Wavefront sets of solutions to linearised inverse scattering problems

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Abstract
A certain integral operator T, which arises in some linearised inverse scattering problems, is shown to be a pseudodifferential operator and its points of ellipticity are explicitly described. Consequently for the equation Tf=g, one can find the relationship between the wavefront sets of f and g. From this viewpoint a class of algorithms called the migration schemes and used extensively in geophysics for imaging the Earth's interior can be understood clearly.