Abstract

In borehole electromagnetics, both cylindrical and planar interfaces are present, leading to nonseparable field equations. The problem is two-dimensional (2-D), and the finite-element method is usually employed for solution.In this paper, the Generalized Haskell Matrix/Layer Eigenstate Propagator method is introduced to this class of problems. In the method, the solution problem is decomposed into a set of one-dimensional (1-D) problems, and then the 1-D solutions are combined to form the final solution. The method employs no approximation, other than discretization of a continuous system as in all computer methods.Induction logs are calculated for the 6FF40 tool and a number of models. Results agree well with those of the finite-element method. An important case in induction-log interpretation is studied; namely, a three-layer formation traversed by a borehole, the center layer being an oil-bearing (resistive) layer sandwiched between two conductive shoulder layers. Simulation shows that conventional correction methods ignoring borehole-bed coupling can lead to resistivities that differ from the true resistivities by a factor of 2 or even higher.

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