How were the crust-mantle, mantle-core, and outer core-inner core boundaries discovered?

Answer 1

First two responders are only partially correct.
for starters since nobody has ever seen any of these boundaries, and because the boundaries are only observed through secondary measurements there are a great deal of assumptions (however valid) made.
When a seismic wave from an earthquake crosses a boundary between two materials with different densities it (the seismic wave) is refracted or bent as it slows down or speeds up, changing it's path and ultimately changing it's travel time. This is in addition to what the previous writer mentioned about shear and pressure waves.
So if the earths interior were made of all the same substance in the same physical state we would know it because we could predict how long it would take a seismic wave to propagate through the earth. We know it is not that simple because the mathematical models require multiple interfaces (i.e. boundaries) to exist in order to resolve the time/distance equations

Answer 2

by the helpof geophysical prospecting we come to know abt these boundaries..
crust-mantle boundary also known as moho:
the speed of p waves suddenly increased when crossed the crust.that shows the dense rocks.which are basalt and ultra mafic pridotite.that makesthe ocean.

mantle-core boundary:
there is a shodow zone in between 105 and 145 degree in which we dont observe any of the sesmic waves whereas at an angle of 145 degree p waves reappear and bend downward(as light bends towards the normal after entering into water fromair).and the speed of p waves also decreases.now this bending of the waves and decrase speed means that wave has entered in the liquide zone where p waves reduce the speed.

outercore-innercore :
at abt 5100km the p waves speed again increased abruptly showing that wave has eneterd in a dense medium that is inner core...

Answer 3

First responder is only partially correct. The boundaries are shown by measurement of earthquake data. The solid part of the earth's innards conducts both transverse and pressure waves, while the liquid part conducts pressure waves only. There are no assumptions involved.

Answer 4

They are assumed. Those boundaries and the mantle and cores themselves are part of the theory of plate tectonics.