The induction logging problem is solved for a two-coil sonde in a borehole surrounded by a bedding sequence which varies arbitrarily in the vertical direction. The solution is based on parallel computation of 500-1 000 m of log data. Both the R and X components of the voltage log are modeled. The problem is solved in the spatial-frequency domain in which a transfer function relates the anomalous borehole voltage for a two-coil sonde to the conductivity spectrum of the formation, resulting in a natural extension of Doll's geometric factor theory. This computationally compact formulation does not require matrices and is designed as a computer aid for log analysts. The mathematical method (with proper conditioning) can efficiently solve the inverse problem of transforming the voltage induced in the receiving coil to a formation conductivity log. This paper establishes the forward method. Numerical results are given for beds of finite thickness for both brine- and oil-base muds. The Fourier method is in good agreement with both a finite-element method and a semi-analytic method.

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