A deviation of about 0.05s between TTBOX traveltimes and the IASP91 Booklet is somewhat unsatisfactory. I have tried several modifications of my code in order to reduce the total number of mathematical operations (especially addition/subtraction). I have also investigated the possibility that the shooting error of 0.001° might be too large. These Experiments yielded differences in the results of about 10-13s or less, which may be neglected.
In order to get an idea what might be the source of the observed deviations I have computed travel times using two other programs.
The two other programs are
Both onset and TauP Toolkit use the method of Buland & Chapman (1983), which computes travel times by interpolation of the τ(p) curve, with τ(p)=Traveltime(p)-pΔ(p). The TauP Toolkit is a completely independent implementation of that method and contains some modifications: The flat earth transformation is avoided by converting the original method into one for spherical media, and linear interpolation between slowness samples is used (at least in the version described by Crotwell et al., 1999) instead of the spline interpolation suggested by Buland & Chapman.
The τ(p) function is computed using an integral equation wich is different from the ray path and travel time integrals used in TTBOX, so the numerics involved is also different.
The travel times computed with these programs are also contained in the data directory of the TTBOX distribution (see section on Reference Data).
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Comparison of P and PKPdf traveltime deviations from the reference data for programs TTBOX
, onset and TauP Toolkit. The curves for 50km sampling in TTBOX are covered by the legend, but are
the same as in the section on TTBOX travel time errors. (label at the y-axis should read "|T(computed)-T(booklet)|") (Plot as PDF) |
The above image shows a comparison of onset (red dotted) and TauP Toolkit (magenta) travel times with the reference times from the IASP91 Booklet. Within roundoff error, onset essentially reproduces the reference data (although the deviation for PKIKP is a little high). The TauP Toolkit deviations, on the other hand, are highly similar to the TTBOX deviations for sufficiently good depth sampling. What is especially intriguing is that the variation of deviation with distance is the same for TTBOX and TauP Toolkit.
The step-like structure of the TauP-curve probably originates in an accumulation of roundoff error: the reference data is rounded to 0.01s, and the TauP output is also rounded to 0.01s, so the difference between the two must be an integer multiple of 0.01s.
The scatter in the onset-curve originates in an ccumulation of roundoff error. onset returns travel times that are corrected for ellipticity (see files in the data directory). The ellipticity correction contained in the output is rounded. J. Schweitzer has compared the uncorrected travel times with the IASP91 booklet and found that onset reproduces them exactly.