There are lists such as the one below detailing how much of different minerals seawater contains:
https://web.stanford.edu/group/Urchin/mineral.html
(For instance )
Would you expect this to be the same at all depths or should sea water at the greatest depths, several kilometers down, for some "mixing reason" contain more heavy elements than shallow water? Maybe there is a difference but miniscule?
To make the question more chemistry focused: Take a column of pure water, several kilometers deep in a controlled environment. Add some heavy compound in the form of a fine grained dust of, for example, gold.
Given enough time and assuming the water does not move around significally the amount of solved gold is expected to be the same at all depths, at least as long as the temperature is the same everywhere in the column?