From:
ftp://ftp.norsar.no/pub/outgoing/johannes/hist/cmb_100_years.pdf:

1896 Emil Wiechert proposes the Earth’s core is of iron
1906 Richard Oldham observes the Earth’s shadow
1907/1911 Several instrumental and theoretical improvements in seismology by the “Göttingen Group”
1912/1914 Beno Gutenberg defines the CMB and calculates first set of global travel-time curves including many core phases Gothenburg, 22 - 26 June 2013 20
1926 Harold Jeffreys proofs the Earth’s core as fluid (rheology)
1936 Inge Lehmann discovers the Earth’s inner core (body waves)
1971 Adam M. Dziewonski and J. Freeman Gilbert proof the Earth’s inner core as solid (eigenmodes)
1973 Gerhard Müller proofs the Earth’s inner core as solid (body waves)


Also: (Miaki)
 
Oldham, R.D., 1906.
The constitution of the interior of the Earth, as revealed by earthquakes.
Quarterly Journal, Geological Society of London, 62, 456-475.
http://books.google.com/books?vid=HARVARD:32044102916210&printsec=titlepage#v=onepage&q&f=false

Bolt, B.A., 1982.  Inside the Earth: Evidence from Earthquakes.  W.H. Freeman and Company.


Discontinuities: (Wikipedia)

Conrad (continental crust); 
Mohorovičić (crust–mantle);
Lehmann (upper mantle);
Gutenberg (mantle–core);
Lehmann (core);