A general relation between a normal-moveout velocity (NMOV) for t-x (time-offset) reflection curves and the geometrical properties of a reflector and a wavefront in the vicinity of the reflector has been found. Furthermore, by considering the reflector as a set of zero-offset reflecting points for different shot locations on the earth's surface, a new formulation of the special 'seismic' parametric description of a reflecting surface allows the arrival times to be related directly to the wavefront equation, without introducing any earth model above the reflector. The NMOV is expressed in terms of the local velocity near the reflector and the curvatures of the reflector and of the near-reflector wavefront. New equations for geometrical migration make it possible to do direct wavefront modeling without earth modeling (above the reflector). If t-x curves are approximated by hyperbolas (i.e., terms higher than those quadratic in the offsets are neglected), all rays in a common-midpoint (CMP) panel with a fixed midpoint have the same reflecting point, for any earth model.