Question

How are seismic waves used to determine the structure of the earth?

Answer 1

Because of the manner of travel of the seismic waves.

Explanation:

First of all, we need to remember that:
P-waves travel through solid, liquid, and gas.
S-waves travel trough solid only.
L-waves travels from focus to directly to the epicenter.

P-waves and S-waves helped scientist to determine the structure of the earth. For example in the core:

At the depth of about `2900` km below the earth's surface, P-waves passing through the earth slow down rapidly and S-waves disappear. These changes in the movement of the two seismic waves indicates that they're passing through a liquid layer which is the outer core. Then at a depth of about `5150` km the P-waves speed up meaning it is again travelling in a solid part of the earth which is the inner core.