Smooth inversion of induction logs for conductivity models with mud filtrate invasion

A robust, efficient method of inversion of induction logging data for smooth 2-D models, appropriate to an environment in which mud filtrate invades flat‐lying layers, is described. An infinite number of solutions exist to the problem of determining a conductivity structure from a finite number of imprecise induction data. Therefore, the inverse problem is regularized such that the smoothest model is sought subject to the condition that the resulting computed log agrees with the field log to a given preset level. At each iteration, the Jacobian sensitivities are approximated using the distorted Born approximation. In most cases, the algorithm converges in 3 to 4 iterations. The resulting maximally smooth models reflect the resolution power of the induction data and are unlikely to result in overinterpretation of the data. Inversion of both synthetic and field data indicates that layer boundaries are well resolved but radial boundaries are poorly resolved by conventional induction logging data.