Inverse Backscattering Problem for the Acoustic Equation in Even Dimensions

We show that the sound speedc(x) of the acoustic wave equation in any even dimension can be uniquely determined by the backscattering data provided that it is close to a constant. In the three-dimensional case, P. Stefanov and G. Uhlmann (SIAM J. Math. Anal.28,1997, 1191–1204) have proved a similar result. Their method takes advantage of the inversion formula for the Radon transform in odd dimensions being a local operator. This is not true in even dimensions. Moreover, the odd-dimensional Lax and Phillips modified Radon transform fails to work in even dimensions. In this paper, we overcome these difficulties and prove an even-dimensional version of Stefanov and Uhlmann's result.