Our analysis in this paper was limited to simple kinematics.
Before pronouncing the double-elliptic approximation
a success, we need to also demonstrate how it
works when used as the basis for an imaging technique;
i.e, how accurately does it model the *dynamics* of the wave
equation? Karrenbach (1991) examines this question in a companion paper.

Figure 4

Two different double-elliptic approximations (dashed curves) fit
to the *q*SV mode of Greenhorn Shale (solid curves).
Left: the approximation is fit in the impulse-response domain, and
so the dashed curve has a simple analytic form.
Right: the approximation is fit in the dispersion-relation domain, and
so is able to closely follow the triplication. This approximating
curve can only be calculated parametrically, however, and so is less useful.

Figure 5

Two different double-elliptic approximations (dashed curves) corresponding
to those in Figure , but this time fit
to the *q*P mode of Greenhorn Shale (solid curves). (The size of the
``*'' in the middle shows the relative scales.)
The discrepancy is much less since there are no troublesome triplications.

12/18/1997