Conclusions

We demonstrate the utility of a ray-based Riemannian wavefield extrapolation method using an adaptive bootstrap approach to calculate the ray-coordinate system directly from the wavefield. This bootstrap procedure allows for frequency-dependent ray-coordinate systems to be computed on-the-fly from the wavefield phase gradient and the velocity model. Coupling this procedure with RWE leads to a general frequency-dependent extrapolation procedure capable of following a wavefront as it propagates, overturns, and even triplicates. We propose that in locations where the ray-coordinate system triplicates, the Jacobian spreading and other required functions may be calculated by cutting the triplication into its constituent branches and using appropriate one-sided finite difference stencils. The full proof of this conjecture, though, remains a topic of future research.