Re: How were the inner and outer core's discovered?- scientific method

The different parts of the Earth's core were hypothesized to be made of 
different kinds (phases) of Fe when seismic waves were studied. Seismic 
waves travel through different materials at different speeds, and so you 
know or can figure out the material by knowing the starting velocity of 
the wave.  Earthquakes have helped in determining the regions of Earth's 
core because we have gained such a good knowledge of where an earthquake 
wave (P or S) originates and where it ends. 

More about this can be found at the following 2 websites: 
 http://www.anl.gov/OPA/factsheets/r3-02.htm
  http://www.anl.gov/OPA/factsheets/r3-02.htm