LITMIR.BIZ

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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 ε_r, 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

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