We demonstrate how we solve the two-point ray tracing problem in the presence of complex geological structures. For a point diffractor (PD) single-ray ray fan, we define surface-to-subsurface mapping (and vice versa) which maps the subsurface angles (take-off dips and azimuths) of individual traced rays to their surface locations. This mapping provides us with an interpolated ray for any subsurface angle or any surface location. We also introduce the reliability factor, which is based on a high-order interpolation technique in which we integrate several physical parameters calculated along the rays. This factor serves as a way of measuring the quality of the surface-to-subsurface mapping, and allows us to obtain a full ray (wave) field representation at any location, similar to wave equation methods. The same methodology is used for Common Reflection Point (CRP) specular ray pairs which are traced from a given subsurface location, with various opening angles and azimuths and a given reflector directivity, to the surface.
