  The vertical slice transform takes a function on the n-dimensional unit
sphere to integrals of that function over spherical slices parallel to the last
coordinate axis. This transform arises in thermoacoustic tomography. We obtain
new inversion formulas for the vertical slice transform and its singular value
decomposition. The results can be applied to the inverse problem for the
Euler-Poisson-Darboux equation associated to the corresponding spherical means.
