Motivated by questions arising in seismology the author studies an integral transform where a real valued function in \({\mathbb{R}}^ n\) is related to its integrals over spheres centered on a hyperplane. The author derives an inversion formula in two steps. First a so-called backprojection is performed, where averages are computed over all spheres passing through a point. The searched-for function is then determined by applying the Hilbert transform and a pseudo-differential operator on the backprojection. A Fourier transform version and the corresponding operator in spatial domain are given. The condition which is claimed to be the characterization of the range of the transform is only necessary but not sufficient. Finally two- and three-dimensional applications in seismology are discussed.