A heterogeneous example

Figure 3 shows a heterogeneous model example. The left and top parts of the model are isotropic (the same elastic constants as the isotropic example in Figure 2), while the block to the right is anisotropic with ${\hbox{\rm C}}_{11} = .75$,${\hbox{\rm C}}_{33} = .75$,${\hbox{\rm C}}_{55} = .225$, and ${\hbox{\rm C}}_{13} = 0.$.(This is just a slower version of the ``strongly anisotropic'' medium in Figure 2.)

Along the top edge of the anisotropic block in Figure 3 (marked by the horizontal dashed line), the wavefronts correctly refract into the anisotropic block. Inside the anisotropic block, the waves correctly start to triplicate. Along the left edge of the anisotropic block, however, something strange happens. The wave inside the block starts out slightly faster than the direct wave in the isotropic part of the model. Towards the bottom of the block the direct isotropic arrival becomes faster. This is not strange; it is a correct result of the anisotropy in the model. What is disturbing is that the contoured traveltimes do not show the fastest arrivals, but the ``direct'' arrivals. There should be waves refracting across the vertical boundary; instead the wavefronts on either side have become decoupled.