Abstract：Tomography is an inverse problem of integral geometry. Tomography has three essential properties: (1)it is an inverse problem, and produces physical model by making inversion of observation data; (2)observation data are correlated with the physical model by performing integration, in other words, observation data must be expressed as the integration of the physical model; (3)it must use a curves(or curved surfaces) as its integral manifold, and it deals with what integral manifold condition allows us to determine a function itself from the functional integration over the manifold. Tomography can be subclassed into linear anal nonlinear ones. The linear-nonlinear classification of tomograplly is similar to that of integral equation. CT technique in medical diagnostics belongs in linear tomography. Traveltime inversion (interval velocity) in seismic exploration belongs in nonlinear tomography, In iteration, nonlinear tomography can be usually reduced into linear tomography, which, therefore, is an important problem in theoretical and practical studies. Linear tomography mainly involves forward and inverse Radon transforms. It will be very valuable in theory and practice that we research into generalized forward and inverse Radon transforms by adopting Fourier integral operator, and inversely solve for singularity of transformed function by using micro partial analysis theory of Fourier integral operator. The purpose of migration is to inversely solve for the singularity (interrupted surface of interval velocity) of wave equation coefficient, However, the present migration (wave field continuation) aims at inversely solving for the singularity of wave equation solution There is no definite correlation between solution singularity and coefficient singularity, The generalized Radon transform and the singularity inversion provide a new opproach for inversely solving for the singularity (migration) of wave equation coefficient.
