Oct 4 (Reuters) - Shares of oil and natural gas company Amplify Energy Corp plunged nearly 63% and were headed for their worst day of trading after an oil rig operated by the company's unit was linked to a "catastrophic" oil spill off southern California.

The U.S. Coast Guard, heading a clean-up response involving federal, state and city agencies, on Sunday announced an around-the-clock investigation into the origin of the spill, which has spread across 13 square miles of the Pacific Ocean.

Kim Carr, the mayor of Huntington Beach, the beachside city near Los Angeles that is bearing the brunt of the spill, said in a news conference that the rig was operated by Beta Offshore, a California subsidiary of Houston-based Amplify Energy.

Amplify CEO Martyn Willsher said at a press conference that the pipeline had been shut off and remaining oil suctioned out. He said divers were still trying to determine where and why the spill occurred.

Roth Capital Partners also suspended its target price on Amplify Energy.

"Until we are able to have a discussion with management to confirm this is from an AMPY property, the extent of the spill, the estimated cost of clean-up and any insurance coverage that may apply, we are temporarily suspending our target price, our estimates and moving our rating to Neutral," the brokerage said in its note.

Up to Friday's close, Amplify had more than quadrupled in value. The stock was down 55% at $2.61 in premarket trading. (Reporting by Arunima Kumar in Bengaluru; Editing by Saumyadeb Chakrabarty)