Some surge protectors work by "redirecting" surges to the equipment ground, which is pretty much the definition of a ground fault. In this case, it's definitely possible that surge suppressors could be tripping GFCI receptacles/breakers (given a large enough surge).
As for the AFCIs... When electrical contacts separate, they often create an arc between the contacts. This arc spans the gap until the contacts are too far apart, and the arc can no longer be sustained. It's possible (in theory) that the GFCI tripping could create a large enough arc, for long enough to cause the AFCI to trip. It's not likely that a properly functioning GFCI would do this, but if the GFCI was old and worn it could be opening the contacts slow enough that a detectable arc is being produced.
Determining if the GFCI tripping is causing the AFCI to trip, is a simple test. Simply press the test button on the GFCI. If the AFCI trips, you'll have figured out half the problem. If the ACFI does not trip, you could repeat the test using a receptacle tester with a GFCI test function.
![enter image description here](https://i.stack.imgur.com/RCjG1m.jpg)
If it's determined that the GFCI is causing the AFCI breaker to trip, replacing the GFCI receptacle may resolve that part of the issue.
Figuring out if the surge suppressor is tripping the GFCI, is a more difficult proposition. It will likely require you to monitor the supply voltage over some time, to identify and document possible surges.
The AFCI worked as designed. It detected some small arc within the wiring and shut the circuit down. An AFCI has three detection modes: overcurrent, arcing and ground fault. Even a small amount of current imbalance will set the thing off. Be happy.
Best Answer
GFCI's must break neutral
GFCIs (of all types) are required to break hot and neutral, unlike regular fuses, switches, or breakers. This is not spelled out in UL 943, but is implied by the requirement in UL 943 6.7.2.2 that a GFCI must still trip and disconnect the load circuit from power if the line-hot and line-neutral connections are interchanged.
Some AFCIs also break neutral, although they are not always required to
Because early AFCI designs were derived from GFCIs, they inherited the property of breaking the neutral (as well as being sensitive to gross ground faults). However, some more modern designs (Mod 3 THQL AFCIs, most notably) dispense with the ground-fault detection, and thus may or may not break the neutral wire. (As to the standards: UL 1699 13.3 requires receptacle-type AFCIs to break neutral, whereas circuit-breaker/loadcenter-type AFCIs have the option to not do so.)