Control the edges of a warped surface

I'm trying to create a jagged random edge leading up to the raised surface.

Something like the jpeg I've attatched but I want the edges to be a bit more random.

I've tried a culling pattern, but then I cant interpolate the curves and they become wavy.

I've tried looking at the forum but I'm struggling to find the language to articulate what I actually want to do.

Any assistance or direction is appreciated. Thanks!