Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

. A
as transfer function between A and B in the wave number domain, which
contains the information about the internal resistivity distribution.
A vertical sounding of this distribution is made by considering
h
R as a function of frequency, k being fixed, or vice versz.
If the array covers the whole globe, the sphericity of the Earth re-
quires the replacement of the krigonometric functions by spherical
harmonics in spherical coordinates Cr,B,A):
a: Garth' s radius ; p:(cos@ : Associated' spherical function. The trans-.
fer functions have then the form
The first and still basic investigations of the Earth's deep conduc-
tivity structure have been carried out by this approach (SCHUSTER,
CHAPMAN and PRICE).
If the array of stations covers only a region of Limited extent, it
may be !impracticable to de'compose the observed field into wave-
spec-tral components or it may be even impossible because only a small.
section of the source field structure has been observed. In that
case vertical array soundings are carried out preferably with response
functi.ons in the frequency-distance domain.
Suppose the source field is quasi-uniform ,i.n one horizon.ta1 direc-- j
tion, say,
U = UCw,y) and V : V(w,y). Ls't
* . %
be the inverse Fourier transform of R. Then, if V is given by the
,. A
roduct of R with U in the (u,k) domain, V will be given by a
corlvolution 05 R with IJ in the (w,y) domain:
+w
with .R U = 1 RCw,y-n) UCq)dq.
-m