Fourier method for inverse source problem using correlation of passive measurements

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Abstract

We consider the inverse source problem for a Cauchy wave equation with passive crosscorrelation data. We propose to consider the cross-correlation as a wave equation itself and reconstruct the cross-correlation in the support of the source for the original Cauchy wave equation. Having access to the cross-correlation in the support of the source, we use a Fourier method to reconstruct the source of the original Cauchy wave equation. We show the inverse source problem is ill-posed and suffer from non-uniqueness when the mean of the source is zero, and provide a uniqueness result and stability estimate in case of non-zero mean.
Original languageEnglish
Publication date2023
Publication statusPublished - 2023
Event11th Applied Inverse Problems Conference - Georg-August-Universität, Göttingen, Germany
Duration: 4 Sept 20238 Sept 2023

Conference

Conference11th Applied Inverse Problems Conference
LocationGeorg-August-Universität
Country/TerritoryGermany
CityGöttingen
Period04/09/202308/09/2023

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