Concept of Validation

The validation follows a quite simple approach: take some reference travel times from some standard source and compute travel times for the same velocity model, seismic phase, focal depth and epicentral distances as given in that reference. The absolute deviation between reference and computed values is a measure for the quality of the program. The references used in the following tests are described in the section on reference data.

The procedure is implemented in routine MKTTBOXVALID. Phase name, focal depth, vertical discretization interval for the velocity model, path to the velocity model and path to the reference data file are input parameters of this routine. You can study how the error decreases when the vertical discretization gets finer.

I have chosen to test P and S wave travel times because these are very important for earthquake localization. Additionally, PKIKP and SKIKS have been chosen because rays that travel through the inner core may get very close to the coordinate singularity of the flat earth transform, what makes the computation of these phases close to 180° difficult.

Only surface foci are considered, because I do not think that deeper foci would give significant new information for the validation problem. But it would be easy to include deeper foci into the test procedure - one simply has to produce a reference data file for the desired depth.

At distances where triplications occur, only the earliest of the two or three possible onsets is used, although TTBOX returns all solutions.

MKTTBOXVALID creates three plots: the absolute difference between computed and reference travel time, the computed and reference travel times as travel time curves and the shooting error, which shows how good TTBOX estimated the ray parameter needed to arrive at the given epicentral distance.


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