Six Americans and one Brit set off from New Zealand’s Bay of Islands for Newcastle, Australia, just north of Sydney, nearly a month ago aboard the historic wooden schooner Nina. It was supposed to be a leisurely sail across the Tasman Sea, but nobody has heard from or seen the crew in more than three weeks. Now, rescue teams say they have “grave concerns” for finding any survivors, but will not give up hope.

Rescue Coordination Center New Zealand, or Rccnz, has organized two extensive sea-based searches revolving around different scenarios, covering a combined area of some 500,000 square nautical miles. On Friday, the team shifted to a third scenario, scouring the waters off Northern New Zealand in case the crew had abandoned ship and attempted to raft to safety.

“We have tasked a twin-engine fixed-wing aircraft to search the shoreline and coast starting at Tauroa Point, searching along 90 mile beach, north of Northland, and out to and around Three Kings Islands,” said Mission Controller Neville Blakemore. “While we have grave concerns for the crew on board Nina, we have not given up hope of finding survivors.”

The seven-team crew on board Nina spanned in age from 17 to 73, and included commercial captain David Dyche, his wife Rosemary and son, also named David. The group departed from a marina in Opua, about three hours north of Auckland, on May 29, and has not been heard from or seen by any other vessel in the area since June 4, when the U.S.-flagged ship was 425 nautical miles (685 kilometers) northwest of Cape Reinga. They were expected to arrive in Newcastle, Australia, more than 1,100 nautical miles away, on June 8.

The historic 70-foot (21m) schooner was built in 1928, but is equipped with a satellite phone, a spot device that allows regular tracking signals to be sent manually and an emergency beacon, according to Maritime New Zealand. The emergency beacon was never activated, leaving some to posit that the crew hastily abandoned ship.

Rccnz began its investigation on June 14 amid concerns from family and friends. Its records show that conditions at the last known position for the vessel on June 4 were very rough, with winds of 50 mph (80 kmh), gusting to 68 mph, and swells up to 26 feet (8 meters).

New Zealand meteorologist Bob McDavitt took the last known satellite phone call from 73-year-old Evi Nemeth on board the ship. “The weather’s turned nasty, how do we get away from it,” she said.

“She was quite controlled in her voice; it sounded like everything was under control,” McDavitt told the New Zealand Herald. The meteorologist said he advised Nemeth to head south and brace for a storm with strong winds and high seas. The next day he got a text that read: “Any update 4 Nina? … Evi.” He urged the crew to stay where they were and ride out the storm another day. He then sent a series of follow-up texts, but got no reply.

Rccnz is liaising with the Australian Maritime Safety Authority and said it will continue to review search options in the coming days.

Mr. Dyche purchased Nina -- an award-winning racing ship during the early part of the 20th century -- in 1988 and set sail with his family in 2008. In a blog post, his wife wrote that their dream was to circumnavigate the planet, “meet people, learn about their culture and see the beauty of the world.”