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Simultaneous one-dimensional inversion of loop-loop
electromagnetic data for both magnetic susceptibility
and electrical conductivity

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Colin G. Farquharson, Douglas W. Oldenburg & Partha S. Routh.

[Submitted to GEOPHYSICS.]

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ABSTRACT

Magnetic susceptibility affects electromagnetic loop-loop observations in ways that
cannot be replicated by conductive, non-susceptible Earth models.
The most distinctive effects are negative inphase values at low frequencies.
Inverting data ``contaminated'' by susceptibility effects for conductivity alone
can give misleading models: the observations strongly influenced by susceptibility
will be under-fit, and those less strongly influenced will be over-fit to compensate,
leading to artifacts in the model.
Simultaneous inversion for both conductivity and susceptibility enables reliable
conductivity models to be constructed, and can give useful information about the
distribution of susceptibility in the Earth.
Such information complements that obtained from the inversion of static magnetic data
because electromagnetic measurements are insensitive to remanent magnetization.
We present the capabilities of an algorithm that simultaneously inverts
susceptibility-affected data for one-dimensional conductivity and susceptibility models.
The solution is obtained by minimizing an objective function comprising a sum-of-squares
measure of data misfit and sum-of-squares measures of the amounts of structure in
the conductivity and susceptibility parts of the model.
Positivity of the susceptibilities is enforced by including a logarithmic barrier
term in the objective function.
The trade-off parameter is automatically estimated during the course of an
inversion using the GCV criterion.
This enables an appropriate fit to the observations to be achieved even
if good noise estimates are not available.
As well as synthetic examples, we show the results of inverting airborne
data-sets from Australia and Heath Steele Stratmat, New Brunswick.

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Last update: 26 October 2001.
Colin Farquharson
(farq@geop.ubc.ca)