2.3.1). These currents dissipates very quickly, and they produce a secondary magnetic field that contains the information relating to the variations of resistivity in the subsoil that are connected to the shape and dimension of the buried conductor that is likely to be the target of the survey. (J.D. McNeill, 1980).
In fact, what the instrumentation measures is a voltage drop (in nV/m2). This voltage (the so‐called transient), which becomes null in a few milliseconds, is sampled by a receiving unit during the time off, to eliminate interferences; the receiving unit is connected to the receiving coil. The receiver performs the sampling of the transient in several acquisition channels working with increasing time windows. Since the current penetrates deeper as time passes, portion of the subsoil at increasing depth can be investigated.
In addition, the velocity of propagation of the electric current is directly proportional to the resistivity (inversely proportional to the conductivity) (A. Menghini e A. Viezzoli, 2012).
From the above it follows that the first data analysis is carried out in terms of the variation of the voltage with respect to the time (Figures 2.3.7 and 2.3.8).
The basic mathematical theory is the one already illustrated in Chapter 2.2 for the FDEM theory and, in general, we can say that the response recorded from the subsoil is a mathematically complex function of conductivity and time; however, during the late stage, the mathematics simplifies considerably, and it can be shown that during this time the response varies quite simply with time and conductivity as (McNeill 1980):
Figure 2.3.4 The circular‐shaped receiving coil of the ProTEM (Geonics Ltd.) system.
Figure 2.3.5 The square‐shaped receiving coil of the TDEM system.
Where:
e(t) = output voltage from a single‐turn receiver coil of area 1 m2
k1 = a constant
M = product of Tx current x area (a‐m2)
σ = terrain conductivity (siemens/m = S/m = 1/Ωm)
t = time (s)
As it can be noted from ((2.3.1)) the measured voltage e(t) varies in function of σ3/2, so it is intrinsically more sensitive to small variations in the conductivity than conventional resistivity. Also, during the late stage, the measured voltage is decaying at the rate t−5/2, which occurs very rapidly with time. Eventually, the signal disappears into the system and the background noise, and further measurement is impossible. This is the maximum depth of exploration for “that” particular system.
In the case of TDEM soundings, on the other hand, it was observed earlier that as time increased, the depth to the current loops increased too, and this phenomenon is used to perform the sounding of resistivity with depth. Thus, Equation (2.3.1) can be inverted to read (since ρ = 1/σ):
(2.3.2)
The voltage induced, and perceived at the receiver coil, is the product of the receiver coil Moment M (Area times the number of turns) multiplied by the time derivative of the vertical magnetic flux density (equation (2.3.3)).
where μ is the magnetic permittivity an M is the transmitter loop moment (L2I) length of the side. This equation gives some important points about transient soundings. Because e(t)IM, is inversely proportional to time and the current diffuse downwards with time, it is more difficult to sound more deeply unless the transmitter moment is increased. To do this one can either increase the transmitter current, the wire turns, or both (Ranieri, 2000). Also, the transmitter loop area determines a deeper exploration depth.
Figure 2.3.6 Scheme of injection of the current with a TDEM system. (a) In the cycle of injection of the current it can be recognized the time‐on, when the current is injected (in one direction and the opposite direction); the time‐off, when the transmitter is switched off and measurements are executed; the Ramp Time representing the time needed by the transmitter to switch off and on completely. (b) It is also illustrated how the induced electro‐motoric force varies during the different phases of the cycle. (c) The schematic variation of the secondary EM field is illustrated, during the phases of the cycle.
As for the investigation depth, this depends upon the geoelectric section explored and its geoelectric characteristics.
On this matter, however, the transient electric field reaches a maximum at the diffusion depth (dd) which is what the skin depth ∂ is to FDEM (Ranieri, 2000):
(2.3.4)
Finally, it is now important to describe a process relating to the following: let us assume that a confined object of given dimension and resistivity is buried in a homogeneous half space at a given depth below ground surface.
At the moment when the primary electric field at the transmitter is off, this will generate a current in the ground (Eddy current) because of its associate magnetic component. At this very time, the current flow shall be distributed solely on the surface of the object mentioned above. The magnetic field in the object shall be exactly the same as that due to the primary. This moment is called Early Time.
From now on, the current starts circulating inward with respect to the object, and the magnetic field is induced by these currents. However, because of Ohmic losses this current starts to decrease (and this is depending on the physical properties of the object). Because of this (and of Faraday’s law for that matter) the magnetic (secondary) field also decreases. This moment is identified as intermediate time.
Figure 2.3.7 Example of decaying curve of the measured
