Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

6.4. Quasi-linearization - of the one-dimensional inverse problem
of electromaqnetic induction (Sc1~mucl:er's PSI-alqorithm)
In the one-dimensional problem it is possible to a certain extent
to linearize the inverse problem by introducing new suitable parameters
and data instead of the old ones.
Assume a horizontally layered half-space with L layers having conductivities
u , , . u and thicknesses d
L 1' d2' ..-, dL-l
CdM = m). Let the upper edge of layer m be at z = h and assume
m
that layer conductivLties and thicknesses satisfy the condition
Let k = q. Then the pertinent equation for a quasi-uniform
m
external field is
The transfer function is, as usual,
C(w) = - f,(o)/£;(o) .
Introduce instead of f the new function
m
In the TE-case f and ff are continuous across boundaries, i.e.
As a consequence of (6.48) and
(6.49) + is discontinuous across
boundaries:
'?
z=h
m
The variation of. £ in the m-th layer is
m
. .
-k (z-h )
m
fm(z) = A; e +
+km ( z -hm)
~ m + e
1