Reconstruction of a time-dependent potential from wave measurements. (23rd August 2017)

• Record Type: Journal Article
• Authors: Gerken, Thies; Lechleiter, Armin
• Is Part Of: Inverse problems. Volume 33:Number 9(2017:Sep.)
• Publication Date: 2017-08-23
• Subjects: dynamic inverse problems -- parameter identification -- wave equation with time-dependent parameter -- Fréchet-derivatives -- inexact newton regularization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa7e07
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We add a time-dependent potential to the inhomogeneous wave equation and consider the task of reconstructing this potential from measurements of the wave field. This dynamic inverse problem becomes more involved compared to static parameters, as, e.g. the dimensions of the parameter space do considerably increase. We give a specifically tailored existence and uniqueness result for the wave equation and compute the Fréchet derivative of the solution operator, for which also show the tangential cone condition. These results motivate the numerical reconstruction of the potential via successive linearization and regularized Newton-like methods. We present several numerical examples showing feasibility, reconstruction quality, and time efficiency of the resulting algorithm.