Geomagnetic Perturbations (GMPs) - Ultra and Extremely Low Frequency Electromagnetic Fields - page 277

Fig. 7.4 Variations of the ground-specific resistance with depth as observed in the continental
landmass. Adapted from Schwarz ( 1990 )

and

2 ı B

r . r ı B / Dr . r ı B / r

one obtains

r . r ı B / r

2 ı B D 0 Œ r E Cr . V B 0 /:
(7.9)

1 1

r . r ı B / C

Combining Eqs. ( 7.7 ), ( 7.8 ), and ( 7.9 ) we finally come to

1
0 r

1
0

1

2 ı B C

@ t ı B D . r ı B / r Cr . V B 0 /: (7.10)

This is the so-called quasi-stationary equation for magnetic field that can be applied
to the moving conductive medium. For example, this equation can describe the
co-seismic phenomena in the earth-fixed reference frame.
As a solution of Eq. ( 7.10 ), i.e., ı B , is known, the electric field, E ,inthe
motionless reference frame can be found from Eq. ( 7.7 )

E D m . r ı B / V B 0 : (7.11)

The Earth's conductivity at the continents varies with depth as schematically
shown in Fig. 7.4 . The conductivity of the upper sedimentary rock is higher than
that of lower layers of rock basically due to the presence of groundwater. The
enhancement of the rock conductivity at the higher depth is believed to be due to
the increase of the ionic conductivity of the rock, which in turn results from the
increase of the pressure and temperature with depth.
Now we consider the seismic waves propagating in the upper layers of the
Earth's crust. To simplify the problem, we shall ignore the conductivity variations