How can the extent of fault rupture during an earthquake be converted into a measurement of average fault slip of displacement of the rocks on either side of the fault? Make sure that you begin at first principles.

Fault rupturing by the earthquake is largely governed by the Elastic rebound theory. In geology, the elastic rebound theory is an explanation of how energy is released during an earthquake. It explains that as rocks on opposite side of the fault are subjected to some force and shift.

They gather energy and deform slowly unless their internal strength increases causing a sudden movement occurs along the fault. This results in the releasing of the accumulated energy and rocks move back to their original but unreformed shape.