Can a large earthquake trigger earthquakes in distant locations or on other faults?

Sometimes.

Earthquakes, particularly large ones, can trigger other earthquakes in more distant locations though a process known as dynamic stress transfer/triggering. This means that the energy from the seismic wave passing through can cause a new earthquake, usually in already vulnerable locations prone to frequent earthquakes (e.g., volcanic regions). Examples of large events that triggered distant seismicity include the 1992 M7.3 Landers earthquake, 2002 M7.9 Denali earthquake, and the 2004 M 9.1 Sumatra earthquake that ruptured an area ~1300x200 square km, and triggered aftershocks from northern Sumatra to just south of Myanmar.

If a triggered earthquake is within a distance of about 2-3 fault lengths of the fault rupture associated with a mainshock, the earthquake is considered to be an aftershock, not a triggered event.

The fault length is related to the earthquake size:

• M4 ~ 1 km long
• M7 ~ 40-60 km long
• M9.1 Sumatra fault ~ 100's of km long

Learn more:

• Some Facts About Aftershocks to Large Earthquakes in California (USGS OFR 96-266)
• Earthquake nucleation by transient deformations caused by the M = 7.9 Denali, Alaska, earthquake (Nature, 2004)