  We study integral transforms mapping a function on the Euclidean space to the
family of its integration on some hypersurfaces, that is, a function of
hypersurfaces. The hypersurfaces are given by the graphs of functions with
fixed axes of the independent variables, and are imposed some symmetry with
respect to the axes. These transforms are higher dimensional version of
generalization of the parabolic Radon transform and the hyperbolic Radon
transform arising from seismology. We prove the inversion formulas for these
transforms under some vanishing and symmetry conditions of functions.
