Image copyright UWNews Image caption A blue whale estimated to be around 20m long, swimming off Baja California

Researchers believe that California blue whales have recovered in numbers and the population has returned to sustainable levels.

Scientists say this is the only population of blue whales to have rebounded from the ravages of whaling.

The research team estimate that there are now 2,200 of these giant creatures on the eastern side of the Pacific Ocean.

But concerns remain about their vulnerability to being struck by ships.

At up to 33m in length and weighing in at up to 190 tonnes, blue whales are the largest animals on the planet.

The California variety is often seen feeding close to the coast of the state, but they are found all the way from the Gulf of Alaska down to Costa Rica.

Soviet secrecy

Writing in the journal, Marine Mammal Science, researchers from the University of Washington say the California blue whales are now at 97% of their historical levels.

The real key finding here is that they are close to recovery which is a bit of a surprise Dr Tevor Branch, University of Washington

Working out that this species is now back at its traditional numbers required some dogged scientific sleuthing.

Whaling nations concentrated their hunting efforts on the colder waters of the Antarctic and until the practice was banned in 1966 some 346,000 of the animals were killed by harpoon.

The numbers of blue whales caught in the Pacific was much lower, approximately 3,400 between 1905 and 1971.

Much of this hunting was carried out by Russian fleets.

However most of the data on the catches was kept secret under the Soviet regime. Scientists have only recently been able to get access to this information in the archives.

However the location and size of the catches didn't give any clues to the types of blue whales that had been caught. There are two distinct populations, the California group and others that live near Japan and Russia.

To figure out which whales were which, the scientists turned to song.

"We were trying to separate the catches into east and west, but we didn't know the boundary between the two," said Dr Trevor Branch from the University of Washington.

Image copyright UWNEWS Image caption A cow and calf in the waters off the California Channel Islands

"So we used the current locations of where they sing to figure out the dividing line. Their repetitive calls are different."

By being able to accurately work out the numbers lost to whaling, the research team was able to calculate a historic population.

Now back at 97% of their past numbers, the team believes that a rise in population has slowed down as these whales have reached the capacity of what the ocean system can support.

One concern for the scientists at present are ship strikes.

Most of these happen off the coast of California, and so worried are the authorities that they are now paying merchant shipping to slow down.

"Our perspective is that we'd rather there were no ship strikes at all, and they are over the legal limit," said Dr Branch.

"They have to do something to stop it, but 11 per year is so much lower than historic catches."

This new data suggests that there could be an 11-fold increase in ships before there is a 50% chance that the population will drop below what is considered "depleted" by regulators.

"My impression is that they are fairly robust," said Cole Monnahan, also from the University of Washington and the lead author on the paper.

"If you can whale them pretty extensively for 50-70 years and they are able to recover I think that says a lot about moving forward.

"In terms of things like climate change, it is hard to predict but I don't think we would expect a precipitous drop off."

While applauding the success of the conservation efforts in the California region, the scientists are well aware that not all whale populations have managed to rebound. In Antarctica, blue whales are at approximately 1% of their historic numbers.

"California blue whales are recovering because we took actions to stop catches and start monitoring," said Cole Monnahan,

"If we hadn't, the population might have been pushed to near extinction - an unfortunate fate suffered by other blue whale populations."

Follow Matt on Twitter @mattmcgrathbbc.