There must be some relationship. Please read an article "The chemistry of trace elements in surface geothermal waters and steam, Iceland"  in the chemical geology journal by hanna kaasalainen and Andri stefansson for your answers.

Yes, obviously there is, because hydrothermal alteration is a metasomatic process. There are a lot of studies on fossil and modern geothermal systems, you could have a look at some papers and references therein (they are just examples): 

Perhaps you should find out what the identity is of the alteration minerals, and then consider what trace elements would fit into the crystal lattice of these secondary minerals. 

Lithogeochemical investigations of geothermal systems are complementary to studies of fluid chemistry and hydrothermal mineralogy, and can assist with the characterization of upflow geometries, permeable horizons, system volumes, mineral abundances, and downhole stratigraphy and stratigraphic offsets. Despite the relevance of this information to the understanding of hydrothermal processes and geothermal field exploration and development, lithogeochemistry is a tool that is under-utilized by the geothermal research sector and industry.

The bulk-rock chemical signature of cuttings from a geothermal well is the product of multiple variables: the primary chemical composition of the unaltered host rock; chemical losses and gains due to water-rock interaction; alteration susceptibility of the precursor rock; pseudo-enrichment/-depletion of elements that were not leached or deposited due to overall mass change effects (i.e., closure effect signatures – a phenomenon related to constant analytical sums of 100%); and if not mitigated, contamination from sources including drilling mud components and metal casing/drill pipe fragments.

To quantify mass gains or losses properly, one should correct for "closure effects", a.k.a "constant-sum" effects. See the following reference if you are un familiar with this:

Gifkins, C., Herrmann, W., and Large, R., 2005. Altered volcanic rocks – A guide to description and interpretation. Arc Centre of Excellence in Ore Deposits, University of Tasmania, Hobart, 288 p.

I have two papers (one in the 2015 GRC Transactions and one in review in Geothermics) related to a field-wide lithogeochemical study of the Reykjanes geothermal field in Iceland that I will make available to you once they are published.

I started work on hydrothermal alteration in geothermal fields and relations between alteration mineral and trace and  rare earth elements back in the days. i attached the first paper  i found about the subject. I hope İt will be useful for you, too. 

During the transportation of the geothermal fluids, some of the element suits  gets in the solution because of the fluid-rock interaction. In the geothermal system, alteration mineral deposites and element redistribution occurs along the fault zones and fractures. Christensen et al. (1983) have been determined five distinctive element suits and  related alteration minerals in the field.