Geomagnetic Perturbations (GMPs) - Ultra and Extremely Low Frequency Electromagnetic Fields - page 293

A quasistatic magnetic field originated from the magnetic moment is given by
Eq. ( 7.5 ). Substituting Eq. ( 7.57 )for M into Eq. ( 7.5 ) gives the expressions for
components of the magnetic perturbations, ıB r and ıB , that just coincide with
the expressions given by Eqs. ( 7.51 ) and ( 7.52 ).
So, we have shown that the magneto-dipole approximation can be applied for the
diffusion zone in the distance range given by Eq. ( 7.48 ). We will make use of this
approximation in the next section more than once.
In conclusion, let us estimate the magnitude of the electromagnetic perturbations
in the diffusion zone. Since the magnetic perturbations in Eq. ( 7.51 ) and ( 7.52 )
increase in time, the maximum value t r=C l should be taken from the
time interval ( 7.49 ) in order to obtain this order-of-magnitude estimate

u 0 SB 0 C l

2 m r 2 ;E 0 max C l ıB max :

ıB max (7.58)

In contrast to the seismic zone, the magnitude of the electromagnetic signals falls off
with distance more rapidly, i.e., as r 2 , while in the seismic zone ıB max / E 0 max /
V 0 , that is, the magnitude decreases as r 1 . This conclusion has been confirmed by
numerical calculations (Surkov 2000b ; Molchanov et al. 2002 ).

7.2.8 Rayleigh Surface Wave in a Conductive Half-Space

Among all types of seismic waves detected at teleseismic distances from the source
the surface seismic waves have the most intense amplitude. In a theory the amplitude
of primary/longitudinal and secondary/transverse seismic waves in perfectly elastic
media decreases inversely proportional to distance r from the seismic source
whereas the amplitude of Rayleigh surface wave varies with distance as r 1=2 (e.g.,
see Aki and Richards 2002).
Consider a quasi-harmonic Rayleigh wave propagating along horizontal x-axis
in a perfectly elastic half-space z <0. The origin of coordinate system is placed on
the boundary of the half-space. The z -axis points vertically upward while x-axis is
positive parallel to the velocity C R of the Rayleigh wave. In such a case the elements
of medium move on elliptic trajectories in the vertical z x plane. The components of
mass velocity is given by (e.g., Viktorov 1975 )

exp .qk R z /

1 C s 2 exp .sk R z / exp .i /;

V 0
q

2qs

V x D (7.59)

V z D iV 0 exp .qk R z /

1 C s 2 exp .sk R z / exp .i /;

2

(7.60)