I believe the geologic setting of a particular terrain determines the type and kind of deposits likely to occur. Also plate tectonics determines the mineralization potentials of certain geologic environment will have although preculiar to geologic settings. If the magma is the mixed type It will produce varieties of mineral deposits inclusive of traventine deposits.
Trace element fingerprinting might be your best bet. There is a wealth of information about this in the ore deposits literature. In particular, I would look at the Y/Sr ratio of the travertine. Looking at a high/low field strength element can give insights. But Rare Earth Element profiles might also be of use. Good Luck with this interesting project!