The electromagnetic fields registered by a magnetometer installed on the surface of the Earth comes from two main sources. Source signals at short periods, less than 1s (high frequencies, higher than 1 Hz), originate from magnetic field disturbances trapped in the leaky wave guide formed by the Earth’s surface and the ionosphere as a result of lightning discharges (Simpson and Bahr, 2005). Both the Earth’s surface and the ionosphere are highly conductive compared with the atmosphere. The second source, at longer periods (>1 s), that can be utilised in EM sounding prospecting, is due to fluctuations in the magnetic field produced by the effect of the dynamic nature of the solar wind pressure as explained in figures 2.1 and 2.2 (Kivelson and Russell, 1995). Since this source is relevant to us, as it is that which MT and GDS soundings seek to exploit, we describe it briefly.
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Figure 2.1: A simple illustration of magnetopause boundary separating an un-magnetized solar wind (left) from a magnetosphere containing no plasma(right). Also conspicuous from the figure is the deflection of electron and protons in opposite direction that leads to the magne-topause current. Figure modified from Kivelson & Russell (1995)
2.1 EM signal source
The solar wind (source is the sun) is a continual stream of plasma (made up of charged electrons and protons) flowing outward from the sun towards the Earth. Before reaching the magnetosphere, the net charge of the solar wind is zero. At the magnetopause (bound-ary of the magnetosphere), the solar wind exert a pressure on the magnetosphere and the pressure is countered by Earth’s magnetic field. That is, at the magnetopause, the Earth’s magnetic field acts as an obstacle to the pressure from the solar wind; on encounter of the Earth’s magnetic field, the protons and electrons that constitute the plasma of the solar wind are deflected in opposite directions (charges in plasma are polarised) generating an electric field that produces a current (current is the flow of electrons and protons in opposite directions) known as magnetospause current. However, the solar wind pressure is dynamic due to fluctuations in its intensity and velocity. The fluctuations in the solar wind pressure on the magnetosphere cause the magnetopause current to also fluctuate leading to the generation of electromagnetic fluctuations (Parker, 1958) with frequencies lower than 1 Hz (periods longer than 1 s) on the Earth’s surface. The fluctuations of the magnetopause current cause a fluctuating magnetic field on the Earth’s surface. These changes are called geomagnetic activity and the fluctuating waves generated are used in electromagnetic induction studies. Because the pressure of the solar wind is dynamic, the size of the magnetosphere varies with changes in the density and velocity of the so-lar winds. When the pressure of the soso-lar wind increases, the magnetopause’s currents increase as the magnetosphere shrinks and the magnetic field measured on the surface of the Earth rises. .
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Figure 2.2: Cross section of a simple model of the magnetosphere in the noon-midnight meridian. The geomagnetic field is perfectly confined by the sheet currents flowing on the magnetopause. A second current sheet flows across the midplane of the magnetotail and joins with the magnetopause currents at the flanks of the tail. The solar wind flow is deflected at the bow shock and flows around the magnetosphere, constituting the magnetosheath. Modified figure after Kivelson &
Russell (1995)
2.1 EM signal source
Figure 2.2 is a cross section of the model of the magnetosphere, again modified from Kivelson & Russell (1995). A sudden increase in the solar wind dynamic pressure will compress the magnetosphere and move the magnetopause nearer to the Earth, and simul-taneously the magnetopause current intensifies. The movement of the magnetosphere’s boundary and the intensification of the current, a result of a strong and prolonged cou-pling of the solar wind to the magnetosphere leads to intense geomagnetic activity often called a magnetic storm that is observed on the Earth’s surface as a sudden increase in the geomagnetic-field intensity of a few tens of nanotesla . The duration of a typical storm lies between 1-5 days (Kivelson & Russell (1995), page 407). The largest geomagnetic field fluctuations (about an order of a few hundred nT) occur during magnetic storms (Simp-son and Bahr, 2005), which takes place due to irregular increases in the rate at which plasma is ejected from the sun. These geomagnetic field fluctuations induce currents in the subsurface. The induced currents then diffuse downwards into the Earth and the rate of attenuation of these currents depends on the conductivity of the subsurface. The process is commonly used to probe depths of several hundred kilometres through what is known as a passive EM induction technique. The induction process is governed by the time dependent diffusion equation which we proceed to derive in the next section. But before we proceed to look at the diffusion equation, lets mention briefly the nature and effects of Sq variations.
Sq variations
As discussed above, the magnetic field observed on the Earth’s surface due to the interac-tion of the solar wind with the main field at the magnetosphere fluctuates. Therefore at any geomagnetic observatory or station, the daily record of the geomagnetic fluctuations often shows a large number of random changes in the field that represents the superposition of many spectral components. The general increase in amplitude of the spectral compo-nents is proportional to increasing period. These spectral field variations have as origin the unique current sources in the ionosphere and magnetosphere as previously discussed under EM signal source. However, there are days that are undisturbed by solar-terrestrial and particle activity. On these days the geomagnetic records are changing smoothly espe-cially during the daylight hours (Campbell et al., 1997). Indeed, the smooth/systematic changes depend primarily on local time and latitude (Encyclopedia Britannica Online).
These slow smooth changes or variations are overshadowed by essentially 24-, 12-, 8-, and 6-hour period spectral components (Campbell et al., 1997) in the field configuration with few of the irregularly appearing, shorter or longer period changes present. On such days, the oscillations of the three orthogonal field components (Hx, Hy andHz) produce records that are anticipatively similar to others recorded many days earlier. Such records describe the "‘quiet daily geomagnetic field variations"’. When the small but persistent effects at-tributed to the lunar tidal forces are put aside, the changes are commonly referred to as
’Sq’ meaning solar quiet fields or the Sq Daily variations or Diurnal variations. The spec-tral lines at periods of the order of 105 s are harmonics of Sq daily variation (Simpson and Bahr, 2005) which can be utilised in electromagnetic induction studies to probe mantle depths and beyond.
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