Electromagnetic Methods in Geophysics. Fabio Giannino
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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 εr is 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.
REFERENCES
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.
10 Leucci, G. (2015). Geofisica Applicata all’Archeologia e ai Beni Monumentali. Dario Flaccovio Editore, Palermo, pp. 368.
11 Persico, R., Piro, S., and Linford, N. (2018). Innovation in Near‐Surface Geophysics Instrumentation, Application, and Data Processing Methods. Elsevier. pp. 534.
12 Persico, R. (2014). Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing. Wiley.
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14 Turner, G. and Siggins, A.F. (1994). Constant Q attenuation of subsurface radar pulses: Geophysics, 59, 1192–1200
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2.2. FREQUENCY DOMAIN ELECTROMAGNETIC (FDEM) METHOD: OPERATIVE PRINCIPLE AND THEORY
2.2.1. EM Waves and Fundamental Quantities
The so‐called “low induction number” FDEM methods are based over a rather complex theoretical background that is the theory of the EM waves propagation. It is beyond the scope of this book to illustrate in detail the physical and mathematical aspects of the EM theory hence, a reasonably simplified vision of the features of the EM theory shall be given. Other textbooks, such as Nabighian, 1988 just to cite one example, may be taken as a reference for an in‐depth into the EM theory. However, the reader shall gain all the information and details necessary to support comprehension of the FDEM methodology and its application for the practical aspects for shallow modeling of the subsoil for many types of applications.
The introduction to this theory, is illustrated through two typical examples, schematizing simple laboratory tests (Figure 2.2.1).
Being a coil made of metal (copper, for example) connected to an ammeter as illustrated in the sketch of Figure 2.2.1, above.
Let the magnet be standing still in a position close to the coil (Figure 2.2.1– 2). No electric current is measured at the ammeter, under this condition.
Figure 2.2.1 1) The magnet does not move and no electric current is measured; 2) when the magnet is moved towards the coil, a positive sign electric current is measured; 3) when the magnet is pushed outside the coil, a negative sign electric current is measured
(modified from F. Giannino, 2014).
When the magnet is moved towards the coil (Figure