At oil prices under $40/barrel, no oil company is going to do any exploring any time soon. There's an economic reason for that.
Exploration is definitely decreasing, but its not going to completely stop.
Exploring and mapping isn't cheap, but it's the least capital intensive of the process.
Oil companies don't stop looking for oil when it's cheap -- they simply stop developing their reserves.
Because they know that, in the long run, there's more "up" in the oil market than there is "down".