Hard to tell from the photo but it looks very similar to the pulpit on the 80's Carver we used to have. That one was bolted on with three large bronze bolts, with the nuts accessible inside the anchor locker. AKDoug is right, that's exactly how our Carver pulpit was constructed too and just as Doug mentioned, water was seeping into the core and rotting the plywood. We actually had to get it re-done soon after we bought the boat, not because the anchor damaged it, but because the previous owner plowed into something and the force cracked and lifted the the pulpit upward and opened a space for leakage between the bow/deck and the bolt holes through the deck into the anchor locker. We had a new one re-fabricated using the old one as a pattern. Yours looks undamaged but in the course of our replacement, I used new, longer bronze bolts and glassed in small square marine fiberglass pads and very large bronze fender washers to beef everything up. Don't know if your configuration is the same, but if you can get to the nuts in the anchor locker, big hefty washers might make it stronger. I did probably go overboard. The boat may fall to pieces someday but that pulpit will never budge.
(I think I still have creases on my body from doing all that work with my head and shoulders jammed inside the anchor locker door, and my ribs on the sill of the anchor locker hatch. It was a rectangular door and I only fit sideways, left side down or right side down, so all the work was done overhead, sideways. That was fun.)
