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The spectral Lanczos decomposition method gives a very efficient finite-difference solution of Maxwell’s equations in the diffusive limit. We have adapted this method to simulate borehole induction logging with an array tool used in oil and gas exploration. The tool has a magnetic point dipole transmitter operating at several frequencies and receiver dipoles located at different distances from the transmitter. Numerical examples show that effects of the borehole, invasion, and eccentricity of the tool in the hole are important to the proper interpretation of real logs.

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