Is denting terrain in real time possible?

I’m making a snowboarding game and I want to push the snow terrain in a bit when the player runs over it. Any clue on how to achieve this or are there some illusions I could use to make it look like the terrain is changing?

Instead of modifying the terrain data, most games with this sort of mechanic will use a render-texture and a vertex displacement shader. This is just one of many tutorials I found which covers it; you can adjust how deep the effect works.

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