We've had a small "nature pond" in our garden for -- ooh -- 25 years.
So I know a bit about looking after ponds. That said:

Today we were admiring the frog spawn, and looking for creatures, when I
decided to test the depth -- at its deepest it was about 2 feet when I
made this pond. I pushed a stick down into the accumulated muck to test
this; there seems to be about 9" of solid matter at the deep end, under
the lilies and weeds, which must be roots.

Anyway, this is my question: Bubbles rose -- quite natural of course,
but we noticed a smell, which set me thinking: so that's gas, and should
I stir the whole pond up a bit to get rid of it?

I did notice that there's quite a large accumulation, by now, of muck,
so also wondered if I ought to remove a certain amount of this stuff, in
order to "freshen" the water?

This particular pond (roughly 9' long, 5' wide, 2' deep at max) is
about 12 years old now, and I've never really removed muck. I do net it
in winter to prevent [most] leaves entering the water, and we have a
small pump which moves the water a bit from one end to the other, 12
hours a day.

Comments appreciated!
John