Аннотация
A mathematical model of the well resistivity-sounding problem is investigated. The model leads to an inverse problem of identification of the unknown coefficient (conductivity) in an elliptic equation in R2 inside a cylinder. The forward problem is formulated as a mixed BVP in axisymmetric cylindrical coordinates. Measured data along the axis of the well are assumed to be available. Owing to the ill-conditioned nature of the inverse problem, a logarithmic transformation is applied to the unknown coefficient, and the inverse problem is studied as a minimization problem for the residual functional. For the radial electrical-sounding case, an effective numerical method is proposed for interpreting the data of a well sounding. The method is implemented for realistic conductivity distributions, with both noise-free and noisy data.