Nonlinear Frechet derivative and its De Wolf approximation
Name
Wu - Zheng_Nonlinear Frechet.pdf+ref-2.pdf
Size
527.34 KB
Format
Adobe PDF
Checksum (MD5)
ac9849a5c9b6e9fe4d4460c4c807f353
Author(s)
Wu, Ru-Shan
Zheng, Yingcai
Date Issued
2012
Publisher
Massachusetts Institute of Technology. Earth Resources Laboratory
Series/Report no.
Earth Resources Laboratory Industry Consortia Annual Report;2012-26
Abstract
We introduce and derive the nonlinear Frechet derivative for the acoustic wave equation. It turns out that the high order Frechet derivatives can be realized by consecutive applications of the scattering operator and a zero-order
propagator to the source. We prove that the higher order Frechet derivatives are not negligible and the linear Frechet derivative may not be appropriate in many cases, especially when forward scattering is involved for large scale
perturbations. Then we derive the De Wolf approximation (multiple forescattering and single backscattering approximation) for the nonlinear Frechet derivative. We
split the linear derivative operator (i.e. the scattering operator) onto forward and backward derivatives, and then reorder and renormalize the nonlinear derivative series before making the approximation by dropping the multiple backscattering terms. Numerical simulations for a Gaussian ball model show significant difference between the linear and nonlinear Frechet derivatives.
Subjects
Scattering
Modeling
Persistent DSpace Link
