Schmucker, 1970 (Scripps) - MTNet

Schmucker: Geomagnetic Variations 71
Furthermore, h shall be small compared to the wave length of the source
fi:eld, yielding k • h « 1, but large in comparison to the skin-depth value P3
of the substratum. This ensures that the wave number k of the incident field
drops out of the following relations.
The application of the recurrence formula (5.44) gives
which when substituted above yields
G 2 (d) '" (kh) -1
1 + KIh tanh (KId)
G/O)::;: KI h + tanh (K I d)
C(d) KIh
c(O) = KIh cosh(KId) + sinh (KId) '"
d
1--h+d
(5.58)
The approximation becomes valid when PI is about three times the thickness
d as seen from the asymptotic behavior of the curves in figure 32. Hence, a
finite ratio d/h limits the uniformity of c in the top layer even for those frequencies,
for which PI »d. We infer from (5.58) and figure 32 that c remains
uniform within d/(h + d) percent as long as PI > 3d, thereby setting
limits for Price's method.
1.0
JJ
.Y..!!1
£(0)
.6
.,
.2
Fig. 32. Attenuation of tangential
electric field variations C .(z) within
the top layer of a special 3-layer
model, shown as function of skindepth
value to thic.kness of the top
layer. Solid curves: real part of
C(d)/ C(O); dashed curves: imaginary
part.
Consider, for instance, the induction in a 4 km deep ocean (