Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

the surface. Only near certai-n sulfidic ow-veins the "effective"
decay time T may be in the order of fractions of seconds due to
0
induced polarisation and the propaga-tion terrrt may not be necessarily
small against unity.
The air just above the ground nas'a resistivity in the order of
loi4. Qm, yielding a time constant T of about 10 minutes, Hence,
0
fast fluctuations "propagate"
>
while slow variations "diffuse"
.from their ionospheric sources to the Earth's surface,
For geomagnetic soundings only the field at and below the Earth's
surface matters, regardless how the primary field reaches the
surface. It is necessary, however, to make --- one definite assumption -
about the nature of the primary field in the following sense:
Non-di'.'ergent vector fields such as .... E and - H 5n uniform domains
can be decomposed into two parts
-
F = fI +
ZI1
* 6
- -
= rot(rT) + rot ro't(rsS)
h
where - r denotes a unit vector in some specified direction, here
the z-direction. T and S are scalar Cunctions of position, It is
readily seen that the so-called "toroidal" part fI is orthogonal
A
to 2, i.e, in tne here considered case XI is tangential to planes
z = const. The remaining so-called "poloidaln' part zII of F has
three components:
rF"
\ I
VI /
\ \ 1 1 / r
Let now PI and gII be a "toroidal" and a "poloidal" diffusion
vector, both satisfying
V'P - = iwpoo(l +. T~)I',
from which the toroidal and poloidal parts of .-. H are derived by
definition as follows:
-