Geoscience Reference
In-Depth Information
with depth as well as the local inhomogeneities by considering the case of a
homogeneous medium with constant conductivity . This means that the second
term on the right-hand side of Eq. (
7.10
) is equal to zero, so that we arrive at the
following equation, which has the form similar to Eq. (
1.14
),
2
ı
B
Cr
.
V
B
0
/;
@
t
ı
B
D
m
r
(7.12)
where
m
D
.
0
/
1
stands for the coefficient of magnetic diffusion or magnetic
viscosity in the conducting ground. This coefficient is measured in m
2
/s.
Equation (
7.12
) is referred to as the diffusion-type equations. Here the second
term on the right-hand side of equation plays a role of the source of the GMPs. In
the case of ideal magnetohydrodynamics, that is, the case of perfectly conductive
medium when
!1
,Eq.(
7.12
) reduces to the form similar to Eq. (
1.18
)
@
t
ı
B
Dr
.
V
B
0
/:
(7.13)
This means that the magnetic field lines are “frozen in a conducting medium” and
can be considered to move with the medium. This point is studied in any detail in
Sect.
1.1.3
. If the conductivity is finite, the magnetic field perturbations can diffuse
through the conducting medium.
More usually we measure the electric and magnetic field variations in the
reference frame moving together with ground and instruments, that is at the
background of vibrations caused by the seismic wave propagation. One can use
Eqs. (
1.6
)-(
1.8
) for transformation to the moving reference frame. Substitution
Eq. (
7.11
)for
E
into Eq. (
1.6
) gives the electric field
E
0
in the moving reference
frame
E
0
D
m
.
r
ı
B
/:
(7.14)
These equations should be supplemented by the proper boundary conditions at
the ground-atmosphere interfaces.
7.2.3
Diffusion and Seismic Zones
The EQs, volcano eruptions, and underground explosions are the sources of the
most intense seismic waves propagating in the Earth's crust. The seismic waves
radiated by the underground acoustic sources can interact with rock inhomogeneities
and ground surface forming a variety of scattering waves. The net field of the
elastic displacements is very complex because it includes the primary longitudinal
and transverse waves coming from the source and a number of reflected waves.
Among them are the surface wave modes such as Rayleigh and Love modes (Love
1911
), which are formed at the large distance (Aki and Richards
2002
; Scholz
1990
). In spite of complexity of the seismic wave field, modern seismometers are
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