How are Earth's rotational changes due to large earthquakes calculated?
Earthquakes, specially those at subduction zones, result in redistribution of mass (as one plate slides on top of the other). This change in distribution of mass causes changes in gravitational field that can be measured by satellites such as GRACE.

Now angular momentum is conserved. If we know the change in mass then we can calculate the change in moment of inertia and thus the change in the angular velocity.