Seismic Data
Lithospheric Plates | Seismic Waves | Seismic Tomography | Hollow Planet Model
 Lithospheric Plates
To fairly address the question, consider the modern view of the Earth's interior.
 We believe the Earth's crust is typically about 25 miles thick beneath continents, and 6 miles thick beneath the oceans (which are on average about 2.5 miles deep). A rigid layer including the crust and upper part of mantle is called the lithosphere (picture).
Massive plates of lithosphere
50 to 186 miles thick
cover the earth with no gaps. They move and float on the molten mantle. We know that plate movement is a reality because hundreds of satellite monitoring stations now measure the slightest movements of the Earth's crust. 
Faults are places where moving plates meet. Over time, some plates are pushed up, and some are pushed down into the earth. (Could this have been the fate of Atlantis?) Earthquakes
are sudden slippings of masses of rock along fault surfaces, most likely due to the mechanism of elastic rebound. Earthquakes cause compression waves to travel through the Earth.
Seismic Waves
Seismic waves are recorded by stations all over the globe and this data has been used to map the probable interior of the Earth.  Most of what we know about the structure of the Earth deeper than the deepest drill holes ( 5 km or 3.1 miles ) comes from seismic wave data.
This data is a key to our question regarding the possibility of a hollow earth.
For more, see Lecture 16 Earth's Interior from UC Santa Cruz. I like the part about Xenoliths, "alien rocks", brought up in magmas that provide some mantle rock specimens.
How can recording earthquakes tell us what is inside the earth?
Seismic Tomography
Imaging the inside of the earth with seismic waves is similar to imaging an unborn baby with ultrasound. Waves move at different speeds based on density and elacticity. For example,
8,948 miles per hour in bedrock
4,474 miles per hour in glacial till
3,355 miles per hour or slower in soft sediment
There are 3,000 different
stations around the world which have measured more than 86,000 earthquakes since 1964.  ( Also see 45. Here are some local stations. ) Each event is recorded and archived automatically by many stations and with the exact time and distance between stations is known the speeds of the waves can be calculated. This system of open data sharing is important for world wide monitoring of nuclear tests as well.
Using
a system of linear equations, locations of seismic events are automaticly determined within minutes and are publicly released.
Analysis of quake travel times and amplitudes yields a three dimensional map of wave paths through the Earth.
Traveling waves that move from a material of  one density into a material of a different density will change direction according to
Snell's Law, and seismic waves do change speed within the earth and follow curved paths.
The same data analyzed in different ways can reveal different things about the inner earth. For example, in December, 2003,
Raffaella Montelli of Princeton University and colleagues mapped the locations of 32 moving mantle plumes (click to enlarge).
Lamprecht's Hollow Planet Model
The first illustration under seismic tomography is taken from
Jan Lamprecht's "A Feasibility study of possible Hollow Worlds." Lamprecht claims that a shell 800 to 1000 miles thick would not allow waves to be detected around the world as they currently are, but shows a hollow planet model that does.
Lamprecht on hollowplanets.com also cites some seismic puzzles that may be solved by the Hollow Earth  theory, including tens of thousands of Earthquakes with epicenters deeper than 150 Km which should not exist
because, due to the pressure and heat, below 150 Km there is no known material which will not flow. Another mystery addressed are waves which slow down instead of speeding up when passing through the denser--but more elastic(?)--core. Can over 30 years of collected seismic data be interpreted in another way, a way that permits a hollow earth? This does indeed seem unlikely, especially when you consider the richness of the data and the work of people like Montelli, but is it impossible?
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