(Adds detail on investigation in 4th paragraph, Boeing shares)

By Alasdair Pal, Cordelia Hsu and Adam Jourdan

SYDNEY/SANTIAGO, March 12 (Reuters) - Investigators from Chile's aviation authority are headed to New Zealand to head up the probe into a sudden midair dive by a LATAM Airlines Boeing 787 plane that left more than 50 people injured, the country's regulator said Tuesday.

The plane, which was headed from Sydney to Auckland, dropped abruptly in mid-air before stabilizing, causing passengers to be thrown about the cabin. One person was seriously injured, with about 50 suffering minor injuries.

The cause of the apparent sudden change in trajectory of the flight has not yet been explained. Safety experts say most airplane accidents are caused by a cocktail of factors that need to be thoroughly investigated.

Chile's DGAC aviation body said in a statement it will take the lead on the investigation under international rules governing aircraft accident investigations, known throughout the industry by their legal name "Annex 13".

LATAM is based in Chile and the flight, which had 263 passengers and nine crew members, was due to continue on to Santiago after stopping in Auckland.

New Zealand's Transport Accident Investigation Commission said on Tuesday it was seizing the cockpit voice recorder and flight data recorder of the flight.

"My neighbour who was in the seat two over from me, there was a gap in between us, as soon as I woke I looked and he was on the ceiling and I thought I was dreaming," Brian Adam Jokat, a Canadian citizen residing in the UK who was travelling on the plane, said on Tuesday.

Photos taken by Jokat after the incident showed damage sustained to the ceiling of the airplane where he said fellow passengers had hit it.

DGAC is working with New Zealand's TAIC on the investigation.

"TAIC is in the process of gathering evidence relevant to the inquiry, including seizing the cockpit voice and flight data recorders," the New Zealand agency said, referring to the so-called "black boxes" that will provide more information on the flight's trajectory and communications between pilots.

LATAM did not respond to a request for comment on whether it had given the black boxes to TAIC. The airline said earlier on Tuesday it would assist the relevant authorities on any investigation into the "strong shake" during the flight.

New Zealand's Civil Aviation Authority said in a statement it would also assist in the investigation if required.

There has been renewed debate over the length of cockpit recordings in the aviation industry since the revelation that voice recorder data was overwritten on the Alaska Airlines Boeing 737 MAX 9 jet that lost a panel mid-flight in January.

Boeing shares ended down 4.3% on Tuesday. (Reporting by Alasdair Pal and Adam Jourdan; Editing by Jamie Freed and David Gregorio)