I think the answer is 'no', in the sense that 'seismology (i.e., the study of waves propagating within the Earth) tells us the details in a far superior way'. See this paper for an informative treatise: <PERSON>, S. G. (1980). Discovery of the Earth’s core. American Journal of Physics, 48, 705-724, and these lecture notes http://www.geo.uu.nl/~berg/geodynamics/lecturenotes.pdf on Geodynamics.
Interesting additional tools that you'll find in these works are:
1. Figuring out the mass of the Earth (using <PERSON>'s laws). People found that the average density of the Earth had to be $5500$ kg/m$^3$, while rocks at the surface only had a density of about $2700$ kg/m$^3$, so the interior of the Earth had to be of higher density. Under the assumption that pressure alone cannot be responsible for the increase in density, the high densities had to come from chemical changes such as the presence of metals, particularly because of the Earth's magnetic field. Under the assumption that the pressure was responsible for the high density, the Earth's interior could be gaseous, for example, plain air is more compressible than just rocks, so the Earth's interior could be air (as proposed by Benjamin Franklin in the US!).
2. A second clue that the Earth had to have a radially varying density came from the Earth's moment of inertia (which was a known quantity, based on astronomical measurements such as the Earth's axial precession), which makes it possible to create models that relate density and radius. Of course, with neither quantity well-known, you couldn't do too much with this. 439
But assuming an iron core (with known density, and responsible for the Earth's magnetic field) overlaying a mantle (with density close to that of the Earth's surface), the first radial profiles could be made.
3. Models could be made that concerned themselves with the rigidity/deformation of the Earth under forces, such as the response to ocean tides, terrestrial tides and the Chandler wobble. These could be used to even construct some radial profiles of some approximate elastic properties. Only in the 1960s, after seismology was a firmly established technique, people additionally found additional non-seismic evidence of the Earth's eigenvibrations/free oscillations where the Earth (as a whole) rings like a bell, which was a very useful independent tool to verify layered profiles of the Earth's elastic properties, and which were important in the discovery of, e.g., the solid inner core.
4. The rigidity (from the previous point, and mentioned in the first point) can be linked to densities using (thermodynamical) equations of state. Hence, figuring out the appropriate relations between density/pressure/rigidity was of large importance.
5. Similarly, with the assumption that the Earth was made with the rest of the solar system, it was possible from the spectral lines of the sun and the chemical makeup of meteorites to figure out the likely bulk chemical composition of the Earth (https://en.wikipedia.org/wiki/Chondritic_uniform_reservoir). If you additionally know the pressure, density and rigidity information, you can make relatively informed guesses about candidate materials that must be present. That is, similar to the answer by a_donda, one must still test how materials really behave in these strange pressure and temperature regimes, which is mostly laboratory work using, e.g., a Diamond Anvil Cell.
6. Similarly, these lab experiments can tell us that for a given pressure on a given material, what the expected temperatures can be.
But if you want very solid answers about the 'nature' of the Earth's core, all the most direct answers come straight from seismology. That is the best method to actually constrain the location of the (elastic) properties within the Earth, at a much higher accuracy than any of the other methods can. As secondary consequences, we can use these measurements to make chemical hypotheses about the makeup of the core etc., but those are entirely based on the assumption that the seismic data is correct....so they're not an 'independent' kind of measurement/model! 70