Quote from an interview I got from a US navy pilot some years ago:
"nothing flies in a radius of 1200 miles from the Saratoga unless we say so"
The Saratoga is the air craft carrier of the 6th fleet.
Obviously neither side wants to shoot at the other, them being allies in NATO etc, but can you honestly see the Turkish navy arresting a US ship on the high seas because it carried out searches on the continental shelf belonging to yet another state? Apart from the obvious issue of the interest of a US company etc there is the other issue, of letting Turkey or any other second rate nation dictate to the US where its ships can and cannot go. This is one area where the Americans are adamant.
The first message to Turkey came from Egypt, when the foreign minister told them to bug off. The second and louder message came from the US State Department spokesman when he stressed that the area in question belongs to Cyprus and only Cyprus. Turkey apparently did not understand the meaning behind these messages.