The inverse problem of the direct current conductivity profile of a layered earth

We present a direct (noniterative) inversion algorithm for the determination of the conductivity profile of a layered earth from the measurements of the apparent resistivity with the Schlumberger array. The necessary conditions for the existence of a one‐dimensional (1-D) continuous conductivity profile are determined, and the uniqueness of the solution is proved for complete and precise data. Examples are given in which the conductivity profile is determined from analytical data, incomplete and imprecise artificial data, and raw field data.