The MT technique is a passive technique that involves measuring fluctuations in the natural electric (E) and magnetic (B) fields in orthogonal directions at the surface of the Earth. The orthogonal components of the horizontal electric and magnetic fields are related via a compleximpedance tensor,Z:
Ex Ey
¼ Zxx Zxy Zyx Zyy
Bx=0 By=0
or E¼ZB=0 (2:50)
Z is complex, being composed of both real and imaginary parts.
Therefore, each component,Zij, ofZhas not only a magnitude, but also a phase (cf. Equations (2.35) and (2.36)):
a;ijð!Þ¼ 1
0!Zijð!Þ2 (2:51)
ij¼tan1 ImZij ReZij
!
: (2:52)
To illustrate the physical meaning ofimpedance phase, we will use an analogy based on thermal conditions within a wine cellar (Figure 2.10). The temperature inside the wine cellar doesn’t vary as much as the temperature outside, because some of the signal gets attenuated as it penetrates through the walls, which have a lower thermal conductivity than air. This attenuation is analogous to the
Temperature ( C)o
0 –10 10 20 30
SUMMER WINTER
Outside Inside
Period (Months) Phase lag Figure 2.10Attenuation of
thermal waves passing through the walls of an idealised wine cellar. The walls act as a low-pass filter, such that inside the wine cellar only seasonal temperature variations are detected. These temperature variations are not only attenuated compared to the outside temperature variations, but are also phase shifted owing to the time required for the heat to diffuse through the walls. The attenuation and phase lag are analogous to the attenuation of electromagnetic waves as they penetrate into the Earth.
34 Basic theoretical concepts
attenuation of electromagnetic waves as they penetrate into the Earth. In addition to attenuation, there is also a phase lag, owing to the time required for the heat to diffuse through the walls – (i.e., the time at which the outside air temperature reaches a maximum will not be the time at which the inside temperature peaks, which will be later). In the ideal case, a stone-walled cellar might actually be colder in the summer than in the winter – a gourmet’s delight: a nice cool white wine to accompany a seafood salad in summer, and a room temperature red wine to enjoy with a hearty roast in winter!
Being a tensor,Zalso contains information about dimension- ality and direction. For a 1-D Earth, wherein conductivity varies only with depth, the diagonal elements of the impedance tensor,Zxx
andZyy(which couple parallel electric and magnetic field compon- ents) are zero, whilst the off-diagonal components (which couple orthogonal electric and magnetic field components) are equal in magnitude, but have opposite signs, i.e.,:
Zxx¼Zyy¼0 Zxy¼ Zyx
1-D: (2:53)
For a 2-D Earth, in which conductivity varies along one hori- zontal direction as well as with depth, Zxx and Zyy are equal in magnitude, but have opposite sign, whilstZxyandZyxdiffer, i.e.,:
Zxx¼ Zyy
Zxy6¼ Zyx
2-D: (2:54)
For a 2-D Earth with thex- ory-direction aligned alongelectro- magnetic strike,Zxx andZyyare again zero. Mathemematically, a 1-D anisotropic Earth is equivalent to a 2-D Earth.
With measured data, it is often not possible to find a direction in which the condition thatZxx¼Zyy= 0 is satisfied. This may be due
Period increasing
1-D INDUCTION 2-D INDUCTION 3-D INDUCTION GALVANIC DISTORTION
EM skin depth >>
dimensions of body Small
subsurface body
σ1 σ2
Figure 2.11Scale dependence of dimensionality. A 3-D body of conductivity2embedded in a conductivity half-space of conductivity1induces a 1-D responses for MT sounding periods that are sufficiently short that their skin depths are small compared to the shortest dimensions of the 3-D body. As the sounding period increases, the inductive scale length will eventually extend sufficiently to encompass at least one edge of the anomaly, and the MT transfer functions appear multi-dimensional. For sufficiently long periods, such that the electromagnetic skin depth is very much greater than the dimensions of the anomaly, the inductive response of the anomaly becomes weak, but a so-called galvanic response that is frequency independent (i.e., real) remains (see Chapter 5).
2.9 The impedance tensor 35
to distortion or to 3-D induction (or both). Generally, the dimen- sionality evinced by data is scale dependent. Consider any general- ised, homogeneous, 3-D conductivity anomaly embedded in an otherwise uniform Earth. For short MT sounding periods, corres- ponding to electromagnetic skin depths that are small compared to the shortest dimensions of the anomaly, the transfer functions should appear 1-D. As the sounding period increases, theinductive scale lengthwill eventually extend sufficiently to encompass at least one edge of the anomaly, and the transfer functions appear 2-D. As the sounding period increases further, edge effects from all sides of the anomaly will eventually be imposed on the transfer functions, resulting in transfer functions that are evidently 3-D (Figure 2.11).
For sufficiently long periods, such that the electromagnetic skin depth is very much greater than the dimensions of the anomaly, the inductive response of the anomaly becomes weak, but a non- inductive response persists. The non-inductive response of the anomaly creates a frequency-independent distortion of MT transfer functions that can be stripped away (as we shall see in Chapter 5).
36 Basic theoretical concepts
Chapter 3
Planning a field campaign
The choice of equipment used in a particular survey should depend on the depth range under consideration: in crustal studies, induction coil magnetometers are used frequently, the sampling is quick and the ‘processing’
(described in Chapter 4) is usually performed in the field. Fluxgate magnetometers provide a response at longer periods than induction coils, and are used if larger penetration depths are under consideration. In many cases, data from very short to very long periods are desirable, and two different sensors are combined at each site. It is vital that anybody writing or modifying processing software has access to all information regarding the analogue electronics of the system (e.g., calibration coefficients for filters) that is to be used in conjunction with the software.
We suggest a rule of site spacing: not too close and not too sparse. The question whether we should deploy magnetotelluric sites along a profile, or as a 2-D array is discussed in the context of the geological complexity of the target area, the available hardware and the financial resources. In many cases, a trade-off has to be found between the desire to have many sites and hence a good spatial resolution and the wish to achieve high-quality data by occupying sites for a long time.