Images with 'wavy sine effect'

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Hello all,

I was wondering if it is possible (and ofcourse, how) to create a 'wavy sine effect' over certain images every few frames to make it wave.

I recorded a video directly from my emulator (it's from Super Metroid for the SNES) while playing with some background layers for reference to show you what I mean:

Video (4,51 MB)

It's not the waving up and down ~32 pixels, but rather seperate horizontal lines waving left and right ~1-2 pixels (you might have to zoom the video). As you can see both the background and the water overlay have that wavy effect, although the water overlay might be a bit hard to see.

Sprites used in-game:

Background:


Water overlay:


If anyone could take a look at it and tell me if this is managable with standard BlitzMax functionality (or with some graphics module), I'd be happy.