Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

Eqs. (4.35aIb) admit a representation of the field values outside
the anomalous layer in terms of the boundary values of the con-
tinuous tangential component of E .
-a
A physical interpretation of Green's vector G subject to (4.33)
-i
is as follows: Reflect the normal conductivity structure for
z < z and z > z2 at the planes z = z and z = z and place a unit
1 1 2
dipole in x -direction at r and an image dipole at
i ,. --o " 'm
r' = r + 2 (zm - z0)zI the moment being, the same for the vertical
-0 -0
dipole and the opposite for the two horizonta~l dipoles. Then the
tangential. component of G!") vanishes at z = z and G!~) is a
-1 111' -1
solution of (4.32) for - r E Vm.
Hence, if Vm is a uniform half-space, G (m) is constructed from the
-i
whole-space formula (4.15) . Eq. (4.3'5) then reads :
m
Eaz = (-1) / J? ( ~ {x-x j )E (g)+ (y-yo)Eo
(5) ld~,
ax CIY
'm
where R = [r - - r 1, k2 = iww cr
--O 0
Eqs. (4.36a-c) contain as important subcase the condition at the
air-earth interface (m = 1, zl = 0, k = 0).
0
Because of the limited range of the kernelstin applications of the
surface integral on1y.a small portion of Smm:ust be cocsj.dered.
For Eax and E the contribution of the region nearest to r is
aY -0
most important. Assuming E and E to be cionstant within's sma1.l
ax aY
disc of radius p centered perpendicularly over r the weight from
-0
(4.36a.b) is
where h = lz - zo[ . There is a contributiorr to E onl-y if Ea,, and
m az
E have a gradient along x and y direction kespectively.
aY