Increasing stability for inverse source problem with limited-aperture far field data at multi-frequencies
arxiv(2024)
摘要
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^(x̂,k) for all observation directions in some neighborhood of a
fixed direction x̂ 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 Hölder 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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