Weighted Blend

[Ofnuts]

I would try something like this:

• get a selection on the shore line
  
• then:
  
• duplicate the initial layer
  
• apply a blur
  
• repeat a couple of times with increasing blurs
  
• blend the layers: given them an opacoy of 1/N, N being their order in the stack from the bottom: lowest is 100%, next is 50%, then 33%, 25%...
  

With just two (60 and 120) blurs and stretching the contrast  a bit:

   

Assuming that you start with the selection already set, it should not be too hard to script if you want many layers.

For script help, see https://www.gimp-forum.net/Forum-Scripting-questions