The search area of the Pacific Ocean for missing flight instructor William James McAdams is so vast that the U.S. Coast Guard called off formal operations in the hours after the plane he was flying vanished, a Coast Guard spokesman said Wednesday.

Twelve days after McAdams allegedly stole a 2011 G1000 Skyhawk 1TG, tail number N191TG, from his employer, Advantage Aviation, authorities still have no additional information about McAdams or the whereabouts of the plane, Palo Alto police Sgt. Brian Philip said on Wednesday.

McAdams allegedly took the aircraft on May 8 at 1 a.m. without permission and flew south. The last radar ping put him near the Mexican border about 70 miles out into the Pacific Ocean, according to the Federal Aviation Administration (FAA) and Palo Alto police.

The U.S. Coast Guard initiated a "call-out" and began a search after being alerted that McAdams and the plane were missing, Coast Guard spokesman Petty Officer Bill Colclough said. But once they identified the search area, the agency suspended any official search.

Given the speed of the aircraft, which was traveling at about 134 mph and the timeline of the last known position, the search area was deemed "unreasonable," Colclough said.

The plane could be in an area of about 120,000 square miles, he said.

"That's an extremely large area. Typically, we can search with a combination of aircraft and rescue boats an area between 100 and a couple of thousand square miles," Colclough said.

"We can saturate an area of that size," but to search the massive area would emaciate Coast Guard resources and personnel, he said.

The Coast Guard instead issued a safety-net message notice. The message went to all vessels and mariners to be on the lookout for the aircraft or for any person or persons associated with the plane, Colclough said.

If McAdams landed or crashed at sea, the water temperatures are cold, ranging from 50 to 70 degrees, Colclough said. The seas are variable, with a number of jetties and breakwaters in the area that can alter the effects of ocean waves and currents.

The Federal Bureau of Investigation, the FAA and U.S. and Mexican coast guards have been apprised of the search for McAdams, with Palo Alto police taking the lead.

Police have not identified a motive for McAdams' sudden departure. But he faces three charges in Orange County, Florida, stemming from a "dating violence" incident with a woman in a resort hotel room on April 24, according to an arrest affidavit in that state.

McAdams faces two felonies for aggravated battery with a weapon and false imprisonment and one count of misdemeanor battery after an alleged argument with the unknown woman.

His family has said the accusations against him are out of character and they are devastated by the reports.