Step 3: Global phases.
In this section you will use the Preliminary Reference Earth Model (PREM) to get a better idea of global P phase arrival times. PREM is a radial model, that means that the velocities only change as a function of depth (radius). To be able to calculate travel times that are appropriate for PREM we should use the spherical ray parameter. Instead, we will use a script in which the PREM model is modified using the Earth Flattening Transformation. We simulate the spherical model with a stack of layers whose thicknesses and velocities have been adjusted so that the travel times that we calculate will be (close to) correct. The most important difference between horizontal layered models and spherical models is that some rays never arrive back to the surface in a horizontally layered model, whereas all rays eventually end up at the surface in a spherical model. To accomplish this, the Earth flattening approximation highly exaggerates the depths and velocities near the center of the Earth.
Table 2. PREM Preliminary Reference Earth Model. z = depth, r = radius, Vp = P wave velocity, Vs = S wave velocity, rho = density, and P = pressure.
| z(km) | r(km) | Vp(km/s) | Vs(km/s) | rho(g/cc) | P(GPa) |
| 0.0 | 6371.0 | 1.45 | 0.00 | 1.02 | 0.0 |
| 3.0 | 6368.0 | 1.45 | 0.00 | 1.02 | 0.0 |
| 3.0 | 6368.0 | 5.80 | 3.20 | 2.60 | 0.0 |
| 15.0 | 6356.0 | 5.80 | 3.20 | 2.60 | 0.3 |
| 15.0 | 6356.0 | 6.80 | 3.90 | 2.90 | 0.3 |
| 24.4 | 6346.6 | 6.80 | 3.90 | 2.90 | 0.6 |
| 24.4 | 6346.6 | 8.11 | 4.49 | 3.38 | 0.6 |
| 71.0 | 6300.0 | 8.08 | 4.47 | 3.38 | 2.2 |
| 80.0 | 6291.0 | 8.08 | 4.47 | 3.37 | 2.5 |
| 80.0 | 6291.0 | 8.08 | 4.47 | 3.37 | 2.5 |
| 171.0 | 6200.0 | 8.02 | 4.44 | 3.36 | 5.5 |
| 220.0 | 6151.0 | 7.99 | 4.42 | 3.36 | 7.1 |
| 220.0 | 6151.0 | 8.56 | 4.64 | 3.44 | 7.1 |
| 271.0 | 6100.0 | 8.66 | 4.68 | 3.47 | 8.9 |
| 371.0 | 6000.0 | 8.85 | 4.75 | 3.53 | 12.3 |
| 400.0 | 5971.0 | 8.91 | 4.77 | 3.54 | 13.4 |
| 400.0 | 5971.0 | 9.13 | 4.93 | 3.72 | 13.4 |
| 471.0 | 5900.0 | 9.50 | 5.14 | 3.81 | 16.0 |
| 571.0 | 5800.0 | 10.01 | 5.43 | 3.94 | 19.9 |
| 600.0 | 5771.0 | 10.16 | 5.52 | 3.98 | 21.0 |
| 600.0 | 5771.0 | 10.16 | 5.52 | 3.98 | 21.0 |
| 670.0 | 5701.0 | 10.27 | 5.57 | 3.99 | 23.8 |
| 670.0 | 5701.0 | 10.75 | 5.95 | 4.38 | 23.8 |
| 771.0 | 5600.0 | 11.07 | 6.24 | 4.44 | 28.3 |
| 871.0 | 5500.0 | 11.24 | 6.31 | 4.50 | 32.8 |
| 971.0 | 5400.0 | 11.42 | 6.38 | 4.56 | 37.3 |
| 1071.0 | 5300.0 | 11.58 | 6.44 | 4.62 | 41.9 |
| 1171.0 | 5200.0 | 11.73 | 6.50 | 4.68 | 46.5 |
| 1271.0 | 5100.0 | 11.88 | 6.56 | 4.73 | 51.2 |
| 1371.0 | 5000.0 | 12.02 | 6.62 | 4.79 | 55.9 |
| 1471.0 | 4900.0 | 12.16 | 6.67 | 4.84 | 60.7 |
| 1571.0 | 4800.0 | 12.29 | 6.73 | 4.90 | 65.5 |
| 1671.0 | 4700.0 | 12.42 | 6.78 | 4.95 | 70.4 |
| 1771.0 | 4600.0 | 12.54 | 6.83 | 5.00 | 75.4 |
| 1871.0 | 4500.0 | 12.67 | 6.87 | 5.05 | 80.4 |
| 1971.0 | 4400.0 | 12.78 | 6.92 | 5.11 | 85.5 |
| 2071.0 | 4300.0 | 12.90 | 6.97 | 5.16 | 90.6 |
| 2171.0 | 4200.0 | 13.02 | 7.01 | 5.21 | 95.8 |
| 2271.0 | 4100.0 | 13.13 | 7.06 | 5.26 | 101.1 |
| 2371.0 | 4000.0 | 13.25 | 7.10 | 5.31 | 106.4 |
| 2471.0 | 3900.0 | 13.36 | 7.14 | 5.36 | 111.9 |
| 2571.0 | 3800.0 | 13.48 | 7.19 | 5.41 | 117.4 |
| 2671.0 | 3700.0 | 13.60 | 7.23 | 5.46 | 123.0 |
| 2741.0 | 3630.0 | 13.68 | 7.27 | 5.49 | 127.0 |
| 2771.0 | 3600.0 | 13.69 | 7.27 | 5.51 | 128.8 |
| 2871.0 | 3500.0 | 13.71 | 7.26 | 5.56 | 134.6 |
| 2891.0 | 3480.0 | 13.72 | 7.26 | 5.57 | 135.8 |
| 2891.0 | 3480.0 | 8.06 | 0.00 | 9.90 | 135.8 |
| 2971.0 | 3400.0 | 8.20 | 0.00 | 10.03 | 144.2 |
| 3071.0 | 3300.0 | 8.36 | 0.00 | 10.18 | 154.8 |
| 3171.0 | 3200.0 | 8.51 | 0.00 | 10.33 | 165.2 |
| 3271.0 | 3100.0 | 8.66 | 0.00 | 10.47 | 175.5 |
| 3371.0 | 3000.0 | 8.80 | 0.00 | 10.60 | 185.7 |
| 3471.0 | 2900.0 | 8.93 | 0.00 | 10.73 | 195.8 |
| 3571.0 | 2800.0 | 9.05 | 0.00 | 10.85 | 205.7 |
| 3671.0 | 2700.0 | 9.17 | 0.00 | 10.97 | 215.4 |
| 3771.0 | 2600.0 | 9.28 | 0.00 | 11.08 | 224.9 |
| 3871.0 | 2500.0 | 9.38 | 0.00 | 11.19 | 234.2 |
| 3971.0 | 2400.0 | 9.48 | 0.00 | 11.29 | 243.3 |
| 4071.0 | 2300.0 | 9.58 | 0.00 | 11.39 | 252.2 |
| 4171.0 | 2200.0 | 9.67 | 0.00 | 11.48 | 260.8 |
| 4271.0 | 2100.0 | 9.75 | 0.00 | 11.57 | 269.1 |
| 4371.0 | 2000.0 | 9.84 | 0.00 | 11.65 | 277.1 |
| 4471.0 | 1900.0 | 9.91 | 0.00 | 11.73 | 284.9 |
| 4571.0 | 1800.0 | 9.99 | 0.00 | 11.81 | 292.3 |
| 4671.0 | 1700.0 | 10.06 | 0.00 | 11.88 | 299.5 |
| 4771.0 | 1600.0 | 10.12 | 0.00 | 11.95 | 306.2 |
| 4871.0 | 1500.0 | 10.19 | 0.00 | 12.01 | 312.7 |
| 4971.0 | 1400.0 | 10.25 | 0.00 | 12.07 | 318.9 |
| 5071.0 | 1300.0 | 10.31 | 0.00 | 12.12 | 324.7 |
| 5149.5 | 1221.5 | 10.36 | 0.00 | 12.17 | 329.0 |
| 5149.5 | 1221.5 | 11.03 | 3.50 | 12.76 | 329.0 |
| 5171.0 | 1200.0 | 11.04 | 3.51 | 12.77 | 330.2 |
| 5271.0 | 1100.0 | 11.07 | 3.54 | 12.82 | 335.5 |
| 5371.0 | 1000.0 | 11.11 | 3.56 | 12.87 | 340.4 |
| 5471.0 | 900.0 | 11.14 | 3.58 | 12.91 | 344.8 |
| 5571.0 | 800.0 | 11.16 | 3.60 | 12.95 | 348.8 |
| 5671.0 | 700.0 | 11.19 | 3.61 | 12.98 | 352.3 |
| 5771.0 | 600.0 | 11.21 | 3.63 | 13.01 | 355.4 |
| 5871.0 | 500.0 | 11.22 | 3.64 | 13.03 | 358.0 |
| 5971.0 | 400.0 | 11.24 | 3.65 | 13.05 | 360.2 |
| 6071.0 | 300.0 | 11.25 | 3.66 | 13.07 | 361.8 |
| 6171.0 | 200.0 | 11.26 | 3.66 | 13.08 | 363.0 |
| 6271.0 | 100.0 | 11.26 | 3.67 | 13.09 | 363.7 |
| 6371.0 | 0.0 | 11.26 | 3.67 | 13.09 | 364.0 |
You will use Scilab again. First copy the files Y:\Intro_seismology2002\tables\PREM.dat
and Y:\Intro_seismology2002\scripts\prem.sci to your own directory.
Start Scilab and change to your own directory: chdir('Z:\yourname');
1. Both 'prem.sci' and the program of step 2 (raytracer.sci) have one implicit
restriction on the earthquake's location built-in. Which restriction is
this?
2.
Run the script prem.sci. The program takes a while to finish; be patient.
Print the output plot. Connect the symbols of the travel time curve, pay extra
attention to the shadow zone of the outer core and the triplications.
Label each part of the travel time curve with the appropriate phase name
(you can use figures 4.14 and 4.19 from your textbook to guide you).
Also label the core shadow zone.
Finally, look at the upper mantle P-velocity structure of PREM (see also figure
1.1 in your book). Can you recognize features in the travel time curve which
are due to the complexity of the upper mantle structure?