Fabio Giannino - Electromagnetic Methods in Geophysics

Table 2.1.1 Values of the relative dielectric constant ε r, electrical conductivity σ, electromagnetic‐wave velocity, and attenuation in some geophysical materials (Davis and Annan, 1989. With permission of John Wiley & Sons).

Table 2.1.2 Wavelength values λ as a function of the frequency at several electromagnetic‐wave velocities of propagation (From Leucci, 2015).

The electromagnetic waves transmitted by a standard antenna are irradiated through the ground in a generally elongated elliptical cone. The radiation lobe is generated by a horizontal dipole antenna, to which some protection elements are added (often metallic foils) which reduce the emitted radiation upwards (shielding). When a dipole antenna is placed in the air, the path of the radiation is approximately perpendicular to the antenna axis. When instead it is placed in contact or near the ground and/or the surface of the investigated materials, there is a change in the shape of the radiation lobes due to the coupling with the ground.

Variation of both the shape and the lobe directivity also occurs at the variation of h/λ, where h is the height from the ground of the antenna and λ is the wavelength of the pulse in the first medium (air).

The radiation cone (related to the first Fresnel zone ) that intercepts a horizontal flat surface illuminates an ellipse‐shaped area with the major axis parallel to the antenna’s trailing direction (Annan et al., 1991). The radiation lobe in the subsoil enables “ looking ” not only directly under the antenna but also in front, back, and sides as the antenna travels along the ground. This is known as horizontal resolution (Leucci, 2019). Two reflecting points separated by a distance less than the first Fresnel zone radius ® are considered indistinguishable as observed from the earth’s surface. The first Fresnel zone radius is given by the following:

(2.1.23)

and, in addition to velocity and frequency, is also depth dependent. Since the Fresnel zone generally increases with depth, the spatial resolution also deteriorates with depth.

Figure 2.1.7 Elliptical cone of GPR penetration into the ground.

In a simple way the angle of the cone is defined by the relative dielectric constant of the material traversed by the electromagnetic waves and by the frequency of the transmitter antenna. An equation that can be used to estimate the width of the transmission beam at various depths (the footprint) is (Conyers and Goodman, 1997):

(2.1.24)

where A is the approximate dimensions of the radius of the footprint, λ is the wavelength of the electromagnetic impulse, D is the depth at which the reflecting object is located, and ε ris the relative dielectric constant of the crossed medium ( Figure 2.1.7).

Among other constraints (Conyers and Goodman, 1997), in a GPR survey, the central frequency of the antenna is chosen to obtain a viable compromise between the desired penetration depth and vertical resolution. Moreover, the lateral resolution is important in planning the acquisition geometry and in particular, the spatial sampling along the survey line (inline spacing) and the distance between consecutive lines (crossline spacing). The latter requirement is seldom fulfilled due to time and positioning problems.

1 Annan, P.A., Cosway, W.S., and Redman, J.D. (1991), Water table detection with ground penetrating radar Soc. Exploration Geophysicists Ann. Meeting, Houston, TX, USA Expanded Abstracts, 494–496.

2 Conyers, L.B. (2004). Ground‐Penetrating Radar for Archaeology, Alta Mira Press, Walnut Creek, CA.

3 Conyers, L.B. (2013). Ground‐Penetrating Radar for Archaeology, 3rd Edition. Alta Mira Press. 258 pp.

4 Conyers, L.B. and Goodman, D. (1997). Ground Penetrating Radar: An Introduction for Archaeologists, Alta Mira Press, Walnut Creek, CA.

5 Campana, S. and Piro, S. (2008). Seeing the Unseen. Geophysics and Landscape Archaeology Geophysics and Landscape Archaeology. Taylor & Francis.

6 Davis, J.L. and Annan, A.P. (1989). Ground‐penetrating radar for high resolution mapping of soil and rock stratigraphy, Geophysical Prospecting, 37 (5), pp. 531–551.

7 Fruhwirth, R.K. and Schmoller, R. (1996). Some aspects on the estimation of electromagnetic wave velocities Proc. 6th Int. Conf. on Ground Penetrating Radar (GPR’96) (Sendai, Japan, 30 September–3 October) pp. 135–8.

8 Keller, G.V. (1987). Rock and Mineral Properties, in Electromagnetic Methods in Applied Geophysics, vol. 1, chap. 2, ed. M.N. Nabighian, Soc. Expl. Geophys.

9 Leucci, G. (2019). Nondestructive Testing for Archaeology and Cultural Heritage A Practical Guide and New Perspectives, Springer International Publishing.