The significance of crustal effects
The fundamental weakness in the Bondar method is in dealing with the crust. At the 1999 OSlo workshop on IMS station location calibration, Istvan Bondar pointed out that crustal effects could introduce errors of +-1.2 seconds. These errors of course depend on the size of variations between different regions.

We show here for a simple model containing two regions with different traveltime curves, Bondar's method may produce errors equal to half the difference in traveltimes. For example, if the difference in predicted traveltime between two regions is 4 seconds, we find that in some situations Bondar's method can be off by nearly 2 seconds when compared with 3-D raytracing methods.

The example at right shows a world comprised of just two geographic regions. The crust in the upper left corner is slower than the rest. At mantle depths the model is identical everywhere. The traveltime curves for slow and fast crust regions are shown in gray. The red curves shows Bondar's distance-weighted traveltime prediction. It diverges from the first traveltime curve after crossing the boundary between regions and assumptotically approaches the second traveltime curve. However, raytracing through this model reveals a very different behavior. Rays which travel through both regions have traveltimes mid-way between each curve, regardless of range. Each ray makes one pass through the slow and fast crust.

This is the dominant error introduced by the distance-weighted traveltime approach. This figure demonstrates how errors can be generated equal to half the difference between the traveltimes of each region.

Summary: The crust at source and receiver are equally significant regardless of how much of the ray path falls in each region.

A more complex example of this has been observed prior to this study in the case of sources in India being recorded north of Tibet. Much of this ray path lies in Tibet. Paths solely in Tibet can be late by up to 7 s due to the thick crust. Bondar's approach to India-to-Kahzakstan paths predicts late arrivals because much of the path lies in Tibet. Yet real data does not show a drastic delay for this path. This is because the only crust sampled by the ray lies outside Tibet.

Mantle variation is less important
The same test be performed introducing variations only in the mantle. While there is some descrepancy between the distance-weighted method and ray theoretical predictions, the error is much smaller than for crustal variations. Since rays cross the boundary at mantle depths, the length of the ray path in each region is essentially a function of the distance to the boundary between regions.

Real situations may be more complex than the crust or mantle variations discussed here. However, these examples illustrate the end member possibilities.