paul sava


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© 2007 PC Sava

Page updated on
April 1, 2018

Huygens wavefront tracing


Traveltime computation is widely used in seismic modeling, imaging and tomography. The two most commonly used methods are ray tracing and numerical solutions to the eikonal equation. Eikonal solvers are fast and robust, but limited to computing only the first arrival traveltimes. Ray tracing can compute multiple arrivals, but lacks the robustness of eikonal solvers.

An alternative method of traveltime computation is equivalent to a numerical solution to the eikonal equation, but formulated in a ray coordinate system. A first-order discretization of this equation is simply interpreted in terms of the Huygens principle. A new wavefront is computed from the current wavefront using an explicit finite difference scheme, thus the name "Huygens wavefront tracing". This method is different from wavefront construction, since it involves a straight finite difference solution in ray coordinates. In contrast, wavefront construction is computing new wavefronts using ray tracing in Cartesian coordinates.

The two frames below depict a finite frequency wavefront computed with time-domain finite-differences. The wavefront is overlain on the smoothed velocity model. The second frame depicts the equivalent wavefront computed by Huygens wavefront tracing. It shows good match with the finite difference wavefront, both at the first and at the later arrivals. The density of points on the wavefront is a good indication of the amplitude of the waves.

References

Sava, P.C., Fomel, S., 2001, 3-D traveltime computation using Huygens wavefront tracing, Geophysics, v. 66, no. 3, pp. 883-889. (PDF)

Figures can be used freely for non-profit educational purposes by acknowledging their source:
© Paul Sava, Center for Wave Phenomena, Colorado School of Mines
http://www.mines.edu/~psava