Model ak135-F


The ak135 velocity model has been augmented with a density and Q model by combining the study of travel times with those of free oscillations.

The attached velocity and density model is the product of two pieces of work.


(1) The velocity model below 120 km depth comes from the work of

Kennett B.L.N., Engdahl E.R. & Buland R. (1995)
Constraints on seismic velocities in the earth from travel times Geophys. J. Int, 122, 108-124

The original continental structure for the uppermost layering is given at the end of the file.

This model probably gives a reasonable representation of spherically averaged structure below 760 km depth - the upper mantle as in iasp91 is an artificial construct which gives a good fit to the ensemble of observed times out to 30 degrees. The structure in D" should also be regarded as representative.

The representation of the velocity model is via pointwise values in velocity and linear interpolation in radius was used as the basis of the travel time calculations - note that unlike iasp91 this is not a parameterised model. Any suitable interpolation scheme may be used where appropriate.

A software conversion is available for reading velocity models into the iasp travel time software and ellipticity corrections have been constructed for all the phases represented by that software.

(2) Modified density and Q models come from a study by

Montagner J.P. & Kennett B.L.N. (1995)
How to reconcile body-wave and normal-mode reference Earth models? Geophys. J. Int., 125, 229-248

This study introduces a density model and Q to the velocity distribution from the travel time work to try to fit observations of free oscillation frequencies. An averaged uppermost structure is imposed on the ak135 velocities.

The version of the model represented here is isotropic, even though the paper investigates the inclusion of anisotropy as well.

The complex density structure in the upper mantle with a density inversion reflects the absence of a low velocity zone in the wavespeed model. For a spherical average either a low shear wave zone or a low density zone is needed to match the free oscillation frequencies. the Q values are those needed to bring the 1 Hz travel time velocities into a match with the free oscillations and also give a good fit to observed Q values for the normal modes.

NB: The upper mantle density model should be treated with caution and may well change with further work

Model ak135-f


Velocity model for travel times (continental structure)
    Depth     density   P vel      S vel    Q kappa     Q mu  
      km       Mg/km3   km/s       km/s 

     0.000              5.8000     3.4600     
    20.000              5.8000     3.4600      
    20.000              6.5000     3.8500     
    35.000              6.5000     3.8500      
    35.000              8.0400     4.4800      
    77.500              8.0450     4.4900      
   120.000              8.0500     4.5000      

Spherical average structure
    Depth     density   P vel     S vel    Q kappa     Q mu
      km       Mg/km3    km/s     km/s
      0.00    1.0200    1.4500    0.0000  57822.00      0.00     0.000
      3.00    1.0200    1.4500    0.0000  57822.00      0.00     0.000
      3.00    2.0000    1.6500    1.0000    163.35     80.00     0.000
      3.30    2.0000    1.6500    1.0000    163.35     80.00     0.000
      3.30    2.6000    5.8000    3.2000   1478.30    599.99     0.000
     10.00    2.6000    5.8000    3.2000   1478.30    599.99     0.000
     10.00    2.9200    6.8000    3.9000   1368.02    599.99     0.000
     18.00    2.9200    6.8000    3.9000   1368.02    599.99     0.000
     18.00    3.6410    8.0355    4.4839    950.50    394.62     0.000
     43.00    3.5801    8.0379    4.4856    972.77    403.93     0.000
     80.00    3.5020    8.0400    4.4800   1008.71    417.59     0.000
     80.00    3.5020    8.0450    4.4900    182.03     75.60     0.000
    120.00    3.4268    8.0505    4.5000    182.57     76.06     0.000

120.00 3.4268 8.0505 4.5000 182.57 76.06 0.000 165.00 3.3711 8.1750 4.5090 188.72 76.55 0.000 210.00 3.3243 8.3007 4.5184 200.97 79.40 0.000 210.00 3.3243 8.3007 4.5184 338.47 133.72 0.000 260.00 3.3663 8.4822 4.6094 346.37 136.38 0.000 310.00 3.4110 8.6650 4.6964 355.85 139.38 0.000 360.00 3.4577 8.8476 4.7832 366.34 142.76 0.000 410.00 3.5068 9.0302 4.8702 377.93 146.57 0.000 410.00 3.9317 9.3601 5.0806 413.66 162.50 0.000 460.00 3.9273 9.5280 5.1864 417.32 164.87 0.000 510.00 3.9233 9.6962 5.2922 419.94 166.80 0.000 560.00 3.9218 9.8640 5.3989 422.55 168.78 0.000 610.00 3.9206 10.0320 5.5047 425.51 170.82 0.000 660.00 3.9201 10.2000 5.6104 428.69 172.93 0.000 660.00 4.2387 10.7909 5.9607 1350.54 549.45 0.000 710.00 4.2986 10.9222 6.0898 1311.17 543.48 0.000 760.00 4.3565 11.0553 6.2100 1277.93 537.63 0.000 809.50 4.4118 11.1355 6.2424 1269.44 531.91 0.000 859.00 4.4650 11.2228 6.2799 1260.68 526.32 0.000 908.50 4.5162 11.3068 6.3164 1251.69 520.83 0.000 958.00 4.5654 11.3897 6.3519 1243.02 515.46 0.000 1007.50 4.5926 11.4704 6.3860 1234.54 510.20 0.000 1057.00 4.6198 11.5493 6.4182 1226.52 505.05 0.000 1106.50 4.6467 11.6265 6.4514 1217.91 500.00 0.000 1156.00 4.6735 11.7020 6.4822 1210.02 495.05 0.000 1205.50 4.7001 11.7768 6.5131 1202.04 490.20 0.000 1255.00 4.7266 11.8491 6.5431 1193.99 485.44 0.000 1304.50 4.7528 11.9208 6.5728 1186.06 480.77 0.000 1354.00 4.7790 11.9891 6.6009 1178.19 476.19 0.000 1403.50 4.8050 12.0571 6.6285 1170.53 471.70 0.000 1453.00 4.8307 12.1247 6.6554 1163.16 467.29 0.000 1502.50 4.8562 12.1912 6.6813 1156.04 462.96 0.000 1552.00 4.8817 12.2558 6.7070 1148.76 458.72 0.000 1601.50 4.9069 12.3181 6.7323 1141.32 454.55 0.000 1651.00 4.9321 12.3813 6.7579 1134.01 450.45 0.000 1700.50 4.9570 12.4427 6.7820 1127.02 446.43 0.000 1750.00 4.9817 12.5030 6.8056 1120.09 442.48 0.000 1799.50 5.0062 12.5638 6.8289 1108.58 436.68 0.000 1849.00 5.0306 12.6226 6.8517 1097.16 431.03 0.000 1898.50 5.0548 12.6807 6.8743 1085.97 425.53 0.000 1948.00 5.0789 12.7384 6.8972 1070.38 418.41 0.000 1997.50 5.1027 12.7956 6.9194 1064.23 414.94 0.000 2047.00 5.1264 12.8524 6.9416 1058.03 411.52 0.000 2096.50 5.1499 12.9093 6.9625 1048.09 406.50 0.000 2146.00 5.1732 12.9663 6.9852 1042.07 403.23 0.000 2195.50 5.1963 13.0226 7.0069 1032.14 398.41 0.000 2245.00 5.2192 13.0786 7.0286 1018.38 392.16 0.000 2294.50 5.2420 13.1337 7.0504 1008.79 387.60 0.000 2344.00 5.2646 13.1895 7.0722 999.44 383.14 0.000 2393.50 5.2870 13.2465 7.0932 990.77 378.79 0.000 2443.00 5.3092 13.3017 7.1144 985.63 375.94 0.000 2492.50 5.3313 13.3584 7.1368 976.81 371.75 0.000 2542.00 5.3531 13.4156 7.1584 968.46 367.65 0.000 2591.50 5.3748 13.4741 7.1804 960.36 363.64 0.000 2640.00 5.3962 13.5311 7.2031 952.00 359.71 0.000 2690.00 5.4176 13.5899 7.2253 940.88 354.61 0.000 2740.00 5.4387 13.6498 7.2485 933.21 350.88 0.000 2740.00 5.6934 13.6498 7.2485 722.73 271.74 0.000 2789.67 5.7196 13.6533 7.2593 726.87 273.97 0.000 2839.33 5.7458 13.6570 7.2700 725.11 273.97 0.000 2891.50 5.7721 13.6601 7.2817 723.12 273.97 0.000 2891.50 9.9145 8.0000 0.0000 57822.00 0.00 0.000 2939.33 9.9942 8.0382 0.0000 57822.00 0.00 0.000 2989.66 10.0722 8.1283 0.0000 57822.00 0.00 0.000 3039.99 10.1485 8.2213 0.0000 57822.00 0.00 0.000 3090.32 10.2233 8.3122 0.0000 57822.00 0.00 0.000 3140.66 10.2964 8.4001 0.0000 57822.00 0.00 0.000 3190.99 10.3679 8.4861 0.0000 57822.00 0.00 0.000 3241.32 10.4378 8.5692 0.0000 57822.00 0.00 0.000 3291.65 10.5062 8.6496 0.0000 57822.00 0.00 0.000 3341.98 10.5731 8.7283 0.0000 57822.00 0.00 0.000 3392.31 10.6385 8.8036 0.0000 57822.00 0.00 0.000 3442.64 10.7023 8.8761 0.0000 57822.00 0.00 0.000 3492.97 10.7647 8.9461 0.0000 57822.00 0.00 0.000 3543.30 10.8257 9.0138 0.0000 57822.00 0.00 0.000 3593.64 10.8852 9.0792 0.0000 57822.00 0.00 0.000 3643.97 10.9434 9.1426 0.0000 57822.00 0.00 0.000 3694.30 11.0001 9.2042 0.0000 57822.00 0.00 0.000 3744.63 11.0555 9.2634 0.0000 57822.00 0.00 0.000 3794.96 11.1095 9.3205 0.0000 57822.00 0.00 0.000 3845.29 11.1623 9.3760 0.0000 57822.00 0.00 0.000 3895.62 11.2137 9.4297 0.0000 57822.00 0.00 0.000 3945.95 11.2639 9.4814 0.0000 57822.00 0.00 0.000 3996.28 11.3127 9.5306 0.0000 57822.00 0.00 0.000 4046.62 11.3604 9.5777 0.0000 57822.00 0.00 0.000 4096.95 11.4069 9.6232 0.0000 57822.00 0.00 0.000 4147.28 11.4521 9.6673 0.0000 57822.00 0.00 0.000 4197.61 11.4962 9.7100 0.0000 57822.00 0.00 0.000 4247.94 11.5391 9.7513 0.0000 57822.00 0.00 0.000 4298.27 11.5809 9.7914 0.0000 57822.00 0.00 0.000 4348.60 11.6216 9.8304 0.0000 57822.00 0.00 0.000 4398.93 11.6612 9.8682 0.0000 57822.00 0.00 0.000 4449.26 11.6998 9.9051 0.0000 57822.00 0.00 0.000 4499.60 11.7373 9.9410 0.0000 57822.00 0.00 0.000 4549.93 11.7737 9.9761 0.0000 57822.00 0.00 0.000 4600.26 11.8092 10.0103 0.0000 57822.00 0.00 0.000 4650.59 11.8437 10.0439 0.0000 57822.00 0.00 0.000 4700.92 11.8772 10.0768 0.0000 57822.00 0.00 0.000 4751.25 11.9098 10.1095 0.0000 57822.00 0.00 0.000 4801.58 11.9414 10.1415 0.0000 57822.00 0.00 0.000 4851.91 11.9722 10.1739 0.0000 57822.00 0.00 0.000 4902.24 12.0001 10.2049 0.0000 57822.00 0.00 0.000 4952.58 12.0311 10.2329 0.0000 57822.00 0.00 0.000 5002.91 12.0593 10.2565 0.0000 57822.00 0.00 0.000 5053.24 12.0867 10.2745 0.0000 57822.00 0.00 0.000 5103.57 12.1133 10.2854 0.0000 57822.00 0.00 0.000 5153.50 12.1391 10.2890 0.0000 57822.00 0.00 0.000 5153.50 12.7037 11.0427 3.5043 633.26 85.03 0.000 5204.61 12.7289 11.0585 3.5187 629.89 85.03 0.000 5255.32 12.7530 11.0718 3.5314 626.87 85.03 0.000 5306.04 12.7760 11.0850 3.5435 624.08 85.03 0.000 5356.75 12.7980 11.0983 3.5551 621.50 85.03 0.000 5407.46 12.8188 11.1166 3.5661 619.71 85.03 0.000 5458.17 12.8387 11.1316 3.5765 617.78 85.03 0.000 5508.89 12.8574 11.1457 3.5864 615.93 85.03 0.000 5559.60 12.8751 11.1590 3.5957 614.21 85.03 0.000 5610.31 12.8917 11.1715 3.6044 612.62 85.03 0.000 5661.02 12.9072 11.1832 3.6126 611.12 85.03 0.000 5711.74 12.9217 11.1941 3.6202 609.74 85.03 0.000 5762.45 12.9351 11.2041 3.6272 608.48 85.03 0.000 5813.16 12.9474 11.2134 3.6337 607.31 85.03 0.000 5863.87 12.9586 11.2219 3.6396 606.26 85.03 0.000 5914.59 12.9688 11.2295 3.6450 605.28 85.03 0.000 5965.30 12.9779 11.2364 3.6498 604.44 85.03 0.000 6016.01 12.9859 11.2424 3.6540 603.69 85.03 0.000 6066.72 12.9929 11.2477 3.6577 603.04 85.03 0.000 6117.44 12.9988 11.2521 3.6608 602.49 85.03 0.000 6168.15 13.0036 11.2557 3.6633 602.05 85.03 0.000 6218.86 13.0074 11.2586 3.6653 601.70 85.03 0.000 6269.57 13.0100 11.2606 3.6667 601.46 85.03 0.000 6320.29 13.0117 11.2618 3.6675 601.32 85.03 0.000 6371.00 13.0122 11.2622 3.6678 601.27 85.03 0.000