Aftershock

This quest is from The College of Winterhold, given by Tolfdir. You must have completed The Staff of Magnus (Quest) to receive it. It would seem this quest is repeatable, much like the thieves guild quests.

"There have been reports of some sort of magical anomaly in Skyrim. Tolfdir fears it is a side-effect of Ancano's meddling with the Eye of Magnus, and has asked that I look into it. He suggested I take the Staff of Magnus with me, just in case."

The location may vary for the quest. When the Dragonborn arrives, an anomaly is found spawning Magic Anomalies which are highly resistant to magic. The Dragonborn but first defeat all of the apparitions then use the Staff of Magnus to close the anomaly.

Quest Reward
The Jarl's are paying The College of Winterhold for clearing the anomaly's throughout skyrim. As Archmage, you receive 1000 gold each time this quest is completed.