Schmucker, 1970 (Scripps) - MTNet

as general solution of (5.30), yielding
with
Schmucker: Geomagnetic Variations
-K z
v
A e
v
G)z) = -Kv z
- B e
v
Kv z
Ave + Bv e
63
(5.33)
(5.34)
Let us consider two limiting cases. When the skin-depth value of the v th
layer is large in comparison to the wave length of the source field, yielding
Pv k » 1, then
(5.35)
and the incident field penetrates through this layer as if it were nonconducting.
When, to the contrary, Pvk « 1, then
K v = (1 + i)/p v ' (5.36)
i. e., the attenuation of the incident field within this layer is determined
solely by its skin-depth value and is independent of k.
The surface ratio of internal to external parts is the same for vertical and
horizontal variations and given by
Kl G1(0) - k
S(k) = I(k, t)/E (k, t) = K G (0) + k
I 1
(5.37)
as is readily inferred from the continuity condition for the horizontal plane
z = O. We consider X and Y as components of a horizontal variation vector
H, setting
X=k/k'H
x
Y=k/k·H.
Y
(5.38)
The ratio of vertical to horizontal variations follows then from (5.28) as
with
Z/H = iT(k)
1 - S(k) k
T(k) = 1 + S(k) = K G (0) •
1 1
(5.39)
The internal electric field vector of the associate toroidal current mode
has the components
c. =k /k.c. c. =-k /k.c.
x Y Y x
C = ifv(k, t, z) exp[i(k. r)]
(5.40)