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The solution of a multi-frequency 1d inverse medium problem consists ofrecovering the refractive index of a medium from measurements of the scatteredwaves for multiple frequencies. In this paper, rigorous stability estimates arederived when the frequency takes value in a bounded interval.It is showed thatthe ill-posedness of the inverse medium problem decreases as the width of thefrequency interval becomes larger. More precisely, under certain regularityassumptions on the refractive index, the estimates indicate that the power inH\"older stability is an increasing function of the largest value in thefrequency band. Finally, a Lipschitz stability estimate is obtained for theobservable part of the medium function defined through a truncated traceformula.

Stability for the multifrequency inverse medium problem