3. The Earthquake occured on the other side of the Earth
Explanation:
One of the main difference between P-waves and S-waves is that P-waves can travel through solids and liquids, while S-waves can only travel through solids. They are not able to travel through liquids.
So, if a seismic station showed only P waves, it means that there was some area in liquid state between the seismic station and the hypocenter of the earthquake. Inside the Earth, the outer part of the core is made of liquid, so this means that there outer core was along the line connecting the seismic station and the hypocenter and "blocked" the S-waves: therefore, the earthquake occurs on the other side of the Earth.
4. In order to determine with precision the location of the epicenter
Explanation:
One seismic station is only able to determine the distance of the epicenter - so, by using one seismic station only, we are only able to tell that the epicenter is located on a point along a circle, centered around the seismic station.
If we use two seismic station located at different points, we can draw two circles of possible locations for the epicenter, one for each seismic station. The intersection between the two circles will give us the exact location of the epicenter. However, two circles have two intersections: therefore, there is still an ambiguity concerning the exact location of the epicenter.
If we use three stations, therefore, we can draw three circles, and they have one intersection only: this intersection will give us the exact location of the epicenter.
