**1. Inner-core P-wave velocity:**

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 x^{2} – 2.5514x^{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

Note:I have attached the needed material that will help to solve the question and the answers should be a doc file not pdf.

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