next up previous [pdf]

Next: Acknowledgments Up: Alkhalifah and Fomel: Source Previous: Discussion


The behavior of the traveltime field shape as a function of source location in an inhomogeneous medium provides a platform for many useful applications. We present eikonal-based equations that relate traveltime field changes with respect to the source perturbations. These equations are linear first-order differential equations that depend on the background traveltime and velocity fields. Their solutions describe the first- and second-order changes in the traveltime field as a function of the source location. These equations are equivalent to the plane wave expansion extracted from dynamic ray tracing, such as the one used for Gaussian-beam migration. They can be solved efficiently by finite-difference solvers on a regular grid. The solutions are used to estimate the traveltime shape for neighboring sources. The accuracy of the equations depends on the complexity of lateral velocity variations as well as on the source perturbation distance.