Numerical solutions for the electromagnetic response of a measurements-while-drilling (MWD) resistivity tool in a layered formation are developed. Because of the highly conductive mandrel on which the transmitter and receiver coils are mounted, the geometry of the problem is two-dimensional. To take advantage of the problem geometry, a boundary integral equation approach is initially applied for accurate evaluation. Then the problem is simplified to one-dimension by using the image current concept. This solution is equivalent to that of a vertical magnetic dipole in a layered medium, yielding significant savings in computer time. The tool responses calculated from the two methods match each other very closely, and the accuracy of both methods is verified. Correction charts are generated to correct the thin-bed response for shoulder bed effects.

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