San Mateo County Sheriff's office said it received reports of "a small airplane flying erratically" on the evening of January 14 before witnesses said it "disappeared from sight".

"Later in the evening, debris was found in the ocean near the coastline, consistent with parts from a plane," sergeant Philip Hallworth said.

Around 30 volunteers, drones and additional officers were dispatched on January 15 to recover the crashed plane.

Sergeant Hallworth said a commercial fishing boat spotted the body of a dead woman in the water after the crash.

The woman was identified as 27-year-old San Francisco resident Emma Willmer-Shiles and police believe one other person was onboard the four-seat light aircraft.

The ill-fated joy flight travelled from Hayward Airport over San Francisco Bay to Half Moon Bay Airport on the evening of January 14 and crashed during the return journey.

A caller on Fox News said they had "heard the engine splutter" before they lost sight of it along the coast.

In a podcast aimed at fans of the Canard aircraft last year, Mr Ferrier said he'd purchased the plane as a way of transporting he and his then girlfriend Ms Petit and their black labrador across the US.

Mr Ferrier told the podcast about how he had grown up in Armidale, but moved to Canberra at age 12 before getting involved in Cadet air programs.

In 2014 he emigrated to the US for college, where he attended the Massachusetts Institute of Technology (MIT).

"I'm originally from Armidale, which is sort of in the country, then I moved to Canberra, which is the big town capital - then I immigrated to the US for college and they haven't kicked me out yet," Mr Ferrier said.

"I have been hanging around working on American aerospace since."

Mr Ferrier said he had done some glider flying and a little bit of general aviation before leaving Australia, but his love of flying had "really lit on fire when I got to the US".

Mr Ferrier was a highly skilled test pilot after earning an aerospace engineering degree at MIT he had worked for various civil companies as a test pilot.

Ms Petit was also a pilot with family in Maine and the couple had met while Mr Ferrier was a test pilot for Beta Technologies out of Vermont.

Mr Ferrier described them as "Beta was the kind of Teslas, making really good electric vehicles".

"I previously worked at Beta technologies in Vermont, they have some of the largest high performance electric airplanes in the world," he said on the podcast.

He said that work was continuing with the former Armidale man working with a company called Magpie developing new electric aircraft technologies out of California ahead of Monday's crash.

The hosts of the the podcast said that Mr Ferrier had completed an undergraduate degree in 2019 and was striving towards a Masters in the area of flight testing.

Mr Ferrier said he had been greatly inspired by the Rutan Voyager, the first aircraft to complete a non-stop flight around the world without stopping or refuelling.

"I think the story of it, just a bunch of people in the desert grinding away at a dream for however long it was and they actually pulled it off is pretty inspiring," Mr Ferrier said.

"That was such a paradigm shift that was possible it was such an inspiration for me."