Modelling and inversion of seismic data in anisotropic elastic media

Abstract

Seismic data is modeled in the high frequency limit We consider general anisotropic media and our method is also valid in the case of multipathing caustics The data is modeled in two ways First using the Kirchho approximation where the medium is assumed to be piecewise smooth and reection and transmission occurs at the interface Secondly the data is modeled using the Born approximation in other words by a linearization in the medium parameters The main result is a characterisation of seismic data We construct a Fourier integral operator and a reectivity function which is a function of subsurface position and scattering angle and azimuth such that the data is given by the invertible ourier integral operator acting on the reectivity function Using this new transformation of seismic data to subsurface position angle coor dinates we obtain the following results on the problem of reconstructing the medium coecients Given the medium above the interface in the Kirchho approximation one can reconstruct the position of the interface and the angular dependent reection coecients on the interface We also obtain a criterium to determine whether the medium above the interface the background medium in the Born approximation is correctly chosen These results are new in medium with caustics In the Born approximation the singular medium perturbation can be reconstructed