Wave-equation tomography-II , by F. Rocca and Marta J. Woodward

Using simple geometrical techniques, we analyze the Fourier spectrum of the backprojection of an acoustical wavefield generated by a point source and recorded by a point geophone. We show that the spatial width of the backprojection, in the seismic range of frequencies (the width of the seismic ray), is not negligible so that it is useful to consider the effects of dispersion due to lateral inhomogeneities of the medium. We then show the correspondence between bandpassed traveltimes analysis and the Rytov approximation; finally, we analyze the null space of the extended traveltimes inversion and find that it is dependent on the time windowing of the reflected arrivals.


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