This diagram shows a schematic model of the Earth.  We pretend that it just has two uniform layers, an outer high-velocity zone (light blue, representing the magnesium-silicate mantle) and a low-velocity core (yellow, representing liquid iron).  Suppose that P waves travel from an earthquake source at A to a seismic detection station B which is moved to various points on the other side of the Earth as shown in the figure on the left.  The figure on the right sketches wave paths from A to B for various positions of B, assuming that when the seismic waves reach the low-velocity core, the path is bent inward according to Fermat's principle.  

The core produces a "shadow zone" at the Earth's surface, into which seismic waves from A cannot travel.

Are S waves also excluded from the shadow zone?  Explain why or why not.

The "shadow zone" at the surface is actually a ring of points opposite to the earthquake source at A.  Because of the focusing effect of the low-velocity iron core, P waves are excluded from the shadow zone.  Now S waves can only travel in solid material, and they can't travel in a liquid, as discussed in lecture.  Therefore, the shadow zone for S waves includes the shadow zone for P waves, but covers the whole side of the Earth opposite to A (see right-hand figure).

2.  On average, the temperature beneath the Earth's crust increases at a rate of 20 degrees Centigrade per kilometer of depth.  At what depth would water boil?  (Assume the Earth's surface temperature is +20 degrees Centigrade and ignore the effect of increasing pressure on the boiling point of water.)  Show all calculations.
 Water boils at 100 C (at 1 bar pressure).  Starting at an average temperature of +20 C, we need to go up 80 C more to reach the boiling point.  Dividing 80 C by the temperature gradient of 20 C/km, we get 4 km depth.
 

3.  Using data for the values of the Earth's mass and mean radius, verify that the average density of the Earth is 5515 kg/m³ (or 5.515 g/cm³).  Show all calculations.
 Assume that the Earth is a sphere of radius 6378 km = 6378 X 10³ m.
Volume of the Earth = 4 pi (6378 X 10³ )³ / 3 = 1.087 X 10²¹ cubic meters.
Mass of the Earth = 5.9736 X 10²⁴ kg.
Average density =  5.9736 X 10²⁴ kg / 1.087 X 10²¹ cubic meters = 5497 kg/m³.
This approach gives a number a little smaller than the value 5515 kg/m³ because the Earth's actual volume is a little smaller due to oblateness.