It might appear that the power released by these earthquakes, some well beyond the realm of large nuclear weapons, might inspire some to think that thermonuclear reactions are the source of this power. But it seems rather unlikely.
Most naturally occurring energetic events of this nature - earthquakes, asteroid impacts, volcanic eruptions, etc. are purely mechanical in nature (i.e. non-nuclear). Consider the energy released by the Chicxulub impactor is estimated at 50-100 million MT. This surely was not related to a thermonuclear event.
And the 1883 Krakatoa eruption is estimated with an explosive yield of 200 MT. Unless some aliens detonated a thermonuclear device under that volcano, it detonated by purely natural, mechanical forces.
The Great Chilean Earthquake was a "megathrust earthquake" (1).
Quoting from (1):
They result "where one tectonic plate is forced underneath another, caused by slip along the thrust fault that forms the contact between them. These interplate earthquakes are the planet's most powerful,....."
end quote
It seems rather unlikely that thermonuclear reactions result in seismic events on earth.
(1)
https://en.wikipedia.org/wiki/Megathrust_earthquake