The Two-Parameter Approximation to Seismic Reflection Traveltimes

The seismic reflection traveltime curves are complicated, and depend on many parameters. There is a need for simplified equations involving a reduced number of parameters that can be estimated from data and used for moveout correction and velocity model building. Many authors have derived explicit equations for traveltime as a function of offset, involving several parameters depended on velocity. Some authors have also applied the approach in which velocity varies with offset. Here we present a new approach in which the velocity variation with depth or vertical travel time instead of offset. A simple linear variation of velocity is used to derive expressions for traveltime and offset as a function of ray parameter. Only two parameters are involved in defining the velocity depth profile, which leads to an implicit traveltime equation depending on only two parameters. However, the resulting traveltime-offset curves are very accurate for both short and long offsets. Alternatively, a two-parameter equation involving linear variations of slowness with depth or vertical travel time can also be obtained. Both the velocity and slowness expressions can be used for velocity analysis and moveout correction. Synthetic records are used to demonstrate their effectiveness.