Computer Programs in Seismology Validation

Isotropic model test

The travel time routines actually use plane layered travel time techniques. The computations differ from those used for earthquake location because the source and receiver can be at an arbitrary depth in the velocity model. The travel time routines compute the first arrival time for the specific phase. Since the velocity model is very general, special cases must be considered:

direct arrival between source and receiver in the same layer
direct arrival between source and receiver in different layers. The travel time is determined by an iterative technique that searches for the ray parameter that describes the geometric ray.
refracted arrival from layers below or above both the source and the receiver.

The codes also permit a spherical velocity model. An Earth flattening approximation is applied.

Test 1 - Comparison

We compare the program predictions for the "AK135" continental model to those from the TauP Toolkit. The following files are used: DOTAUP (which invokes the Toolkit program taup_time), the Computer Program in Seismology AK135 velocity model file tak135sph.mod and the test script DOTT. The output is given in DOTT.out. An extract of the output is

GCARC  EVDP    P(taup)     P(CPS)                 S(taup)     S(CPS)
---------------------------------------------------------------------------------
    1    10      19.40      19.23 (      0.17)      32.61      32.24 (      0.37)
    2    10      33.83      33.76 (      0.07)      58.90      58.77 (      0.13)
    3    10      47.58      47.46 (      0.12)      83.58      83.34 (      0.24)
.................................................................................
   80    10     729.50     729.24 (      0.26)    1333.53    1333.05 (      0.48)
   90    10     779.71     779.45 (      0.26)    1432.65    1410.12 (     22.53)
  100    10      -1.00     825.11 (   -826.11)    1520.05    1463.68 (     56.37)
  110    10      -1.00     869.90 (   -870.90)      -1.00    1508.96 (  -1509.96)
  120    10      -1.00     914.70 (   -915.70)      -1.00    1547.15 (  -1548.15)
  130    10      -1.00     959.49 (   -960.49)      -1.00    1578.60 (  -1579.60)
  140    10      -1.00    1004.29 (  -1005.29)      -1.00    1603.67 (  -1604.67)
---------------------------------------------------------------------------------

The columns are great circle arc (degrees), source depth (km), taup_time P-wave travel time for a surface receiver, the CPS time96 P-wave travel time. the difference between the two, followed by similar columns for the S-wave time. The comparison is very good. At larger distances the CPS P-time is actually Pdiff and the S-wave time is SKS.

Test 2 - Travel times of direct P and S

The next test focuses on the use of a reference depth in the computations. The reference depth concept was introduced to facilitate placing an atmosphere on top of an elastic Earth model. If the initial layer thickenesses are negative, the layers are assumed to be above the zero-depth datum. With this approach one can continue to have the specification -HS 0 to represent a receiver at the surface. The script DOTREFDEP compares the time96 travel time predictions fo P, SV and SH for the models tak135sph.mod (continental AK135h model), Ttak135sph.mod (AK135h with a very thick first layer), Ftak135sph.mod (the AK135h model, but with the model treated as a flat-Earth rather than a spherical Earth; this model serves to test the progrma for a flat model, and FTtak135sph.mod (the Fak135sph.mod to test the reference depth). The results are given in DOTREFDEP.out

The first few lines of output of this script are

Model: tak135sph.mod
GCARC  EVDP    TP(sec) p(P)(s/km)      T*(P)   TSV(sec) p(SV)(s/km)    T*(SV)   TSH(sec) p(SH)(s/km)    T*(SH)
--------------------------------------------------------------------------------------------------------------
    1   700      80.56       0.02       0.33     146.21       0.03       0.98     146.21       0.03       0.98
    2   700      83.11       0.03       0.34     150.86       0.05       1.01     150.86       0.05       1.01
    3   700      87.18       0.04       0.36     158.26       0.08       1.06     158.26       0.08       1.06
   30   700     316.88       0.08       0.73     569.80       0.14       2.06     569.80       0.14       2.06
   60   700     542.59       0.06       1.00     984.57       0.11       2.85     984.57       0.11       2.85
   90   700     707.88       0.04       1.33    1273.61       0.05       2.81    1303.85       0.08       3.82
--------------------------------------------------------------------------------------------------------------
Model: Ttak135sph.mod
GCARC  EVDP    TP(sec) p(P)(s/km)      T*(P)   TSV(sec) p(SV)(s/km)    T*(SV)   TSH(sec) p(SH)(s/km)    T*(SH)
--------------------------------------------------------------------------------------------------------------
    1   700      80.56       0.02       0.33     146.21       0.03       0.98     146.21       0.03       0.98
    2   700      83.11       0.03       0.34     150.86       0.05       1.01     150.86       0.05       1.01
    3   700      87.18       0.04       0.36     158.26       0.08       1.06     158.26       0.08       1.06
   30   700     316.88       0.08       0.73     569.80       0.14       2.06     569.80       0.14       2.06
   60   700     542.59       0.06       1.00     984.57       0.11       2.85     984.57       0.11       2.85
   90   700     707.88       0.04       1.33    1273.61       0.05       2.81    1303.85       0.08       3.82
--------------------------------------------------------------------------------------------------------------

The columns here are the P, SV and SH travel time, ray parameter and T* (assuming a frequency independent T* operator). You will notice that the SV time at 90 degrees is actually that of SKS while that of SH is actually S

Test 3 - Travel times of pP and sP

The next test focuses on the use of a reference depth in the computations. The reference depth concept was introduced to facilitate placing an atmosphere on top of an elastic Earth model. If the initial layer thickenesses are negative, the layers are assumed to be above the zero-depth datum. With this approach one can continue to have the specification -HS 0 to represent a receiver at the surface. The script pPDOTREFDEP compares the time96 travel time predictions fo P, SV and SH for the models tak135sph.mod (continental AK135h model), Ttak135sph.mod (AK135h with a very thick first layer), Ftak135sph.mod (the AK135h model, but with the model treated as a flat-Earth rather than a spherical Earth; this model serves to test the progrma for a flat model, and FTtak135sph.mod (the Fak135sph.mod to test the reference depth). The results are given in pPDOTREFDEP.out

The first few lines of output of this script are

Model: tak135sph.mod
GCARC  EVDP   TpP(sec) p(pP)(s/km)    T*(pP)   TsP(sec) p(sP)(s/km)    T*(sP)
---------------------------------------------------------------------------------
   30   700  -12345.00  -12345.00  -12345.00  -12345.00  -12345.00  -12345.00
   40   700     509.97       0.08       1.68     589.12       0.08       2.20
   60   700     671.66       0.07       1.73     744.85       0.06       2.33
   90   700     854.06       0.04       1.96     922.24       0.04       2.60
---------------------------------------------------------------------------------
Model: Ttak135sph.mod
GCARC  EVDP   TpP(sec) p(pP)(s/km)    T*(pP)   TsP(sec) p(sP)(s/km)    T*(sP)
---------------------------------------------------------------------------------
   30   700  -12345.00  -12345.00  -12345.00  -12345.00  -12345.00  -12345.00
   40   700     509.97       0.08       1.68     589.12       0.08       2.20
   60   700     671.66       0.07       1.73     744.85       0.06       2.33
   90   700     854.06       0.04       1.96     922.24       0.04       2.60
---------------------------------------------------------------------------------
Model: Ftak135sph.mod
GCARC  EVDP   TpP(sec) p(pP)(s/km)    T*(pP)   TsP(sec) p(sP)(s/km)    T*(sP)
---------------------------------------------------------------------------------
   30   700  -12345.00  -12345.00  -12345.00  -12345.00  -12345.00  -12345.00
   40   700     542.28       0.09       1.86     625.95       0.09       2.34
   60   700     741.83       0.09       2.03     822.90       0.09       2.56
   90   700    1023.82       0.08       2.33    1101.69       0.08       2.91
---------------------------------------------------------------------------------
Model: FTtak135sph.mod
GCARC  EVDP   TpP(sec) p(pP)(s/km)    T*(pP)   TsP(sec) p(sP)(s/km)    T*(sP)
---------------------------------------------------------------------------------
   30   700  -12345.00  -12345.00  -12345.00  -12345.00  -12345.00  -12345.00
   40   700     542.28       0.09       1.86     625.95       0.09       2.34
   60   700     741.83       0.09       2.03     822.90       0.09       2.56
   90   700    1023.82       0.08       2.33    1101.69       0.08       2.91
---------------------------------------------------------------------------------

The -12345 indicates that there is no depth phase at the distance for the given source depth.