Why do waves travel in curved paths through the earth?

Because as they travel through the earth, the density of the material through which they are travelling will vary. This causes the speed of the wave to change which in turn results in a process known as refraction where the waves direction of propagation changes. As the density of the material in the earth continually increases with depth due to the increasing overburden pressure, the speed of the seismic waves will continuousy change with depth leading to continuous small changes in propogation direction which leads to the formation of a curved propagation path.

Geophysicists make use of this phenomenon to estimate the density and structure of the interior of the earth.

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