around a transmitter loop. The EM field is thus generated, in order to diffuse downwards in the form of a plane wave. When the current abruptly interrupts the transmitter loop, this generates a variation in the magnetic field which induces an electromotive force (emf) in the medium (the half‐space below the ground encountered) according to Faraday’s Law of induction.
The magnitude emf is proportional to the rate of change of the primary magnetic field in the conductor. Hence, a current is induced in the conductor (the subsoil) like concentric horizontal eddy currents resembling smoke rings which run below the transmitter and diffuse through the medium (Nabighian, 1979).
As the time from the beginning of the primary generation passes, the induced current is weakened by the ground resistance and the current density increasingly weakens too. Therefore, currents decay over time (and depth for that matter). This phenomenon is, of course, a function of ground conductivity, and it occurs more slowly in highly conductive ground compared to poorly conductive ground (where currents diffuse and decay more quickly).
At this point, the secondary magnetic field generated by the induced currents and the rate of change of the secondary magnetic field, induces a voltage that is measured as a function of time that is sensed by an active receiver sensor (a receiving coil).
The uppermost layers have got a strong influence on the measured signal that is given in terms of nV/m2 at the receiver coil. As time passes and the current penetrates deeper into the ground, then the measured signal provides information on the conductivity of the lower layers, of course. And this is the way a receiver coil records information on the electrical conductivity as a function of depth. This type of information is, in fact, called the TEM sounding.
The period of time in which the transmitter is turned off is called ramp‐off. The on–off time is “designed” to emit signal at selected frequencies. The bandwidth of the system does not correlate directly with the system’s base frequency (which is the time window applied for collecting data), and it is largely determined by the frequency range of the primary EM field. The latter is not easy to establish, and to overcome this difficulty most TEM systems implement a linear shut‐off ramp for the current (Anderson, 1989).
The duration of the off‐ramp is inversely proportional to the high frequency bandwidth. A long linear ramp has the effect of making early time responses resemble a step response. A short linear ramp instead retains the characteristics of an impulse response (Palacky and West, 1991).
When deploying Airborne Transient EM systems these must be capable of handling the great variety of the earth’s responses with different ground conditions and they must cover very wide dynamic range to be effective. A good compromise between a rapid ramp off of the transmitter current and gradual shut off of the transmitter current represent a solution for resulting in early off‐time gates, which is appropriate for mapping near surface resistivity, on one side, and deeper ground penetration on the other. This is of course challenging to achieve at the same time and for one single configuration.
The timing at which the receiver coil TEM measurements are taken are quite narrow, and they are referred to as “time gates.” The early time gates are narrower than those at a late time because they occur when the transient voltage is changing rapidly. Also, at early time gates the SNR is higher and does not need a larger gate to be sampled as happens for late times. The early time gates thus provide information about the near surface, while late time gates provide information about the deeper subsoil.
The gates are spaced with a logarithmically increasing time period in order to minimize distortion of the transient voltage and improve the signal/noise (S/N) ratio at late times, a method called “log‐gating” (Siemon et al., 2009).
The mathematical expressions defining the components of the EM field are defined by the electromagnetic phenomena and are governed by Maxwell’s equations.
As already mentioned in Chapters 2.2 and 2.2 the relationships between electric field E, current J, and electric displacement D are described in two of these, while a second pair describe the relationships between magnetic field H, magnetic induction B, and magnetic polarization M. In quantitative terms, these four constitutive relations are:
(2.4.1)
(2.4.2)
(2.4.3)
(2.4.4)
where σ is electric conductivity, ε dielectric permittivity, μ magnetic permeability, and χ magnetic susceptibility.
The four parameters comprehensively describe the electromagnetic properties of a material. The first relation is effectively the well‐established Ohm’s law in a microscopic context. According to Maxwell’s laws, an alternating current induces secondary currents in a conductive earth. These secondary currents in turn generate secondary magnetic fields, measurable using EM receivers.
The coupling between the E and H fields is described by Ampere’s and Faraday’s law.
The way in which an electric current can generate an induced magnetic field is described by Ampere’s law. If the electric field E is unstable and varies over time then there will be an additional current in the medium known as the displacement current, proportional to the variation of the electric field E. This proportional factor is known as the dielectric permittivity ε. Consequently, an additional contribute, dD/dt, acts to induce the magnetic field H. Since the displacement current acts in exactly the same way as the conductive current J, the total current will be J+ dD/dt. The Maxwell–Faraday equation is a generalization of Faraday's law, stating that any magnetic field that varies through time will be accompanied by a spatially‐varying, non‐conservative electric field, and vice‐versa. The emf induced in a coil is equal to the negative of the rate of change of the magnetic flux.
All AEM data collected on site, are addressed as input for inverse modelling (the inversion data processing) allowing to define a model of the subsoil resulting. In the frequency domain systems, the secondary magnetic field for a stratified subsurface caused by an oscillating (frequency f) magnetic dipole source in the air is calculated using the formulae below (Ward and Hohmann 1988). As mentioned, these are based on Maxwell’s equations and the issue here is to solve the homogeneous induction equation in the earth for the electromagnetic field vector F:
(2.4.5)
(2.4.6)
ω = 2πf is the angular frequency, ε is the dielectric constant, ρ the electrical resistivity, and λ is the wavenumber.
When using horizontal‐coplanar coil pair (Transmitter plus Receiver coil) with a coil separation r and at an altitude h above the surface, the resulting secondary magnetic field Z is given by (Yin and Hodges 2005):
(2.4.7)
(2.4.8)
The
