The location within the Earth along a fault at which the first motion of an earthquake occurs is called the hypocenter or focus.

Here's a breakdown:

* Hypocenter: This is the actual point within the Earth where the earthquake originates. It's often located several kilometers below the surface.

* Focus: This term is sometimes used interchangeably with hypocenter, but it can also refer to the region where the earthquake rupture initiates.

The point on the Earth's surface directly above the hypocenter is called the epicenter. This is the point where the earthquake's effects are often most strongly felt.