Employment of Volcanologists and Petrologists
The first department that comes to mind is obviously academia, i.e. faculty or research positions at universities. However, there are many other career paths available (hopefully: there are not enough academic positions for every student completing a Ph.D...). For volcanologists, there is actually a nice site called volcanologists outside academia. As the name suggests, it compiles various testimonies about people who got a Ph.D. in volcanology but now work outside academia. They have also conducted a survey to gather more data. The results show that there are very diverse employment possibilities, including (but not restricted to):

Outreach/science communication
Museums
Academic publishing
Data analysis
Material science
Instrument companies
Tourism...

I'm not sure for igneous petrologists/geochemists, but I think the possibilities are pretty close.
Edit: I just realized I completely forgot to mention volcano observatories, which represent a &quot;large&quot; source of employment for the community (relative to its size). IAVCEI's Early Career Network has put up a series of videos where observatory workers describe their job. Another series about careers in academia is planned, so stay tuned!