A special case of spontaneous potential (SP) logging, which has a closed-form solution, will be expressed as a convolutional operation. Such a formal demonstration serves two purposes. First, it separates the individual contribution of the tool from that of the earth. Second, it places this logging device within the mathematical context of signal analysis. The special case for which a closed-form solution is known is that where all resistivities are equal. Fourier analysis applied to this solution leads to a product of two functions, of which one is identified as the contribution of the earth and the other of the tool.

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