  We consider the application of the magnetic flux leakage (MFL) method to the
detection of defects in ferromagnetic (steel) tubulars. The problem setup
corresponds to the cases where the distance from the casing and the point where
the magnetic field is measured is small compared to the curvature radius of the
undamaged casing and the scale of inhomogeneity of the magnetic field in the
defect-free case. Mathematically this corresponds to the planar ferromagnetic
layer in a uniform magnetic field oriented along this layer. Defects in the
layer surface result in a strong deformation of the magnetic field, which
provides opportunities for the reconstruction of the surface profile from
measurements of the magnetic field. We deal with large-scale defects whose
depth is small compared to their longitudinal sizes---these being typical of
corrosive damage. Within the framework of large-scale approximation, analytical
relations between the casing thickness profile and the measured magnetic field
can be derived.
