Navy divers probed the murky Hudson River on Tuesday to figure out how to free the USS Intrepid from the mud that has stranded the World War II ship at its Manhattan pier.

The six divers, who could barely see more than 2 feet through the dark water, also were surveying the aircraft carrier's hull for any damage from last week's aborted attempt to tug the ship, now a museum, to New Jersey for renovation.

Crews are working around the clock to remove the mud, including digging a 35-foot trench on one side of the ship, according to Peter Shugert, a spokesman for the Army Corps of Engineers, which is assisting the Navy.

"They want to create an area so they can vacuum the sediment from under the hull," Shugert said.

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The carrier's 16-foot propellers screwed themselves into the sludge as tugs tried to tow the ship from its berth, pulling it a mere 15 feet before giving up. The 27,000-ton ship, which survived five kamikaze attacks, seven bombs and a torpedo hit, is sitting precariously on the muddy speed bump, with its stern about a foot higher than the bow, said Bill White, president of the Intrepid Museum Foundation.

The Navy — called in after last week's fanfare-filled effort flopped — is using clamshell orange buckets swinging from towering steel cranes to remove thousands of tons of thick mud built up at the bottom of the ship.

"We are deep in the throes of this dredging expedition," White said.

Once the sediment is taken to the surface, it is placed on large iron barges and taken to a Staten Island landfill.

Intrepid officials said they hope the $3 million operation will take about a month. Determining the schedule the Intrepid's five-mile trip to a shipyard in Bayonne, N.J., for its $60 million renovation will be up to the Navy and the Army Corps of Engineers.

Click here to view FOXNews.com's Photo Essay of the Intrepid.