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arXiv · 2403.08450

Increasing stability for inverse source problem with limited-aperture far field data at multi-frequencies

Ibtissem Ben Aïcha·Guanghui Hu·Suliang Si
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Abstract

We study the increasing stability of an inverse source problem for the Helmholtz equation from limited-aperture far field data at multiple wave numbers. The measurement data are givenby the far field patterns $u^\infity(\hat{x},k)$ for all observation directions in some neighborhood of a fixed direction $\hat{x}$ and for all wave numbers k belonging to a finite interval $(0,K)$. In this paper, we discuss the increasing stability with respect to the width of the wavenumber interval $K>1$. In three dimensions we establish stability estimates of the $L^2$-norm and $H^{-1}$-norm of the source function from the far field data. The ill-posedness of the inverse source problem turns out to be of H\"older type while increasing the wavenumber band K. We also discuss an analytic continuation argument of the far-field data with respect to the wavenumbers at a fixed direction.

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Ibtissem Ben Aïcha, Guanghui Hu, Suliang Si. 2024-03-13. Increasing stability for inverse source problem with limited-aperture far field data at multi-frequencies. https://arxiv.org/abs/2403.08450

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