A ray travel time wavefront represents a mathematical object called a manifold. In particular, paraxial ray theory contains elements that predict the Gaussian curvature of the wavefront surface. There are locations on this wavefront where the curvature is singular; in geometric optics terms, these are the ray caustic regions. These singular points or lines represent virtual sources. As such, the ray density in the neighborhood of these wavefront surface singularities must be large to model such sources. Conversely in regions of small curvature, the ray density can be low and still adequately represent the wavefront shape. These observations lead us to suggest new ray addition criteria for the wavefront construction algorithm: the distance between two neighboring rays must be less than the radius of wavefront curvature between these rays. This paraxial ray approximation insures that the angle between the neighboring ray slowness vectors is bounded and that the paraxial ray travel time estimate is valid for this interval. For velocity models where the projection of the wavefront upon the receiver plane is multi-valued, the paraxial ray method yields an elegant procedure to interpolate the resulting travel time and complex amplitude fields.