John Washbourne

Wave tracing: Ray tracing for the propagation of band-limited signals: Part 2 — Applications

Modeling seismic propagation is critically important to our work; unfortunately, we often must trade simulation accuracy for reduced computational expense. We present a new seismic-modeling method that is as simple and computationally efficient as Snell’s law ray tracing but provides propagation paths and arrival times more consistent with finite-bandwidth data. We refer to this modeling method as wave tracing and apply it to nonlinear traveltime tomography and depth imaging. By replacing Snell’s law ray tracing with wave tracing, we get better ray coverage, more robust and faster ray bending (fewer iterations), and a much more robust and faster algorithm for nonlinear tomography (fewer iterations, too). A very significant benefit is increased stability and robustness of tomographic inversion with respect to small changes in model parameterization and regularization. A related benefit is the increased stability of depth images with respect to small changes in velocity, which can increase confidence in int...

Wave tracing: Ray tracing for the propagation of band-limited signals: Part 1 — Theory

Many seismic imaging techniques require computing traveltimes and travel paths. Methods to compute raypaths are usually based on high-frequency approximations. In situations such as head waves, these raypaths minimize traveltime but are not paths along which most of the energy travels. We have developed a new approach to computing raypaths, using a modification of ray bending that we call wave tracing; it computes raypaths and traveltimes that are more consistent with the paths and times for the band-limited signals in real data than the paths and times obtained using high-frequency approximations. Wave tracing shortens the raypath while keeping the raypath within the Fresnel zone for a characteristic frequency of the signal.