Types of Errors

The results of travel time computations with TTBOX will almost certainly be different from the values in the reference. For a proper interpretation, it is important to distinguish the types of errors which contribute to this difference:

1.) Reference Errors
These are all errors that may be contained in the reference data. Concerning the IASP91 travel time booklet, such errors may arise from the τ-spline interpolation method used to produce the tables. But the main source of reference error is the roundoff error: The IASP91 booklet gives travel times to only two decimal places (of seconds) which means that the tables are accurate within ±0.005s (the usual 4/5 roundoff means that t=0.01 represents all values from the interval 0.005≤t<0.0149).
2.) Hardware Errors
These are errors that are caused by the used computer system, mainly by the limited numerical resolution (32 or 64 bit?), but also by defective hardware (unlikely).
Errors of these kind can most probably be neglected. (All numerical errors are due to limited hardware resolution, but it's probably not important here if we use 32bit or 64bit hardware.)
3.) Software Errors
These are errors caused by properties of the software: mainly numerically poor formulation of computations, systematical biases due to algorithms, but also real bugs.
The goal of the validation is to determine these errors: it must be determined how large they are, and it would be nice to show that they are neglectible.
4.) Model Errors
Errors which are caused by poor descretization of the velocity model: e.g. using too few depth samples, using depth samples at unsuitable positions, or errors due to interpolation between depths samples.
These Errors can be tuned by varying the descretization parameters.
5.) Shooting Errors
TTBOX uses a shooting method to compute travel times. This requires knowledge of the take off angle at which a seismic ray must be shot to reach the desired epicentral distance. Via the ray parameter, an uncertainty in this angle is transformed into an error in the resulting travel time. TTBOX uses an optimization method to find the correct take off angle. Usually the desired epicentral distance is achieved within ±0.001° (the accuracy at which the optimization stops).

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