1ns of error equates to ~30cm of error (from speed of light), so:
You might get a couple of ns of error from the initial s and p waves. (Assuming on the order of 50cm displacement)
If you’re on the fault and there is a major displacement (say order of 1-2 meters) there might be several more ns of error.
Practically, this seems to suggest that by the time that displacement from an earthquake would cause a significant loss of clock accuracy (say > 10ns), you most likely have bigger problems to worry about..
What effect, if any, might a major earthquake have on the time calculation?