CPT310 Week 5 Discussion Board
1. Inner-core P-wave velocity (25 points)
A nice feature of the PREM model is that seismic velocities are inverted for polynomials. For example, in the lower mantle between radii 3480 and 3630 km, the P-wave velocity is given in km/s as:
Vp = 15.3891 – 5.3181x + 5.5242 x2 – 2.5514×3
Where x = r/a, at radius r, with a whole Earth radius of a = 6371 km. Given the following P-wave velocities as a function of r, invert for 2nd order polynomial that describes the inner-core P-wave velocity as a function of x, as described above. Plot both the observations given below and your polynomial function to show that it is a good fit.
Data for this problem are:
Radius (km) Vp (km/s)
0 11.2607
64.3 11.2931
128.6 11.2258
192.9 11.3040
257.2 11.2158
321.4 11.2323
385.7 11.2365
450.0 11.2199
514.3 11.2351
578.6 11.1638
642.9 11.2234
707.2 11.1809
771.5 11.1805
835.8 11.1888
900.1 11.1708
964.3 11.1207
1028.6 11.1309
1092.9 11.1166
1157.2 11.1004
1221.5 10.9902
2. Density of the core (25 Points)
Use the acceleration of gravity at the core-mantle boundary (g = 10.7 m/s2) to find the total mass and average density of Earth’s core.
Hint: the average density is just given by:
𝜌𝑎𝑣𝑔=𝑀(43)𝜋𝑎3ρavg=M(43)πa3,
Where a is radius. So, you simply need to find the Mass.
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