The best classification of wave mentioned in the question is longitudinal wave.
Explanation:
If the particle displaces parallel in the direction of wave propagation then it is simply called as the longitudinal wave.
As mentioned in the question, the particle of rock is vibrating parallel to the wave propagation i.e north south direction not top down so it is shows the nature of longitudinal wave.
In this wave system particle do not move top down, it only oscillates back forth.
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