HR: 14:25h
AN: S33E-04 INVITED    [Abstracts]
TI: A multi-scale approach to imaging and Frechet derivatives in wave-equation tomography
AU: * De Hoop, M V
EM: mehoop@purdue.edu
AF: Purdue University Mathematics, Center for Computational and Applied, West Lafayette, IN 047907, United States
AU: Van der Hilst, R D
EM: hilst@mit.edu
AF: Massachusetts Institute of Technology, Earth, Atmospheric, and Planetary Sciences, Cambridge, MA 02139, United States
AU: Salo, M
AF: University of Helsinki, Department of Mathematics and Statistics, Helsinki, 11111, Finland
AU: Brytik, V
AF: Purdue University Mathematics, Center for Computational and Applied, West Lafayette, IN 047907, United States
AU: Smith, H
AF: University of Washington, Department of Mathematics, Seattle, WA 098195, United States
AU: Uhlmann, G
AF: University of Washington, Department of Mathematics, Seattle, WA 098195, United States
AB: We discuss a common (PDE) framework for wave-equation transmission and reflection tomography. The development of the associated imaging procedures and optimization, via adjoint states, involves the Frechet derivatives of the solution operators modelling the different types of data. We present the principles of a multi- scale approach to constructing these Frechet derivatives, using curvelets, in velocity models of limited smoothness. The Frechet derivatives would directly appear in the adjoint state formulation based on `fitting' the data, but here we focus on different functionals for optimization, the sensitivity kernels of which can be viewed as generalizations of their ray-geometric counterparts. We discuss commonalities with the multi-scale decomposition of linearized inverse scattering with the generalized Radon transform. The constructions can be naturally integrated with sparsity constrained optimization via multi-scale representations of the model perturbation.
DE: 7260 Theory
DE: 7270 Tomography (6982, 8180)
DE: 7290 Computational seismology
SC: Seismology [S]
MN: 2007 Fall Meeting