We have developed a fast and accurate dynamic raytracing method for 2.5-D heterogeneous media based on the kinematic algorithm proposed by Langan et al. (1985). This algorithm divides the model into cells of constant slowness gradient, and the positions, directions, and travel times of the rays are expressed as polynomials of the travel path length, accurate to the second other in the gradient. This method is efficient because of the use of simple polynomials at each raytracing step.
We derived similar polynomial expressions for the dynamic raytracing quantities by integrating the raytracing system and expanding the solutions to the second order in the gradient. This new algorithm efficiently computes the geometrical spreading, amplitude, and wavefront curvature on individual rays. The two-point raytracing problem is solved by the shooting method using the geometrical spreading. Paraxial corrections based on the wavefront curvature improve the accuracy of the travel time and amplitude at a given receiver.
The computational results for two simple velocity models are compared with those obtained with the SEIS83 seismic modeling package (Cerveny and Psencik, 1984); this new method is accurate for both travel times and amplitudes while being significantly faster. We present a complex velocity model that shows that the algorithm allows for realistic models and easily computes rays in structures that pose difficulties for conventional methods. The method can be extended to raytracing in 3-D heterogeneous media and can be used as a support for a Gaussian beam algorithm. It is also suitable for computing the Green's function and imaging condition needed for prestack depth migration.