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 | 0.1 |
| 1000 | 1 | 0.3 | 0.1 | 0.05 |
| 2000 | 0.5 | 0.15 | 0.05 | 0.025 |
| 3000 | 0.33 | 0.1 | 0.03 | 0.015 |
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