The Kulluk drillship ran aground in heavy seas on Dec. 31 near Kodiak Island.

FORBES: Shell Ships Alaska Drilling Rigs To Asia For Repairs

The borough of Kodiak Island has about 13, 600 people, according to the U.S. Census Bureau.

CNN: Two Coast Guard members shot dead on Alaskan island

The borough of Kodiak Island has a population of about 13, 600, according to the U.S. Census Bureau.

CNN: Feds investigate Alaska Coast Guard shooting deaths

Once they're satisfied that the vessel is seaworthy, it will be towed 30 miles to shelter in Kodiak Island's Kiliuda Bay.

NPR: Grounded Shell Oil-Drilling Ship Refloated

Most of the nearby shore is owned by a native Alaskan corporation on adjacent Kodiak Island, said Steven Russell, of Alaska's Department of Environmental Conservation.

CNN: STORY HIGHLIGHTS

Karluk is a small village in Kodiak Island, Alaska.

WHITEHOUSE: President Obama Opens Tribal Nations Conference

Infrared cameras on a boat accompanying the rig as it was being towed detected no signs of leakage early Monday, according to the unified incident response command, which includes the Coast Guard, Alaska's state environmental conservation department, a drilling company and Kodiak Island officials.

CNN: Alaska drilling rig towed to harbor off Kodiak Island

Their base is on what the city of Kodiak's website calls the second-largest island in the United States, situated in the Gulf of Alaska about 250 miles southwest of Anchorage.

CNN: Two Coast Guard members shot dead on Alaskan island