A generalized Haskell matrix method for borehole electromagnetics: Theory and applications

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.