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.
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.
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.
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
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