The runs here are based on a South African event, but the travel times have been adjusted to give zero error for arrivals based on spherical-earth ray tracing using the iasp91 traveltime tables for the assumed focal depth (2.47 km) and epicenter. The epicentral distances were gotten from a Hypoellipse run with a fixed hypocenter. (Hypoellipse uses spherical-earth geometry when calculating epicentral distances.) The times were calculated using program ttimes, and the output is given in ./sample-runs/ttimes-mine.txt.

The flat-earth iasp91 model contained in ./sample-runs/crustal-iasp-prm is simply the iasp91.mod given in directory ./build-tables except that the upper mantle has been broken into several constant-velocity layers. (This does not matter here, as the Moho heasdwave appears to be the only down-going ray used for these distances.)

To run with tables only requires changing the station list entries so that model 26 is the preferred model (rather than model 1). File ./sample-runs/stations-tab.dat has been written so that tables only are used. If one wants to use tables beyond a fixed epicentral distance, one uses ./sample-runs/stations.dat and change control parameter 51 to a distance which will be the transition between the flat-earth model and the spherical-earth tables. One can see exactly which model (or table) was used for each station and phase by looking in the Hypoellipse .out file at the entry for that station and phase under "c" in the traveltimes and delays section.

As discussed in the SRL paper by Snoke and Lahr, for calculated arrival times based on flat-earth raytracing, there is a systematic error which increases with distance. This can be seen by looking at "resid" in the traveltimes and delays sections in the different .out files. For this example for P-wave arrivals using flat-earth ray tracing (iaspvz.out), there is an error of at most 0.01 s for distances up to 135.7 km, but between 171 and 500 km, the flat-earth error increases from 0.1 to 0.33 seconds.

The method used here for calculating the spherical-earth travel times within Hypoellipse does not work well near the crossover distance (148 km for the P arrival in this case), but for 171 km and greater distances, the table calculations differ by at most 0.01 seconds (iasptab.out). For this example, at the epicentral distance of 135.7 km the "tables-only" output has an error of 0.05 and 0.03 seconds for P and S respectively. Also, the "ain" (which is the take-off angle from the source measured with respect to the upward vertical) are clearly wrong. For the flat-earth-model version, the errors are only 0.01 s for both arrivals and the values for ain are reasonable. The explanation for this discrepancy is that flat-earth raytracing is still okay at this distance, but the interpolation scheme used for tables in the earthquake location programs does not properly take into account the first-order discontinuity in the ray parameter which occurs at the crossover distance (see the "Take-Off Ang" entries for the first arrivals in the file ttimes-crossover.txt). Note that for this focal depth and the iasp91 velocity model, the P and S crossovers differ by about 8.5 km — 148.2 km for P, 156.7 km for S.

Because the flat-earth raytracing is still adequate at the crossover distance, the problem with the tables at this distance can be solved by using the flat-earth raytracing up to the crossover and the tables for distances beyond the crossover. As written, one needs to set manually control parameter 51 to that distance. This is what is done in the run leading to output file iasptabmod.out and summary file iasptabmod.summary. For that run, none of the arrival time errors are greater than 0.01 s.

The files (with their most recent modification dates) in directory ./sample-runs are as follows:

Modif.  date    name                    comment
Mar 11  2000    970721084549p-fixed     arrival times: Hypoe input
Mar 11  2000    crustal-iasp.prm        iasp91 velocity model: Hypoe input
Mar 11  2000    driver-iasptab          hypoe options: uses tables only
Mar 12  2000    driver-iasptabmod       hypoe options: table beyone 160 km
Mar 11  2000    driver-iaspvz           hypoe options: v-z model only
Apr 27  2002    iasptab.out             hypoe output: tables only
Apr 27  2002    iasptab.summary         hypoe run summary and .sum: tables
Apr 27  2002    iasptabmod.out          hypoe output: tables > 160 km
Apr 27  2002    iasptabmod.summary      hypoe run summary: tables > 160 km
Apr 27  2002    iaspvz.out              hypoe out: v-z model only
Apr 27  2002    iaspvz.summary          hypoe run summary: v-z model only
Mar 12  2000    rHypoe*                 script for running all three cases
Mar 11  2000    rHypoe-model*           script for running models only
Mar 11  2000    rHypoe-table*           script for running tables or mixed
Nov 24  2000    stations-tab.dat        stations file for tables only
Nov 23  2000    stations.dat            stations file for v-z model or mixed
May  9  2002    ttimes-crossover.txt    ttimes output near crossover Zero depth
May  9  2002    ttimes-mine.txt         ttimes output to check hypotable output