Since much of our knowledge of Earth's interior is inferred from the behavior of seismic waves and not actual samples, what are some of the assumptions that are made in order for our models to be correct? (Hint: Think of earth materials, physical and chemical parameters, etc.)

The earth's interior comprised of the core, mantel and the crust the core has two layers of the inner and the outer, similar that of the mantle inner and outer, also this impacts the formation of the waves system of the earth as the there travel path changes due to the composition and the structure with varying speeds and velocities.

The seismic waves that travel in a straight path get deflected to the other side due to the places that don't have conductivity and hence a shadow zone for these waves. As they follow the laws of reflection and refraction and encounter various boundaries between different media.

Resulting in the occurrence of earthquakes and volcanic eruptions and landslides on earth. Their propagation depends on the density and elasticity of the medium as the P and the S waves modeling tells us much about the interior of the earth, establishing that earth has a liquid core and shear waves cannot pass through it as demonstrated by Richard Dixon.