 0914 Balgaisha Mukanova Murat Orunkhanv
 Inverse resistivity problem: geoelectric uncertainty principle and
numerical reconstruction method
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Jan 30, 09

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Abstract. Mathematical model of
vertical electrical sounding by using resistivity method is
studied. The model leads to an inverse problem of determination
of the unknown leading coefficient (conductivity) of the elliptic
equation in $R^2$ in a slab. The direct problem is obtained in the
form of mixed BVP in axisymmetric cylindrical coordinates. The
additional (available measured) data is given on the upper
boundary of the slab, in the form of tangential derivative. Due to
illconditionedness of the considered inverse problem the
logarithmic transformation is applied to the unknown coefficient
and the inverse problem is studied as a minimization problem for
the cost functional, with respect to the reflection coefficient.
The Conjugate Gradient (CGM) method is applied for the numerical
solution of this problem. Computational experiments were performed
with noise free and random noisy data.
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