Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

Problem (iii) j.nvol.ves mainly the attenuation of the upward
diffusj.ng anomaly ca by ' uniform surface layers. This a.tte.iiuatri.on
is, however, a second order effect and can be neglected, if
at the considered frequency the widespread normal fieid pene-
trates the surface layers to any extent, i.e. if the modulus
of Q' is sufficiently close to unity.
The inverse problem: Assuming the anomalous body to be a uniform
cylinder, the model parameters zo,'R, cr can be uniquely in-
R
ferred from surface observations, providing the transfer func-
tions for H and FIaz are known for at least two locations and
aY
frequencies. For.ming here the ra-tios
the angles 8 and thereby the position- of the cylinder can be
found, The depth of the cylinder axis being kncwn; the dipole
moment RZf(n) can be calculated. Its argument fixes the size
of the induction parameter n and two determinations of nZ at z
different frequencies the radius R and -the conductivi-ty crz. NOW
R and zo being known, the field of the image dipole can be cal--
culated. The inverse procedure is repeated now with the observed
surface anomaly minus the field of the image dipole until con-.
vergence of the model parameters has been reached.
Interpretation with HIOT--SAVART1s law
. . ~
Let - f he the current density vector within a volume dV at the
Q n n h
point - r = (x, y, z). Then according to UZUT-SAVART1s law in SI
units -the magnetic fieled vector at: the point - r = (x, y , z) due
c'
to the line-current element idV is