You did not say if your pump was external or submerged in your pond?
But since you say you can hear it running, I will assume it is an external pump.
The whirring sound could be something caught in the pump motors cooling fan or a foreign object in the pumps impeller that is rubbing on the casing as it revolves!!??

GFCI outlets trip on ground faults, usually caused by the hot wire to the pump etc, being damaged/ or becoming wet and leaking current to ground.

The GFCI can also trip if moisture is allowed to enter the receptacle [outlet]. It could be in the form of rain/snow/ice melting/or in summer, a blast from a garden hose!
Installing a weatherproof cover over the receptacle, will lessen the chance of these "nuisance trips".

Moisture could also be entering the plug cap on the electrical cord that runs to your pump or the cord itself, could be damaged, allowing moisture in, which can cause a ground fault.
You could have a ground fault in your pump motor? In which case you should repair/replace the motor/pump unit completely.

GFCI receptacles do not trip from current overload. So if your pump was binding/misaligned/bad bearings etc, that is causing a higher current draw, it should not affect your GFCI receptacle.
GFCI circuit breakers, mounted in an electrical breaker panel, are a different matter, they are meant to trip on ground fault or an over current draw.

I would be checking to be sure moisture is not the culprit first, by drying out your GFCI receptacle and covering it up to keep the rain etc, out. Secondly, with the cord un-plugged, check it for wear and tear, broken connectors,or a cracked/loose plug cap.
"Horton"

All of the above. Plus, it is possible that the GFI unit has gone bad. It doesn't happen very often, but sometimes a GFI unit will become very fussy and trip every time anything is plugged in or turned on. After you have checked all of the above possibilities, try changing the GFI if nothing else helps.

Thank you for adding that Larry, I should have mentioned that a GFCI internal ciruit fault, could also cause trips to occur.

Plus the fact that any GFCI device, should be checked/tested every month with, preferably, a GFCI Tester. The are under twenty dollars to purchase but could end up being a life saver.
The little electronic sensing circuit that is inside the GFCI device, is prone to failure, just like any other electronic circuitry. and should be tested, once a month, as the device manufacturer suggests, in the instructions that come with the GFCI device.

I hope we receive feedback on this one, as it would be interesting, to find out what the problem actually was that is causing the GFCI to operate and trip?
"Horton"

I have a little giant pump that does the same thing. I can run a much larger laguna pump from the same GFI and it never trips the unit. The little giant pump trips it in just minuets. The power people said that the pump is drawing to many amps thus kicking the breaker.Might want to get it tested just to see if it is the pump. Not knowing the age of said pump, could be the problem.

I had the same issue and replaced the pump. The new one worked for a year. The new one now kicks the gfi immediately where the old one ran for about 15 seconds. I plugged the old one back in with the same issue. To verify it was the pump I plugged it into the bathroom GFI with the pump submerged. It kicked the breaker as before. The issue is with these pumps. I am trying to get Little Giant to replace the last one but don't have the receipt. They thought it was the breaker but that has proven not to be the case. Personally I think the bearing around the impeller is allowing water to enter the motor. The impeller turns free so I don't believe the current is the issue. I may put in a non GFI breaker just to test but don't want a fountain that is not GFI protected.