the depth to be reached are, in fact, mainly determined by the frequency and therefore by the length of the transmitted wave.
Other factors that must be considered in the study of the electromagnetic wave propagation are the penetration depth and the resolution. The penetration depth decreases as the frequency increases, while radar resolution increases with higher frequencies. The resolution is a crucial point both in defining the acquisition geometry and interpreting georadar data. Resolution relates to how close two points can be, yet still, be distinguished.
On this regard, two “types” of resolution are illustrated and discussed in order to derive their implication in terms of targets detectability, namely the “vertical resolution” and the “horizontal resolution”.
The vertical resolution relates to the (minimum) depth separation between two boundaries to give separate reflection events; it is determined by the bandwidth that is considered about equal to the center (or dominant) frequency. Reflections from two boundaries, separated by a distance Δz, are separated for high center frequency pulses and are merged for low center frequency pulses. The acceptable threshold for vertical resolution generally is a quarter of the dominant wavelength (Sheriff, 1994), although this criterion is subjective and depends on the noise level in the data.
The above criterion implies that the minimum depth separation (Δz) is:
(2.1.22)
On this purpose, the following experimental Table 2.1.2 is given illustrating the relationship between wavelength and frequency of EM emitted waves (Leucci, 2015):
As for the horizontal resolution, instead it refers to how close two reflecting points can be situated horizontally yet be recognized as two separate points rather than one.
Table 2.1.1 Values of the relative dielectric constant εr, electrical conductivity σ, electromagnetic‐wave velocity, and attenuation in some geophysical materials (Davis and Annan, 1989. With permission of John Wiley & Sons).
| Material Type | Relative Dielectric Constant εr = ε/ε0 | Electrical Conductivityσ (mS/m) | EM Waves Velocity V (m/ns) | EM Waves Attenuation α (dB/m) |
|---|---|---|---|---|
| Air | 1 | 0 | 0.30 | 0 |
| Distilled water | 80 | 0.01 | 0.033 | 2*10−3 |
| Fresh water | 80 | 0.5 | 0.033 | 0.1 |
| Salt water | 80 | 3*104 | 0.01 | 103 |
| Dry sands | 3‐5 | 0.01 | 0.15 | 0.01 |
| Saturated sands | 20‐30 | 0.1‐1 | 0.06 | 0.03‐0.3 |
| Limestone | 4‐8 | 0.5‐2 | 0.12 | 0.4‐1 |
| Shale | 5‐15 | 1‐100 | 0.09 | 1‐100 |
| Silt | 5‐30 | 1‐100 | 0.07 | 1‐100 |
| Clay | 5‐40 | 2‐1000 | 0.06 | 1‐300 |
| Granite | 4‐6 | 0.01‐1 | 0.13 | 0.01‐1 |
| Dry salt | 5‐6 | 0.01‐1 | 0.13 | 0.01‐1 |
Table 2.1.2 Wavelength values λ as a function of the frequency at several electromagnetic‐wave velocities of propagation (From Leucci, 2015).
| Freq. (MHz) | P(ns) | λ (m) @ v= c | λ (m) @ v= (1/3) c | λ (m) @ v= (1/6) c |
|---|---|---|---|---|
| 1 | 1000 | 300 | 100 | 50 |
| 10 | 100 | 30 | 10 | 5 |
| 30 | 33 | 10 | 3.3 | 1.65 |
| 100 | 10 | 3 | 1 | 0.5 |
| 300 | 3.3 | 10 | 3.3 | 1.65 |
| 500 | 2 | 0.6 | 0.2 |
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