Method of and apparatus for determining variations in wall thickness in ferromagnetic tubes

A method can include energizing a tube with a longitudinally extending magnetic field generated inside the tube, using a magnetic field-detecting logging tool to generate magnetic flux signals generated inside the tube externally of the material of the tube wall resulting from such energizing at circumferential locations on the inner surface of the tube and at distances along the tube, iteratively using a model of the relationship between the generated magnetic flux signals and the thickness of the tube wall to derive a thickness profile of the tube wall by using (i) the magnetic permeability of the tube material deduced from the magnetic flux signals and (ii) a defect-free flux parameter representative of any non-linearity between the magnetic field strength and flux density in the tube, the iteration including using the model to calculate an initial approximate wall thickness profile using an initial estimate of the defect-free flux parameter.