More or less there's a correlation.
Carbon, which makes up all life, gets laid on the seafloor when marine animals die. The dead animals, some of which have calcium carbonate skeletons, settle on the marine floor and become cemented into sedimentary rock. New sea floor is constantly being made at spreading centers (areas of tectonic plate divergence). The old sea floor is subducted underneath continental crust. Trenches are often the result of subduction zones. Marianas trench is an example. The sedimentary rock, which has carbon in the form of skeletal remains, is buried deap within the crust and eventually makes it to the mantle.
I actually just made a blog post on iron fertilization, which starts this process of carbon burial.
http://thescienceofearth.blogspot.com
Please respond if it doesn't make sense. I kind of wrote imagining you know basics of geology and oceanography.