant, electrical conductivity, and the ratio of skin depth to wavelength at two frequencies.

material	dielectric constant	electrical conductivity Siemens per meter (S/m)	skin depth/wavelength ratio
material	dielectric constant	electrical conductivity Siemens per meter (S/m)	at 10 kHz	at 100 MHz
air	1	0	infinite	infinite
fresh water	80	0.0005	0.12	12
dry sand	4	0.00001	0.19	19
saturated sand	25	0.001	0.05	5
limestone	6	0.001	0.02	2
clay	25	1	0.001	0.1

It is clear from this table that, for the materials considered, induction effects will dominate at the low frequency and wave effects will dominate at the high frequency. This fact allows EMI and GPR to be considered as independent techniques. An exception to this is clay where, even at the higher frequency, the ratio is less than one. The issue of applying GPR in clay will be addressed in Sect. 9.7.

9.4 Realistic Radargrams

Figure 9.22 displays radargrams for a horizontal interface, a sloping interface, and a circle. These are identical to the corresponding radargrams presented in Figs. 9.11, 9.12, and 9.16 except that more traces and the effects of geometric spreading are included in Fig. 9.22.

Figure 9.22. Synthetic radargrams that include geometric spreading for (a) a horizontal interface, (b) a sloping interface, and (c) a circle.

When a time-varying electrical signal moves through electronic components, not all frequencies pass through equally. The amplitudes of some of the frequencies are reduced or completely lost. This is particularly true of GPR antennas. The range of frequencies that can pass through a system is referred to as the system's bandwidth. If a signal begins as a pulse (Fig. 6.27c), some frequency content will be lost within the various electronic components. If the bandwidth of the system is quite large, meaning many frequencies can pass through it unabated, the output may remain pulse-like. If the system bandwidth is reduced, the output signal may appear as that shown in Fig. 6.27b or, for even lower bandwidth, Fig. 6.27a. Introducing bandwidth along with geometric spreading into the radargrams for the horizontal interface, sloping interface, and circle yields the radargrams shown in Fig. 9.23.

Figure 9.23. Synthetic radargrams that include geometric spreading and bandwidth for (a) a horizontal interface, (b) a sloping interface, and (c) a circle.

Another mechanism through which wave amplitude is lost is the conversion of wave energy to induced currents. Table 9.2 presented the ratio of skin depth to wavelength and the competing mechanisms of induction and wave effects were differentiated based on this ratio. Even when this ratio is large and wave effects dominate, there will still be some conversion of wave energy to induced currents, though this loss can be small. The skin depth is a measure of the rate at which wave energy is lost to the creation of induced currents as it propagates. A little less than half of the wave energy is lost to induced currents over a propagation distance of one skin depth. As defined by Equation 7.6, the skin depth is inversely proportional to the frequency which implies that the higher the frequency the shorter the skin depth. This frequency dependence means that more wave energy is lost to induced currents at higher frequencies so that this loss of energy serves to reduce the bandwidth. To illustrate this loss of bandwidth, Table 9.3 presents the percentage of the original wave amplitude remaining after propagating distances of 1 m and 5 m for frequencies of 100 MHz and 500 MHz. Since the skin depth depends on electrical conductivity, materials with three different electrical conductivities are considered.

Table 9.3. Percentage of amplitude remaining for waves of two different frequencies each propagating 1 m and 5 m.

material	100 MHz		500 MHz
	1 m	5 m	1 m	5 m
dry sand	97%	84%	92%	68%
limestone	70%	17%	46%	2%
clay	37%	1%	13%	0%

Table 9.3 can be interpreted within the context of bandwidth by first considering wave propagation in dry sand. For a propagation over a distance of 1 m, there is very little amplitude lost at 100 MHz (3%) or 500 MHz (8%) so it can be concluded that almost all of the wave amplitude at all frequencies remains after the wave propagates 1 m and, in this case, loss of bandwidth is negligible. For a 5 m propagation distance in dry sand, there is a 16% amplitude loss at the low frequency (100 MHz) and a 32% amplitude loss at the high frequency (500 MHz) leading to bandwidth reduction that can be considered slight. Applying the same type of analysis to the limestone, it can be concluded that loss of bandwidth is moderate at a 1 m propagation distance and large for a 5 m propagation distance. Bandwidth limitations are most pronounced for propagation in clay. As indicated by Table 9.3, 63% of the low frequency amplitude and 87% of the high frequency amplitude is lost for aim propagation distance. Almost all of the amplitude is lost in clay for a 5 m propagation distance.

For radar measurements, the appropriate propagation distance is twice the distance from the antenna pair to the reflecting surface because the wave must travel from the transmitting antenna to this surface and then back to the receiving antenna. When considering reflections from a horizontal interface, the two propagation distances, 1 m and 5 m, presented in Table 9.3 correspond to interface depths of 50 cm and 2.5 m, respectively. To illustrate the depth-dependent bandwidth loss associated with conversion of wave energy to induced currents, Fig. 9.24 presents synthetic radargrams for a shallow and deep horizontal interface where the deeper interface (Fig. 9.24b) exhibits a smaller bandwidth than the shallower interface (Fig. 9.24a).

Figure 9.24. Synthetic radargrams that include geometric spreading and bandwidth for a horizontal interface at a depth of (a) 50 cm (b) 1.5 m.

9.4.3 Rayleigh Scattering

There is a mechanism by which wave amplitude is lost in addition to geometric spreading (Sect. 9.4.1) and conversion to induced currents (Sect. 9.4.2). This mechanism is Rayleigh scattering, and it was introduced in Sect. 6.3 because of its role in ground penetrating radar. Soils are composed of individual particles having a specific size and spacing. When Rayleigh scattering occurs, incident wave energy can experience multiple scattering from many particles, such that incident rays in one predominant direction can be redirected so there is no longer a preferred or dominant direction of propagation. The implication of Rayleigh scattering for GPR is that downward incident wave energy is lost through scattering to energy in rays that are no longer downward. The further this incident wave energy must propagate through the scattering material, the more downward energy is lost. When this occurs, the energy reaching a reflecting object is greatly reduced and the energy that does reach the reflector is scattered during its upward propagation, so little or no reflected wave energy reaches the receiving antenna.

Rayleigh scattering will only occur for certain particle sizes and spacings relative to the wavelength. Since GPR antenna have some bandwidth (Sect. 9.4.2) and an associated range of wavelengths, there can always be some Rayleigh scattering. The magnitude of amplitude lost through scattering can vary from minimal to severe depending on the antenna bandwidth and the nature of the host geologic material. In general, Rayleigh scattering has the most profound effect when the geologic material is coarse-grained, such as gravel.

9.4.4 Resolution and Bandwidth

There are a number of ways to characterize the resolution of buried objects using GPR. Here, the implication of bandwidth in resolving buried features will be based on the capacity to resolve a thin layer. Specifically, the layer is bounded above and below by horizontal interfaces. This subsurface structure would be the layer with a wave speed of c₂ in Fig. 9.13a. Figure 9.25a and 9.25b show Synthetic radargrams for a layer thickness of 25 cm for a large and small bandwidth. When the bandwidth is large (Fig. 9.25a), each trace clearly exhibits reflections from the top and bottom of the layer and each of these reflections is quite close in form to a pulse. When the bandwidth is reduced (Fig. 9.25b), the upper and lower interfaces can still be distinguished. However, the waveform is no longer pulse-like and residual oscillations are apparent. When the layer thickness is reduced to 10 cm, both interfaces are clearly distinguishable in the large bandwidth case (Fig. 9.25c). However, for the reduced bandwidth (Fig. 9.25d), the reflections from the two interfaces have blurred together into a single reflection and, for this bandwidth, the thin layer cannot be resolved.

As discussed in Sect. 9.4.2, the bandwidth of GPR antennas depends on their center-frequency. While it might be possible to resolve a thin layer by selecting an appropriately high center-frequency and thereby ensuring an adequate bandwidth, it must also be recalled that there will be a loss of bandwidth associated with induction effects. This loss of bandwidth will depend on both the electrical conductivity of the host soil and the depth of the reflecting surface. A thin layer or object may be resolved using 400 MHz in dry sand, provided that this feature is shallow. However, such resolution may be impossible in more electrically conductive materials, such as limestone or clay.

Figure 9.25. Synthetic radargrams for a 25 cm thick layer with (a) a large bandwidth and (b) a small bandwidth and a 10 cm thick layer with (c) a large bandwidth and (d) a small bandwidth.

9.4.5 Direct Arrivals

For the purposes of interpretation, it can be assumed that the transmitting and receiving GPR antennas are co-located. Since two objects cannot occupy the same space, the antenna pair must be separated by a short distance and this introduces direct arrivals into radargrams. Figure 9.26 shows the transmitting and receiving antennas horizontally separated along with three ray paths. One that has been considered before is the ray from the transmitting antenna to a circular reflector and the reflected ray from the reflector to the receiving antenna. This figure also shows two rays going directly from the transmitting antenna to the receiving antenna. Because GPR antennas can emit rays in all directions, there can be a ray that travels through the air directly from the transmitting antenna to the receiving antenna. If the antenna pair is in contact with the ground, there can be a simliar ray path between the two antennas that propagates through the ground. Even if the antenna pair is slightly elevated above the ground, there can still be a direct ground-propagated ray path. This occurs as a result of refraction (Sect. 9.1.1), where a ray from the transmitting antenna is in a direction in the air such that it will refract to become horizontal upon passing into the ground. This is known as critical refraction. A similar but opposite refraction will occur at the receiving antenna where the horizontal ray in the ground is refracted upward into the air.

Figure 9.26. Illustration of a reflected ray path and the direct ray paths through the ground and the air.

9.5 GPR Instruments

The major elements of a ground penetrating radar system are shown in Fig. 9.27. The physical interface to the subsurface is through the transmitting and receiving antennas. The entire system is controlled by a computer and the operational sequence is as follows:

Figure 9.27. Illustration of the components and operation of a ground penetrating radar system.

Spatial sampling is not a significant concern when dealing with simple, continuous, infinite reflecting surfaces such as a horizontal interface (Fig. 9.9a) or an inclined interface (Fig. 9.12a). This becomes clear for the horizontal interface by comparing Figs. 9.11 a and 9.22a. Both of these figures display radargrams for a horizontal interface with the only difference being the number of displayed traces, 9 and 64 in Figs. 9.11a and 9.22a, respectively. If it is assumed that both of these radargrams are based on antenna positions uniformly spaced along lines of the same length, for example 8 m, the spatial sampling employed would be 1 m for Fig. 9.11a and about 13 cm for Fig. 9.22a. Thus, the only difference between the radargrams is the spatial sampling. For both the fine spatial sampling (Fig. 9.22a) and the coarse spatial sampling (Fig. 9.11a), the horizontal interface is clearly identifiable and it can be concluded that spatial sampling is not an issue in resolving this feature. By comparing Figs. 9.12b and 9.22b, the same can be concluded for a sloping interface.

Figure 9.28. To illustrate the implications of spatial sampling, (a) a series of four buried flat plates is used and (b) a synthetic radargram where a fine spatial sampling is used to adequately resolve this structure.

With this spatial sampling, each plate can be identified as the gaps that occur between the plates. Figure 9.29 presents the same configuration of buried plates with two coarse spatial sampling regimes as indicated by the positions of the antenna pair. In both spatial sampling procedures shown in the figure, the spatial sampling is the same in the sense that the spacing between adjacent measurement positions is the same. For the measurement locations shown in Fig. 9.29a, the antenna pair is consistently positioned over the gaps between the plates and, for these measurement positions, no reflections from any of the plates will reach the receiving antenna. Thus, with this spatial sampling, no reflections will appear in the radargram and it will appear that there are no buried objects. A similar situation occurs in Fig. 9.29b, but here the antenna pair is always located over one of the plates. For each measurement position, a reflection from a plate will be recorded. However, the gaps between the plates will not be detected and the radargram will appear as that for a horizontal interface (Fig. 9.22a).

Both measurement configurations shown in Fig. 9.29 have inadequate spatial sampling since both of these fail to resolve both the plates and the gaps between the plates. The buried structure illustrated in this figure has two horizontal length scales—the dimension of the plates and the horizontal distance between adjacent plates (the gaps). If it assumed that the gaps are broader than the plates, it is possible that the plates will not appear in the radargram. Similarly, if the plates are broader than the gaps between them, it is possible that the gaps will not be resolved and the radargram will incorrectly reveal a subsurface structure that is identical to a horizontal interface. Based on this analysis, it can be concluded that proper spatial sampling depends on the horizontal dimensions of buried features and, for these features to be resolved, it is necessary that a spatial sampling be established so that the distance between adjacent measurement locations is smaller than the smallest horizontal dimension of the subsurface structure.

Figure 9.29. Two examples of spatial under sampling (a) where measurement positions are consistently over gaps between buried plates and (b) where measurement positions are consistently over the plates.

9.6.2 Temporal Sampling

Temporal is a word that is used to indicate that change in some quantity occurs over time. It is known that waves change over both time and space (Sect. 6.1) and here temporal sampling refers to the manner in which GPR data is acquired over time.

In the simple discussion of radargrams (Sect. 9.2.2), a pulse was used to represent the recorded waveform. Bandwidth was then introduced to present the more realistic waveforms typical of GPR measurements (Sect. 9.4.2). As a simple introduction to temporal sampling, a pulse will first be considered and then more complicated issues associated with the dependence of temporal sampling on bandwidth will be discussed.

In order to resolve a pulse in time-based measurements, these measurements must be made over sufficiently small intervals in time such that the pulse emitted and subsequently reflected off some object can be detected. Figure 9.30a shows a pulse as a function of time.

Figure 9.30. Illustration of the effect of inadequate temporal sampling showing (a) sampling times relative to the arrival of a pulse, (b) a radargram for a horizontal interface, and (c) a radargram for a sloping interface.

Figure 9.31. Illustration of the effects of sampling a wave once per period (above) and twice per period (below).

From the above discussion, it is clear that time sampling is quite important to wave-based geophysical measurements. This raises the question of how frequently samples must be acquired. This question is difficult to answer for a pulse, because the time duration of a pulse has not been established. If it had, the answer would be some time interval shorter than the pulse duration. The question is not relevant because real data can be characterized by a bandwidth that limits the frequency content. Thus, a real waveform is characterized by some superposition of waves of various frequencies and temporal sampling can be addressed by considering how a wave of a particular frequency must be sampled. Figure 9.31 displays plots of amplitude versus time for a wave having a particular frequency. The plot on the upper left shows two •'s indicating two time samples of this wave. The time interval shown here is one wave period and these particular sample times have been selected so as to coincide with adjacent wave peaks. The plot on the upper right displays recorded data for this wave as sampled once per period. Sampling once per period yields a sequence of time samples that do not change with time and thus display no wave-like character. It is clear that such a temporal sampling is inadequate to resolve the wave and can be described as tinder sampling. The plot on the lower right is the sampling of the same wave at half-period time intervals. This acquired data corresponds to time sampling at the crests and troughs as indicated on the lower left of Fig. 9.31. At this sampling rate, the oscillatory character of the sampled wave is recovered, but the time-sampled data has a saw-tooth appearance. For this half-period sampling, the wave is marginally resolved. In fact, there is a pathological case for which half-period sampling is inadequate. The amplitude of the wave assumes a zero-value twice per period. Thus, it is possible, either intentionally or unintentionally, to sample twice per period and record nothing but zeros. It is therefore important to temporally sample more than twice per period. Such sampling is referred to as over sampling.

The waveforms characteristic of GPR data have contributions from many frequencies within some bandwidth. It not necessary to consider the temporal sampling at every one of the frequencies but only the highest frequency within the bandwidth. This is illustrated by considering a waveform composed of two distinct frequencies. The sum of two waves of differing frequency is plotted in the upper left of Fig. 9.32.

Figure 9.32. Illustration of the effect of under sampling a wave having two frequency components.

9.6.4 Radargram Display

Thus far, radargrams have been displayed as a sequence of vertical line plots where each plot in the sequence is horizontally offset from the adjacent line plot to represent the horizontal movement of the antenna pair. This type of GPR display is known as a wiggle trace and Fig. 9.23 presents three examples of radargrams displayed as wiggle traces. There is an alternative method for displaying radargrams that uses false-color or gray-scale plotting (Sect. 2.9.2).

A line plot of a trace is shown on the left side of Fig. 9.33 and a comparable display of this trace is given on the right side of this figure. Here, the amplitude at each point in time on the trace is assigned a shade of gray based on the amplitude where the largest positive number is black, the most negative number is white, and intermediate amplitudes are assigned various shades of gray.

Figure 9.33. A trace displayed as a line plot (left) and with the relative amplitudes assigned shades of gray (right).

The wiggle trace radargram is constructed by assembling each trace, displayed as line plot, beside the adjacent trace. Similarly, an alternative display can be constructed by displaying traces as the vertical gray-scale (or false-color) strips side-by-side. This manner of radargram display is known as a pixel fill. Figure 9.34 is a synthetic radargram presented as a gray-scale pixel fill. This particular example is the GPR response of a buried circle and is identical to the wiggle trace display shown in Fig. 9.23c. Depending on the manufacturer, GPR instruments will display radargrams as wiggle trace, pixel fill, or offer the operator the choice of either type of display.

Figure 9.34. A synthetic radargram of the response of a buried circular object displayed as a gray-scale pixel fill.

Loss of wave amplitude can occur through geometric spreading or attenuation as a result of wave energy converted to induced currents. In either case, amplitude loss increases as the propagation distance increases. Since waves that travel greater distances travel for longer times, the amplitude of radar waves are generally weaker at longer times. This can make deeper features more difficult to identify in radargrams. To compensate for this loss of amplitude, gain can be applied to GPR data. Gain simply means a recorded signal is multiplied by a number greater than one. Since weak GPR signals are usually associated with longer travel times, the gain typically applied to GPR data increases with time, e.g, a gain of 10 at 5 ns, 20 at 10 ns, and so on. Figure 9.35a shows a trace that is composed of the reflection from two features where one reflector is deeper and, hence, weaker than the other. The shallow reflection occurs at a time of about 10 ns and the deeper and much weaker reflection occurs at about 40 ns. The deeper reflector can be strengthened by applying a gain that increases with time (Fig. 9.35b). There is no need for gain with the shallow reflector so that a constant gain of one (no gain) is used until about 30 ns with the gain increasing with time thereafter. The trace resulting from applying this gain to the trace in Fig. 9,35b is shown in Fig. 9.35c and it is evident that the response from the deeper reflector is now substantially stronger. It is also evident from the trace with gam that the gain is indiscriminate in that it increases the effect of unwanted components in the signal, the residual oscillations from the deeper reflector, as well as those that are desired.

Figure 9.35. Illustration of (a) a trace showing the response from a shallow and deep reflector, (b) a time-dependent gain, and (c) the trace with the gain applied.

If it is assumed that the reflections shown in Fig. 9.35 are associated with two horizontal interfaces, the radargram for this structure is shown with and without an applied gain in Figs. 9.36a and 9.36b, respectively. The gain has succeeded in making the deeper horizontal interface evident where it was absent without the gain.

Figure 9.36. Synthetic radargram of two horizontal interfaces (a) without and (b) with a time-dependent gain.

The software that comes with GPR instruments allows various forms of user-selected gains and, in general, the default settings for the radargram display includes some gain.

9.7 Limitations and Complications of Ground Penetrating Radar

Ground penetrating radar can be limited by the size and depth of features of interest. Attenuation of the radar wave is controlled by the electrical conductivity of the host material and, if the conductivity is too large, sufficiently high frequencies to resolve a given feature may not penetrate to the necessary depth. This frequently is the case in clay soils. For an object to be detected using GPR, it must reflect the radar wave. Reflections can only occur when there is a change in wave speed. A large change in wave speed will produce a strong reflection and a small change in wave speed will cause a weak reflection. Even when a GPR application is not limited by attenuation, it may be impossible to detect a buried object because it does not present a sufficiently high contrast in wave speed with respect to its surroundings.

Complications can arise in GPR because the transmitting antenna emits waves in all directions, not just downward. Similarly, the receiving antenna will detect reflected waves that arrive from sources other than those that are buried. Misinterpretation of radargrams can occur when reflections result from features on or above the ground surface. If it assumed that all features manifested in a radargram are associated with buried features, objects on or above the ground surface will be interpreted as buried. Figure 9.37a illustrates a GPR data acquisition where the antenna pair is moved from left to right along the ground surface over a buried circular object. Also present is an overhead wire and a wall at the right side of the illustration. The synthetic radargram that includes all three reflectors is shown in Fig. 9.37b. As annotated, the two surface features and the buried feature all appear in the radargram. The wire and the buried circle appear as hyperbolas and the wall appears like a sloping interface. The reason the wall has this manifestation is that, as the antenna pair moves from right to left, it gets progressively closer to the wall. As the distance to the wall decreases, the two-way travel time decreases proportionally. Without any knowledge of the surface features, this radargram would be misinterpreted. Therefore, it is important when acquiring GPR data to note the locations of all features on or above the ground surface that could appear in the acquired data.

Figure 9.37. Illustration of the effects of surface features in GPR data where (a) a buried circular object, an overhead wire, and a wall are present and (b) the resulting radargram.

To minimize the effects of surface structures, some shielded GPR antennas are available. These antennas are contained in a housing surrounded on all sides but the bottom with a radar wave absorbing material. This material inhibits the propagation of radar waves in all but the downward direction and, in so doing, removes or minimizes the potential for a radargram to be contaminated with surface features. The amount of radar absorbing material that is needed to shield an antenna depends on frequency, with more shielding being required for lower frequencies. Shielded low frequency antennas become prohibitively large, so that shielded antennas are typically used only with a high center frequency. Because almost no wave energy is emitted horizontally from a shielded antenna, there will be no air-propagated direct arrival (Sect. 9.26) from a shielded antenna. However, because of critical refraction, there will still be ground-propagated direct arrivals.

Figure 9.38. (a) The location of two GPR acquisition lines and a buried sphere, (b) a synthetic radargram for Line 1, and (c) a synthetic radargram for Line 2.

A final complication that can arise in the interpretation of GPR data is the three-dimensionality of a subsurface structure. It has been assumed to this point that GPR data acquired over a line 'samples' the structure below this line. Because antennas (even those that are shielded) emit waves in many different directions, it is possible to receive reflections from features that do not occur directly below the measurement line. As an example, consider the case of a buried sphere, rather than a circle. Figure 9.37a shows a buried sphere and two GPR lines, one that passes directly over the top of the center of the sphere (Line 1) and another line that is parallel to the first that does not pass over the sphere (Line 2). The sphere will appear as a hyperbola in both radar lines. However, the peak of the hyperbola in Line 1 (Fig. 9.38b) will appear at a shorter time than that for Line 2 (Fig. 9.38c) because this line passes closer to the sphere. These two lines might be interpreted as two buried objects, one deeper than the other, when, in fact, only a single buried object exists. If an excavation is undertaken at the location of the hyperbola peak presented in Line 1, no buried object will be revealed. It is important that GPR data be interpreted with an understanding that all reflecting objects can have some three-dimensional structure and that an object that appears in GPR data may not actually be buried directly below the acquisition line.

9.8 Integrated Case Studies

This section continues with interpretation of data from multiple geophysical techniques at three adjacent areas where utility tunnels are located (Fig. 2.54). Previously, gravity (Sect. 4.13), magnetometry (Sect. 7.12), and EMI (Sect. 7.12) data from these sites has been introduced. Here, acquired GPR data is presented and interpreted in light of the understanding of subsurface conditions derived from the other methods considered.

At each of the three sites, GPR data has been acquired over multiple lines using 200 MHz center-frequency antennas. These antennas are moved in unison, acquiring a trace at 10 cm intervals (the spatial sampling) along each line. At each antenna position, 217 time samples were acquired at time intervals of 0.315 ns. This provided a time window of about 70 ns and a sampling frequency (defined to be one divided by the sampling interval) of about 3000 MHz. Taking the wave speed to be 0.1 m/ns, the travel distance at this speed over the travel time of 70 ns is 7 m. Since this is a two-way travel distance (from the antenna pair to a reflector and back), the maximum object depth that can be detected for this time window is 3.5 m.

The maximum frequency output by an antenna is about twice its center frequency so that the highest frequency from a 200 MHz center-frequency antenna is approximately 400 MHz. The temporal sampling of 3000 MHz is almost ten times higher than the minimum required for 200 MHz center-frequency antennas. The reason such a fine temporal sampling was used here was to produce a presentable radargram. Had temporal sampling been at 400 MHz, only about 30 points would be needed over the 70 ns time window. Such a small number of points would not yield a smooth plotted trace.

9.8.1 Area 1

Three lines of GPR data were acquired in Area 1 (Fig. 9.39). All of these lines are parallel and all extend from north to south.

Figure 9.39. Map of Area 1 showing the locations of GPR lines with the tunnel shown in white.

Because all the GPR lines have identical orientations relative to the tunnel, all lines produced nearly identical radargrams. For this reason, only Line 2 (Fig. 9.39) is considered here. An annotated gray-scale pixel fill radargram for Line 2 is presented in Fig. 9.40. At a travel time of about 18 ns, a horizontal feature appears that, apart from an interruption in the center, extends across the entire radar line. This is characteristic of a horizontal interface so it is identified as a layer in the radargram. For a typical wave speed of 0.1 m/ns, an 18 ns travel time equates to a depth to this interface of 0.9 m. The interface between two soil layers is absent in the center of the radargram where, instead, there are a number of isolated reflections. From Fig. 9.39, it is clear that this is the region of the utility tunnel and it should be expected that any soil interfaces would be destroyed by the tunnel construction. The earliest arrival occurring within the tunnel region is the nearly flat reflector at a time of 5 ns. This is the top of the tunnel at a depth of about 25 cm. Below this more isolated reflectors are present and these are likely to be utilities (pipes, wire, etc.) within the tunnel. A fairly broad horizontal reflection occurs at 40 ns. This is probably the bottom of the tunnel at a depth of 2 m. Below this, there appears to be a repetition of the pattern above. This is consistent with the expectation of multiples of the tunnel features and are so identified on the radargram. No multiples of the layer are evident and this is because the layer appears as a weaker reflector than the tunnel and, as such, its multiples will be even weaker. No gain (Sect. 9.6.4) was applied to the radargram shown in Fig. 9.40. However, had gain been applied, multiples of the horizontal interface would be present.

Figure 9.40. Annotated radargram of the GPR data acquired along Line 2, Area 1 (Fig. 9.39).

The difference between GPR and the methods previously considered is that depth information is easily derived from this technique. The subsurface structure below the radar line shown in Fig. 9.40 can be identified as a soil interface at a depth of 90 cm and a tunnel extending over a depth interval from 25 cm to 2 m. While the horizontal tunnel location could be identified by gravity, magnetometry, and EMI, none of these methods provided the vertical information offered by GPR.

9.8.2 Area 2

Four GPR lines were employed at Area 2. These lines pass completely around the perimeter of the survey region (Fig. 9.41). The reason for this line selection is that it is anticipated that a utility tunnel could extend through this area and, therefore, should pass through two of the vertical cross-sections defined by the perimeter GPR lines. Furthermore, should there be any 'T's' in the tunnel, each would also pass through one of the perimeter GPR cross-sections.

Figure 9.41. Map of Area 2 showing the locations of GPR lines with the tunnels shown in white.

In reviewing the GPR data from Area 2, it should be remembered that, as shown in Fig. 9.41, GPR Lines 1 and 3 are parallel but have opposite directions, in other words, Line 1 extends southward beginning at the northern boundary of Area 2 while Line 3 extends northward from the southern boundary. A similar situation exists for Lines 2 and 4.

Figure 9.42. Annotated radargrams of the GPR data acquired along the four lines in Area 2 (Fig. 9.41).

Radargrams for all four GPR lines are presented in Fig. 9.42. Features that are almost identical to the tunnel presented in Fig. 9.40 appear on GPR Lines 1 and 3. Only the reflection associated with the top of the tunnel is annotated to highlight the location of these reflections. However, both exhibit reflections from utilities within the tunnel, a reflection from the bottom of the tunnel, and multiples as annotated in Fig. 9.40. The tunnel evident in the Line 1 radargram occurs at a distance of about 5 m along the line and corresponds exactly to the tunnel location shown in white on Fig. 9.41. The tunnel that appears on the Line 3 radargram appears at a distance of 9 m along this line. Since the line is about 14 m long and antenna movement for this line is in the opposite direction to that of Line 1, the tunnel in this crosssection is at a distance of 5 m south of the northern boundary. The radargrams for Lines 1 and 3 suggest that a tunnel extends in an east-west direction across Area 2 directly under the sidewalk. This is the precise location of this tunnel (Fig. 9.41).

Line 1 also shows a horizontal reflector of finite extent annotated as the bottom of the sidewalk. There is an interface between the concrete sidewalk and the soil below and, as such, there can be a reflection from this interface. Along this line, the sidewalk is wider than the tunnel on the southern side and this is why the concrete-soil interface appears in the radargram. For GPR Line 3 and the radargram presented for Area 1 (Fig. 9.40), the sidewalk does not extend far beyond the lateral extent of the tunnel, if at all. The bottom of the sidewalk does not appear in these radargrams either because the reflections from the bottom of the sidewalk and the top of the tunnel 'blur' together (Sect. 9.4.4) or the sidewalk is part of the tunnel roof.

Two reflecting features appear in the Line 2 radargam. As annotated, one of these is associated with a sidewalk that is crossed by the radar line at its western end. The second reflector is assumed to be a tunnel that provides utility services to the building south of the Area 2 study region (Fig. 9.41). This feature is subtle, difficult to identify, does not appear like the tunnel manifested in Lines 1 and 3, and probably could not be identified as a tunnel in the absence of information at this site from gravity (Sect. 2.13), magnetometry (Sect. 7.12), and EMI (Sect. 7.12). This tunnel is likely much smaller than the east-west tunnel, which is a main utility tunnel, and is a 'feeder' tunnel to convey utilities from the main tunnel to the building on the south side of Area 2 (Fig. 9.41). While the utilities within the main tunnel might consist of large diameter pipes and bundles of wires, the smaller tunnel probably has smaller diameter pipes and wire bundles that are too small to produce strong reflections. It is also possible that the feeder tunnel is not really a tunnel, but rather a pipe only large enough to contain the utilities necessary for the building it is supplying. Therefore, it could be composed of a different material that has a wave speed only slightly different from the surrounding soil. In this case, the reflection coefficient (Sect. 9.1.2) would be small and, as a result, there would be little reflected wave energy.

There are no reflectors evident in the Line 4 radargram. The two horizontal bands represent the direct transmitted waves that propagate through the air and soil from transmitting to receiving antennas (Sect. 9.26).

9.8.3 Area 3

The GPR line configuration at Area 3 (Fig. 9.43) is the same as that employed at Area 2, namely, four lines around the perimeter of the study region. The motivation for this line placement is, as in Area 2, to intercept tunnels as they pass through the area boundaries.

Figure 9.43. Map of Area 3 showing the locations of GPR lines with the tunnels shown in white.

Figure 9.44. Annotated radargrams of the GPR data acquired along the four lines in Area 3 (Fig. 9.43).

There are several other differences between the radargrams at Areas 2 and 3. The interface between two soil layers that was evident at Area 1 (Fig. 9.40) is absent in Area 2 (Fig. 9.42) but is present in Area 3 (Fig. 9.44). Also, there are multiple reflections from the bottoms of the sidewalks at Area 3 that are absent at Area 2. These differences can be explained by the fact that GPR measurements were made at different times at all three areas. It is likely that soil moisture was higher as result of recent rain at the time of the Area 2 data acquisition. An increase in soil moisture will increase the soil's electrical conductivity which, in turn, will increase the attenuation of radar waves (Sect. 9.4.2). Since concrete is porous, the moisture content of the sidewalks could also increase following rain. Because the soil interface shown in Figs. 9.40 and 9.44 is deeper than the top of the tunnel, radar waves must travel a greater round trip distance to reach this interface and, in so doing, experience greater attenuation. Multiple reflections, by definition, travel multiple round trips between the measurement point and the reflector and, therefore, there will be progressive amplitude loss through attenuation with each successive multiple. It is possible that the weak reflection manifested by the feeder tunnel in Area 2 (Fig. 9.42, Line 2) is a result of attenuation. This is unlikely because the tunnel is quite shallow and once the wave passes through the concrete and into the tunnel, it will travel through the air within the tunnel unattenuated. One final possibility is that the ground was so wet that the tunnel became water-filled in which case there could be substantial attenuation within the tunnel such that there could be no detectable reflections from features within the tunnel.

1. Sensors & Software pulseEKKO 1000 Users Guide, Version 1.1

9 Ground Penetrating Radar: A True Wave-Based Technique