Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

Here a denotes the conducti.vity at the top of the substratum
0
and ~a~ the anomalous vertical field at z = d which is responsible
for driving currents upwards from the substructure to the sheet
and vice versa.
The boundary conditions, reflecting the "thin-sheet origin" of the
variation anomaly, are
(E-polarisation) (H-polarisation)
for z = 0: H' = -K x H H+ = 0,
a Y az ax
-
for z = d: H- = LII x Haz E = x Eaz.
ay a Y
c
The kernel function of the convolution integrals - are -n 5
H " ' ~ - K * I ~ ' ~ ~ *
1 r "7 ip H
KCy) = -
=-> "' = Q ~ Y ) - : ~ Y ~ . ~ -
"Y
hy?
q*
c(i) U-
+m sin(y k ) -7 LB% HCi; "I
1
LII(w,y) = - I -
dk
+
't H"b x
" oik Y
Ha): !
Y Cn~=(W'!C Y
7
)
I L E,
Y-,.-r-,--* . ./-:
sin(y k )
m'
1
Y
LICw,y) = - I - d k . ' LI" Ea; . 2 - . UCLX = -go.
"-0 ik ~-(w,k)
Y n1 Y {hcifl<
s2x.x:,~.c.r := ----
He-e C-
n I1 is the response function of the substructure for the
anomalous TE-field in the case of E-polarisation and C- the
nI
response function of the substructure for the anomalous TM-field
in the case of H-polarisation.
The kernel K is the separation kernel, introduced in Sec.5.1. It
i
connects K and HaZ in such a manner that the source of the
aY
anomaly is "internal" wh.cn seen from above the sheet. The kernels
L are the Fourier transforms of the response functions, intro-
.duced in Sec.7.3, which connect the tangential and horizontal
field components above a layered half-space. Their application
to the anomalous field at z = d implies that H and E diffuse
-a -a
downward into tlie substructure antidisappear for z -p a. ---
They represent
the.inductive coupling of the anomalous field with the
substructure .'