Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

and
An algorithm for the direct problem for spherical conductors can
be formulated as follows. It is designed not to give the transfer
function C: for a given model itself but an auxilary transfer
function
as a direct equivalent to the tranfer function C of plane conm
ductors. To see its connection to C differentiate the characteristic
n'
depth function f: with respect to r, observing that the differen-
tiation of spherical Besselfunctions with respect to their argu-
ment u j.s
and the same for n . Then
n
Hence,
d fm
m = fm + = fm(r/?m - n)
gn n n n
with nC /r as "spherical correction ",
. . n
Continuity of the tangential components of the electric and
A
m
magne.tic field requires that Cn and thereby cm as well are conn
tinuous functions of depth. Let r
L
be the radius of the inner
core of conductivity a surrounded by (L-1) uniform shells, the
L'
-yth shell between r
and rvi-,.
(v = 1,2, ... L).
v