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.
Check 210.8 Ground-Fault Circuit-Interrupter Protection for Personnel.
...The ground-fault circuit-interrupter shall be installed in a readily accessible location.
And 210.12 Arc-Fault Circuit-Interrupter Protection.
...The arc-fault circuit-interrupter shall be installed in a readily accessible location.
Then Article 100, for the definition of readily accessible.
Accessible, Readily (Readily Accessible). Capable of being reached quickly for operation, renewal, or inspections without requiring those to whom ready access is requisite to climb over or remove obstacles or to resort to portable ladders, and so forth.
Best Answer
For all new construction residential dwellings the answer is not too complicated.
For older homes with existing wiring the answer is not as easy. A qualified electrician would need to assess the wiring conditions and even then only by trail and error could they determine if ARC-fault protection would be able to work. In some cases using an ARC-Fault receptacle downstream may be an option, whereas a complete rewire of the existing branch circuit may be needed.
I've elaborated on the answer breaking it up into residential and commerical establishments for educational purposes.
Residential AFCI Requirements
Exceptions:
Existing installations are not required to be updated with ARC-fault protection unless modification to the wiring is done.
Residential GFCI Requirements
Commercial ARC-fault Requirements
Commercial GFCI Requirements