1. To carry out an exploration for some kind of natural resource, especially mineral deposits or oil. We've been prospecting for gold in these mountains for months, but we've come away with little more than a few flecks. Thousands of people rushed to the area to begin prospecting for natural shale gas.

2. To explore a particular region for some kind of natural resource, especially mineral deposits or oil. In this usage, a noun or pronoun is used between "prospect" and "for." The company has begun prospecting an area a few miles off the coastline for oil. I'm prospecting this part of the mountain for cobalt.