can you post your original background image so others can try using it. seems like one should be able to do that with a combination of sine waves and displacement mapping or -compose modulate or -compose multiply.
This is a simple case of two frequencies:
convert tile_water.jpg \
\( -size 128x128 gradient: -rotate 90 -function sinusoid "10" \) \
\( -size 128x128 gradient: -rotate 90 -function sinusoid "7,180,.25" \) \
\( -clone 1 -clone 2 -compose blend -define compose:args=50% -composite \) \
-delete 1,2 -compose modulate -define compose:args=50% -composite \
tile_water_ripples.jpg
PS. A little rotation of one of the gradients might make it look a bit better.
convert tile_water.jpg \
\( -size 128x128 gradient: -rotate 90 -function sinusoid "10" \) \
\( -size 128x128 gradient: -rotate 90 -function sinusoid "7,180,.25" -rotate 5 -crop 128x128+0+0 +repage \) \
\( -clone 1 -clone 2 -compose blend -define compose:args=50% -composite \) \
-delete 1,2 -compose modulate -define compose:args=50% -composite \
tile_water_ripples2.jpg