Читать книгу Electromagnetic Methods in Geophysics - Fabio Giannino - Страница 24

It dates back in the 70s when the electromagnetic technique known as Time Domain Electro Magnetic Method (acronym TDEM) has been developed, almost at the same time, by the Russian, Canadian, and Australian technical and scientific community, for mineral search purposes.

Later in the 80s, TDEM found a wider application for hydrogeological purposes, and recently it has been applied for geotechnical (stratigraphic interpretation of the subsoil) and environmental studies (pollutants search, UXO search) (A. Menghini et al., 2010).

The aim of a TDEM sounding is the reconstruction of a 1D model of the subsoil to detect layers having the same characteristics in terms of electrical resistivity. The depth of investigation of a TDEM survey depends upon the characteristics of the instrumentation employed, the stratigraphic and geological conditions of the medium to be investigated and the background and or other sources of noise.

The main advantage of this technique with respect to other EM techniques (for example respect to the FDEM method), is that the TDEM method employs transient EM field: this means that the measurements of the secondary EM field is done at the receiving coil, when the transmitting coil is switched off for a very short time, called time off. During the time off, the secondary is sampled in wider “time windows,” corresponding to deeper portion of the subsoil.

The above‐described setting put the conditions to avoid (as it happens instead in the FDEM methods) to measure a very small quantity (the secondary magnetic field) in presence of another, much larger, one: the primary magnetic field, produced by the transmitting coil (P.V. Sharma, 1997; Kearey et Alii, 2002; J.D. Mc Neill, 1980). Hence, the signal measured at the receiver coil, is likely to be only due to the “contribution” given by the secondary field associated to the soil material, and not to the signal directly coming from the transmitting coil.

In general, to perform a TDEM sounding one must lay an electric cable describing the shape of either a square or a rectangle (the transmitting loop). Inside the transmitting loop, known electric current flows as it is connected to a transmitting unit fed by a battery, depending on the system and its configuration (Figure 2.3.1) it is possible to inject current into the ground from 2 to more than 150 A, depending on systems design. Also, a grounded transmitter may be employed allowing great exploration depth to be reached.

The dimension of the transmitting loop varies depending on the required investigation depth, and it generally ranges between a few tenths of meters to a square whose side is 500 meters long, for investigation depth down to more than 200 meters (P.V. Sharma, 1997) (Figures 2.3.2–2.3.3). Actually, by using bigger transmitter loop with grounded transmitter, larger exploration depth can be achieved, as deep as 1000 meters below ground level. On this purpose, it is also possible using the so‐called multi‐turn loop to increase the energizing moment (M). In Fact, M = nIA where n is number of turns, I is the current, and A is the area of the loop. As for this aspect, the most important and characterizing parameter is given by the product nA.

Figure 2.3.1 Typical TDEM acquisition scheme.

Figure 2.3.2 A Prototype acquisition TDEM system. All the essential parts of the system are shown.

Figure 2.3.3 Prototype acquisition ProTEM manufactured by Geonics Ltd. (www.geonics.com). All the essential parts of the system are shown.

Receiving loop dimension is in the order of one meter (side or diameter, depending on its shape see Figures 2.3.4–2.3.5).

In the acquisition scheme depicted in Figure 2.3.1 an acquisition system defined as Central Loop is illustrated, where the receiving loop is concentrically positioned with respect to the transmitting loop. In contrast, in the Loop‐Loop or Slingram mode, the transmitter and receiver are coaxial but not concentric: the receiver loop is external with respect to the transmitter loop.

The energizing current is normally injected as a square wave (Figure 2.3.6). To each positive pulse (time on) there follows an equal period during which the current is switched off (time off); then, the direction of the current in the transmitting coil is changed (negative portion of graph in Figure 2.3.6 a), and following this the electric current is again switched off for an equal amount of time. The entire cycle just described, is repeated many times with repetition frequency varying from 0.25 to 250 Hz.

In Figure 2.3.6 b, it is highlighted how in the moment in which the electric current is switched off (turn off), as illustrated in the Faraday’s law, a primary magnetic field is produced, and this tends to become null within a very little time (a few milliseconds). This magnetic field interacting with the subsoil generates induced currents in it, which propagates deeper in the subsoil as time passes (Figure 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.

(2.3.1)

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 σ^3/2, 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)).

(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 tension with time (from Danielsen et al., 2003. With permission of Elsevier)

Figure 2.3.8 Sketch of the decaying curve of the measured tension with time.

At this moment, the current starts to stabilize towards the center of the object, decreasing outwards to the edge of it. At the same time the associated magnetic component starts to decay exponentially with time, with a time constant τ that is given by (McNeill 1980):

(2.3.5)

This moment is known as Late time.

The behavior described above, can be recognized in the 1D soundings as a result of the TDEM survey, and the analysis and forward modeling of the recorded data is addressed at defining a model based on the information that is directly dependent upon the shape, dimension, orientation, burial depth, and electrical resistivity of the target(s).