You can not. You must ignore it for the purposes of additional explorations.
If such a card tells you that you must encounter it on your first exploration on a turn, then you must encounter it the first time you explore that turn. After that exploration, ignore it for the purpose of additional explorations that turn; however, it still counts as the top card of the deck for any other purpose.
Therefore, you are only able to encounter it the first time you explore on your turn.
Had a question that fits in with the previous one-- if an effect allows you to move after you've explored (e.g. Potion of Flying in S&S) and you move to a location with a barrier, then do you encounter it with your next exploration there?
...I assume, "Of course! And then only the first one there." is the answer, but we should leave no nit unpicked. :)
|Andrew L Klein|
No. It's not your first exploration at that location, it's the first exploration of your turn. You've already explored before moving, so it doesn't need to be encountered.
Agree. We had a long discussion once in France wondering why most of the barriers and some items like lances refer to the first exploration of the turn rather than the first exploration of the turn at that location. That would have made more sense IMHO. Maybe they just didn't think of it during tests.