The worst engine surge I have experienced was on departure from HKG . Fortunately, I knew what the noise was and it was not so severe as the ones described here. I am told that the most usual cause is an unexpected disruption to the airflow into the front of the engine. This might be a small cross wind or pocket but unseen and unknowable. When the engines are working hard on the departure, it is the most awkward time for them to experience this.
We were climbing out from Kai Tak in a BA 744 when one of the Starboard engines experienced a surge and shook the a/c a fair bit. We were sitting just over the wing and the noise was close by. But we continued the climb and it was not severe, so we were able to continue our journey all the way to London, but there was no cabin announcement, so I knew it was not serious. That has been the worst in over 40 years of paxing.