pitted travertine vessel sink

My travertine bathroom sink has developed pits in the bottom of the vessel which collects standing water, which molds. Some of the pits seem pretty deep. This is very unslightly, and I would like to know if there is a product that I can use to fill the pitts. The sink has a marbeling type design, so I don't want the fix to look like patchwork. Hopefully, there is something clear to use! Also, I'm confused after reading these forums about to seal or not to seal!?!? Which shall it be?