The effects of the infinite depth of the flat earth model are also visible in the shape of travel time curves. The causes for the distortions are the same as for the ray geometry: linear approximation is not sufficient at great depth if the sample distance is large. But in travel time curves, they become visible more clearly.
The general shape of the PKP triplication is reproduced if the velocity model is sampled with 100km sample distance in spherical coordinates, but the steeper the rays are, the more erroneous the resulting traveltimes become. The loops in the traveltime curve are all artefacts of the poor sampling.
The computation of the reference curve in tha above plot with an 1km sampling in flat earth coordinates took about 2h on a 3GHz PC (0.01deg steps in takeoff angle are quite small), which ist why one cannot always use the finest possible sampling.
A sampling with 100km sample distance in flat earth coordinates produces significantly better results, but a closeup reveals that it is still contaminated by the effects of the vertical stretching applied by the flat earth transformation.
A 10km sampling in flat earth is necessary to overcome the problem (with IASP91). With 10km sampling, the computation takes 7.5min instead of 2h. (yes, Iknow it's still slow. That's the disadvantage of MatLab)