BAY AREA QUAKE : Temblor Costs Will Exceed $4 Billion : Damage: Early dollar estimates of quake destruction were conservative, but handling immediate problems prevents the completion of an accurate assessment.

SAN FRANCISCO —  From the dramatic break on the Bay Bridge, to priceless art objects that crashed to museum floors, to homes that must be razed before they collapse, the depth of earthquake destruction began to sink in across Northern California on Thursday.

The damage total topped $4 billion and was climbing. But officials were too busy confronting more pressing problems to take time out to complete the chore of precisely estimating damage.

“It’s not a priority. . . . Our priority is to restore service,” Pacific Gas & Electric spokesman Clyde Walthall said, noting that more than 100,000 customers remain without either electricity or gas in Northern California.

In what became a familiar refrain of officials, state Office of Emergency Services spokesman Gregory deGiere said the OES dollar estimate--$2.96 billion--given early on Thursday “is not only preliminary and incomplete, it is conservative, too.”

Late on Thursday, Henry Reteria, Oakland city emergency services manager, estimated quake devastation costs at $1.26 billion in his city alone. Reteria said there are more than 1,600 damaged or destroyed residential and commercial buildings. Several will have to be razed. Another 12 city-owned buildings also must be replaced, he said.

Some damage may not be detected for months. State officials quickly inspected hundreds of miles of fragile levees in the Sacramento-San Joaquin River Delta, finding only minor cracks and seepage in isolated spots.

But officials fear that the quake could have weakened already leaky levees so vital to Northern California’s recreation and ecology and California’s water system, and that coming rains could add further strain.

“Nobody really has a handle on the numbers. It is so widespread,” said Tommie Hamner, a top official with the Federal Emergency Management Agency in San Francisco.

FEMA is relying on the state to present it with an estimate. The state in turn is awaiting assessments from local governments.

Cities and counties started reporting early estimates of property damage to the state OES: more than $2 billion in San Francisco, $350 million in the cities of Santa Cruz and Watsonville combined, $100 million in San Benito County, $12 million in San Mateo County and $10 million in Alameda County, not including the late estimate for Oakland or the costs involved in the collapsed Nimitz Freeway that left untold numbers of commuters dead.

Caltrans spokeswoman Anita Yoder said repairs on freeways and highways will cost $500 million to $1 billion, depending on how much it takes to rebuild the Cypress viaduct on the Nimitz Freeway in Oakland.

At first, officials said the Bay Bridge would take weeks to repair. Now, officials give no estimates of how long this process will take. At first, repair work must focus on the lower deck. Workers must shore up the span’s towers, Yoder said. Those towers rest on piers which are sunk into the bay floor. Connections between the lower deck and the piers also must be reinforced, as will pavement and steel girders.

Once all that is done, workers will use a crane to hoist the damaged part of the upper deck from the bridge and place it on a barge. The salvageable portions of the deck will be repaired on the barge. Then it will be lifted back onto the bridge and reconnected, Yoder said.

Only after the upper deck is removed will the extent of damage to the lower deck be visible. Officials have noticed holes in the pavement on the lower deck. But they suspect damage goes far beyond that.

In San Francisco, Mayor Art Agnos estimated that damage exceeds $2 billion, with a fourth of that total needed to repair city-owned buildings and such infrastructure as roads.

According to a preliminary evaluation by structural engineers, at least three older high-rises in downtown San Francisco were not safe for occupancy, said Don McConlogue, an assistant superintendent of the city Building Inspection Department.

The city that so prides itself on its cultural amenities suffered hard hits to its treasures. Across from City Hall, the main San Francisco library, long in need of repair, was deemed unsafe and remains closed.

“I watched that building shake. It was unbelievable. Unbelievable. The side of the building looked like the flag rippling at Candlestick Park,” McConlogue said.

Nearly all Bay Area museums suffered some losses in the quake. The M.H. de Young Memorial Museum lost artwork valued at $3 million to $5 million. There was other damage to objects at the California Palace of the Legion of Honor.

At the Asian Art Museum, losses included several Chinese porcelain works and a few Chinese and Indian statues. Agnos said damaged items were worth $10 million to $15 million.

By Sunday, FEMA and the state Office of Emergency Services planned to have 17 disaster application centers open in stricken parts of the state. At these centers, people will be able to get aid in the form of grants for property losses, housing, unemployment relief, and a variety of other services.