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Spring 2011 Seminars

Monday, April 11th, 2011
Inverse Problems Seminar
Speaker: Axel Osses, Center for Mathematical Modeling, University of Chile
Title: Inverse problems in lithospheric flexure and viscoelasticity        
Location: Amos Eaton Rm 436
Time: 4:00-4:55 PM

I present two different inverse problems linked to elasticity models. The first one (ref.[1]) concerns a problem for the determination of the variable Nazca plate thickness near the subduction trench on the chilean coast. The biharmonic linear plate equation with variable coefficients is used to model the flexure and the principal coefficient depends on the thickness. We discuss the one and two dimensional inverse problems and the connection with a bilaplacian Calderón type problem and some open problems. The second one (ref. [2]) concerns an inverse problem in 3d viscoelasticity, where we discuss a theoretical stability result when recovering the spatial part of a viscoelastic Lamé coefficients from boundary single measurements. The result can be obtained using Carleman inequalities in combination with the P-S wave decomposition and FBI transform. We show a numerical example of recovering the spatial dependence of a viscoelastic parameter in two dimensions. References [1] E. Contreras, A. Osses, Lithospheric flexure modeling seaward of the Chile trench: Implications for oceanic plate weakening in the Trench Outer Rise region, Geophysical Journal International, 182 (1), 97–112, 2010. [2] M. DeBuhan, A. Osses, Logarithmic stability in determination of a 3D viscoelastic coefficient and numerical examples, Inverse Problems, 26, 095006, 2010.


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