Stochastic inversion approach to measurement of tube properties using remote field technique

The remote field technique for the measurement of the oil-well casing properties (thickness, magnetic permeability, and conductivity) is ill-posed. A very low measurement uncertainty, on the order of 100 ppm, is required to resolve the individual casing properties. Only lumped parameters (casing factor and permeability-to-conductivity ratio) can be obtained using the optimization approach. We present a stochastic formulation of the inverse problem, which results in the joint posterior probability distribution of the casing properties. We examine a relationship between the measurement uncertainties of the magnetic field and casing properties, and we show that the results of the stochastic inversion are more informative than the lumped parameters obtained using the optimization approach.