In my mind these both work...
1) I performed a bathymetry survey. I gave the client the bathymetry data.
2) I performed a bathymetric survey. I gave the client the bathymetric data.
A web search shows pages using both words, however I'm not convinced the authors know of a rule or are just using what sounds best to them.
This example from the online cambridge dictionary doesn't sound correct if I use the word "bathymetry":
Atlantic marine species have a shallower upper bathymetric limit in the west than in the east.
Are there any useage rules?