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Applied Math Seminar: Numerical solution to the linearized travel time tomography problem with incomplete data

Speaker: Loc Nguyen (Univ. North Carolina at Charlotte)

Abstract: The travel time tomography is the problem of reconstructing the speed of the acoustics/seismic waves from their first time of arrival. This highly nonlinear problem is still open. In this talk, we propose a new numerical method to solve its linearization with incomplete data. Our method is based on the technique of the truncation of the Fourier series with respect to a special basis of $L^{2}$. By this, we derive a boundary value problem for a system of coupled partial differential equations of the first order. Solutions to this system are the spatially dependent Fourier coefficients of the solution to the linearized Eikonal equation.  We solve this system by the quasi-reversibility method in the finite difference scheme. Numerical results for highly noisy data are presented.

Zoom link will be sent out on Wednesday (Oct 22)

Thursday, October 22 at 4:00pm to 5:00pm

Event Type

Lecture, Colloquia, Seminar

Department
Mathematics, Department of
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