In classical travel time tomography, seismic signals are approximated in the high frequency limit. In wave equation tomography methods, the problem is reformulated in the finite bandwidth sense. Although this inverse problem is nonlinear, it is usually approached in the linearized sense, with the help of either Rytov or Born approximations. In this study, we introduce the asymptotic ray + Born and ray + Rytov formalisms. Notwithstanding its ability to provide computationally efficient methods to model seismic scattering, the introduction of wave asymptotics allows simple geometrical interpretations of Born and Rytov integrals. It also allows qualitative discussion of their respective validity domains, and to identify the principal sources of errors and artefacts. It results that validity conditions for Born and Rytov linearizations are very different. In particular, forward scattering due to spatially extended slowness perturbations is correctly accounted for by Rytov summation (in terms of both wave kinematics and amplitudes), whereas Born approximation clearly fails. Numerical tests with diverse perturbations provide insights on the effects of nonlinearity, and illustrate the role of Rytov summation as a 'slowness smoothing operator' accounting for the actual source bandwidth.

Date Published: 28 October 1996
PDF: 18 pages
Proc. SPIE 2822, Mathematical Methods in Geophysical Imaging IV, (28 October 1996); doi: 10.1117/12.255204

Published in SPIE Proceedings Vol. 2822:
Mathematical Methods in Geophysical Imaging IV
Siamak Hassanzadeh, Editor(s)