In this project we have developed a parametric inversion algorithm
to simultaneously determine the horizontal conductivities, vertical
conductivities, bed boundary positions and dip angle from tri-axial
induction logging data in anisotropic layered media. The inversion
algorithm was first solved in an infinite homogeneous medium to
obtain a good initial-guess model.The variance-based method was
used to locate initial bed boundaries. The inversion problem has
been solved by the method of least squares using the constrained
Gauss-Newton minimization approach. Two globally convergent
strategies based on a robust and efficient version of the
Levenberg-Marquardt algorithm were implemented. The line-search
algorithm was incorporated which guarantees a reduction in the cost
function after each iteration.In the inversion algorithm a
non-linear transformation has been incorporated to impose bounds on
the unknown model parameters. To speed up the computation, the
Jacobian was determined analytically for the whole space inversion.
Boundary-merger routines were added to further accelerate the
inversion procedure. The results show that the reconstructed model
is consistent with the true model.
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