Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

Now
m
Division by f !, (0) :f; (0) yields
If the difference 60 = a - o is small, f2 in the integral may
2 I
be replaced by fl, since the difference f2 - fl is of the order
of 60 = a2 - o leading to a second order term in 6C = C2
1'
- C1.
Hence to a first order in 6s
m
6C(w) = - iwp l6a(z){ f (z,w) 12 dz
O 0 f' (0,~)
Therefore in the Backus-Gilbert procedure the FrGchet derivative
of C is -iwpb{f(~)/f'(o)}~. In the generalized inversion the deri-
vatives of C with respect to layer conductivities and layer thick-
nesses is required, if a structure with uniform layers is assumed.
Let there be L layers with conductivity am and thickness d in
m
the m-th layer, h < z 2 hm+l (hL+l = -).
m - Then (6.38) yields
since in the last case all layers below the m-th layer are dis-
placed too.'
' '6':3 :2 : Pa,rt?al - derivatives in two- and 'three-dimensions
For two-dimensions only the E-polarization case is considered. The
pertinent equation is (cf . (3.5a) )
AE = iwp a E .
0
Considef again two conductivity structures a and a2.
1