FMM home page FMM Method Examples in continuous media Examples in layered media FMM movies


In the following examples, velocity fields are parameterized in terms of bicubic B-splines. Interfaces are parameterized in terms of cubic B-splines. Thus, any spacing can be chosen for the numerical grid on which the FMM is solved. Ray paths can be obtained a posteriori by following the traveltime gradient from the receiver back through the medium to the source.

In the example below, a reflected wavefront is tracked through a heterogeneous medium from a source point located at the surface. Note that the ray paths all reflect from the anticlinal structures contained in the interface.

The bottom plot below shows the convergence of traveltimes for four different grid sizes towards a reference solution calculated on a 50 m grid (described by a total of 1602801 nodes). The four grid sizes are 1000 m (4141 nodes), 500 m (16281 nodes), 250 m (64561 nodes) and 125 m (257121 nodes). CPU times (for a Sun Ultra 5) are also provided.

The next example demonstrates that the new FMM scheme is capable of tracking wavefronts that experience multiple transmissions and reflections in a highly heterogeneous layered medium that includes two layer pinchouts. The schematic diagram below shows the six reflection branches that comprise the complete phase.

Wavefronts corresponding to each of the six branches are illustrated below. Note colour coding and labelling used to associate the wavefront plots with the phase segments in the above diagram.

Finally, we illustrate two representative ray paths. Note that even though these paths are of the same phase, their geometries are very different.


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