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Borehole Resistivity Inversionby Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on April 15, 1997 in partial fulfillment of the requirements for the degree of Doctor of Philosophy ABSTRACT
In this thesis we develop a procedure for performing the inversion of borehole
resistivity data using the software package developed by Western Atlas Logging
Services, Houston, TX. Direct current resistivity methods, named lateral sounding
and conventional laterolog methods, are the main interests in this thesis.
In resistive formations drilled with a conductive mud, where induction methods
are not logged, it becomes imperative to combine these two methods in order
to provide a reliable solution to the inversion problem. Lateral sounding
provides comprehensive information about the resistivity distribution away
from the borehole, while the higher resolution of the laterolog allows for
detailed delineation of the formation.
Computationally, the inversion is performed using the constrained least-squares
Marquardt algorithm combined with singular value decomposition. The nonlinear
inversion problem is linearized after each iteration of the Marquardt method.
One of the main benefits of the algorithm is its ability to incorporate all
resistivity/conductivity methods into a unique solution that is able to explain
and satisfy all measurements. Several levels of inversion analysis are considered,
from one-dimensional inversion to a rigorous and comprehensive two-dimensional
approach. With the two-dimensional approach, the data need not be corrected
for borehole and shoulder bed effects.
We demonstrate the method with multiple synthetic examples in which the algorithm
successfully recovers the formation parameters. Different noise levels, resistivity
contrasts, depths of invasion, and initial guesses are considered. The method
is then applied to field data consisting of lateral sounding logs and laterologs.
The inversion results provide the resistivity variation away from the borehole.
In most cases, the true to invaded zone resistivity ratio and the depth of
invasion clearly indicate the layers with the best reservoir properties. In
general, the field data inversion results agree very well with the available
perforation data.
Return to Theses Return to ERL Home Updated: April, 1999
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