f A Pertubation technique for travel time computation with FD-Eikonal solvers

The theory of first order perturbation is well known and commonly used in classical ray tracing techniques. Desired quantities in a perturbed medium are calculated along rays which propagate through a reference medium. Reference and perturbed medium differ only slightly. First order traveltime perturbation can be used, e.g., for pre-stack Kirchhoff-type migration. In general in migration the correct subsurface model is unknown. Therefore, a simultaneous migration with several macro models should be performed. The results can be used for velocity estimation techniques. The time consuming procedure of computing traveltimes from sources to all subsurface points is performed directly only in one model. For the other slightly deviating models the traveltimes are computed efficiently by perturbation. Moreover, most of the recently developed methods for fast computation of traveltimes are designed for isotropic media. For Kirchhoff-type migration of data from anisotropic media perturbation techniques provide a fast way to compute diffraction surfaces for slightly anisotropic media where the reference medium is isotropic. Here existing tools to compute traveltimes in isotropic media can be used. For highest computational speed we implemented the perturbation formulas into Vidale's method (Vidale, 1988) and call it FD-perturbation method.