DIFFRACTION AND SEISMIC TOMOGRAPHY

Diffraction tomography is formulated in such a way that the data (traveltime-or waveform perturbations) are related to the medium perturbations through the sum of two terms. The first term is the ray integral of ordinary tomography and involves only phase perturbations. The additional diffraction term involves both phase and amplitude perturbations. The diffraction term is linear in the gradients of the velocity perturbation in an acoustic medium, the gradients of the elastic and density perturbations in an elastic medium, and the gradients of the boundary perturbations the wave is crossing. This formulation has the additional advantage that unwanted diffractions from the non-physical boundary of the region under study can be easily removed. Acoustic scattering, elastic scattering, and scattering by boundary perturbations are analysed separately. Attention is paid to the adequacy of the acoustic approximation, and to the difference between perturbations of a boundary level (topography) and perturbations of boundary conditions. These differences are irrelevant for ordinary seismic tomography. All results are based on first-order approximations (Born or Rytov), as is the case for other published methods of diffraction tomography.