Aeration or Filtration?

I have a circular pond on my farm; it's about 100 feet across and about 4
feet deep. The water is murky and I'd like to clear it up. My plan was to
build a filtration system, to pump the water from the pond through a bed of
sand and stone, then let the filtered water run back into the pond.

My cousin has a similar pond and claims that some years back he'd cleared
his up by just aerating the water, no filtration needed.

Any opinions on the two options?

Paul