The branch of Earth science that includes the study of volcanoes and earthquakes is geology.

Here's why:

* Volcanoes: Geology focuses on the Earth's structure, composition, and processes. Volcanoes are a direct result of these processes, specifically the movement of magma (molten rock) within the Earth's crust.

* Earthquakes: Earthquakes are caused by the movement of tectonic plates, which are a fundamental part of the Earth's structure studied in geology.

While other Earth sciences like geophysics and seismology also play a role in understanding volcanoes and earthquakes, geology provides the foundational knowledge for their study.