Using the geometrical ray theory and employing the second-order approximation of the traveltimes, a method to determine the interval velocities of a seismic system is presented. Ignoring faults and other complexities, the seismic system is modeled as a stack of isotropic and homogeneous layers separated by arbitrarily-curved smooth interfaces; the velocity and density of these layers may have any values. Measuring the traveltimes of some specially selected reflected rays, recorded in multiple coverage on the upper border olthe seismic system, the so called Hamilton's point characteristic for reflected events is determined and in consequence the zero-offset diffraction time function is calculated. The interval velocities are calculated through the downward continuation of the zero-offset diffraction time function applying an iterative process layer by layer. This process is controlled by using a focusing principle