Final answer:
The prospector's activity of digging to recover gold is called placer mining, which was heavily used during the California Gold Rush and tends to evolve into more advanced methods as surface deposits are exhausted.
Step-by-step explanation:
The mining activity described in the scenario where a prospector owns a gold mine and digs to recover gold is known as placer mining. This type of mining involves sifting through material in modern or ancient riverbed deposits, generally using water to separate the gold from the sediment and other material. This form of mining was extensively used during the California Gold Rush and is characterized by the initial simplicity and the eventual use of more elaborate methods such as hydraulic mining once the easy-to-reach gold was exhausted.
In the historical context, placer mining gave way to more technologically advanced and capital-intensive mining techniques. When the easy placer deposits were depleted, hydraulic mining, open-pit mining, and underground mining became the primary methods for extracting deeper and less accessible gold deposits. Modern-day mining is often dominated by large companies with the capital to fund the necessary equipment and operations required for deep-earth mining.