BBC News' Clive Myrie reports on the quake and its aftershocks

The quake struck at 0246 local time (0946GMT) with its epicentre in the area of Hector Mine about 30 miles north of Joshua Tree, a desert town east of Los Angeles.

Two people are reported to have been injured after a train was derailed by the quake as it passed near the city of Barstow, east of LA.

All of the carriages remained upright and there are no signs that any of the passengers were seriously injured.

The Amtrak service, the Southwest Chief, was en route from Chicago to LA where it was due to arrive later on Saturday.

A number of power lines were brought down across the area and water mains ruptured, leaving thousands of residents without power and water. However police say they have had no other reports of any significant damage or loss of life.

In LA, buildings rocked and windows shook for about 15 seconds, but it is not known if anyone was injured. The jolt was strong enough to wake millions of people from their sleep.

"That was a bad one," LA resident Lucille Manning told the Associated Press news agency. "Things are bouncing around all over. But we are all right."

Car alarms across the city were set of by the quake.

Near the epicentre of the quake, Gerri Hagman owner of the Homestead Inn in Twentynine Palms said the quake was one of the strongest she had ever felt.

"I'm a native Californian and I've been in a lot of them - this was a whopper," she said.

The tremor was strong enough to shake buildings 70-80km away and was also felt in San Diego and Las Vegas, Nevada.

Rolling motion

A "Quakecam" operated by local TV has recorded a series of aftershocks

Witnesses described the quake as causing a rolling ocean-like motion that lasted for up to a minute, rather than a sharp jolt.

There was at least one strong aftershock shortly after the initial quake and a series of lesser tremors measuring around 4.0 on the Richter scale have been recorded by seismographs in the area.

Resident Evette Zeitlow, from Palm Springs, about 100 miles east of LA, told CNN: "Beams in the ceiling moved. Bottles, jars and containers were flying about.

"It was quite unnerving. It felt as if it was going to be a very, very large earthquake."

Scientists at the California Institute of Technology have given the quake a preliminary strength of 7.0 on the Richter Scale - meaning it is capable of causing considerable damage.

However observers say that although the quake was unusually strong, the fact that its epicentre was in a sparsely populated desert area will minimise the number of casualties.

Last month's earthquake in Taiwan measured 7.6 on the scale and killed more than 2,000 people.

The previous month's devastating quake in western Turkey measured 7.4. It killed more than 13,000.