Even in an industry used to boom and bust, the swiftness of the decline in the oil industry has been amazing. "This one has literally taken everyone's breath away," said John E. Olson, first vice president of Drexel Burnham Lambert stockbrokers in Houston. "The first quarter of the year was high cotton; in the second quarter, the lights went out."

The number of drilling rigs in operation has fallen from about 4,500 at the end of last year to roughly 2,900 today, according to the Hughes Tool Co. rig count, a barometer of economic well-being in Texas that tracks the number of drilling rigs in operation each week.

Small oilfield operators are filing for bankruptcy on a regular basis. And at least 20 small oilfield servicing companies have gone under since April 1. The various suppliers to the oilfields--pipe and drill bit manufacturers, for example--have found their markets dried up. And even the major oil companies, Exxon among them, are cutting their staffs by forced retirements and incentives to leave.

"The landscape is like south Lebanon," Olson said. "The debris is all over."

The decline in oil and gas drilling activity is a sign that the period of rapid growth that marked the economy during the last decade here may finally be slowing. The economic outlook remains bright, but a new reality is setting in, and for the first time in many years, unemployment is now a topic of conversation in Houston.

The strength of the energy industry, which benefited every time the Organization of Petroleum Exporting States (OPEC) raised the price of oil, created in Texas a sense of immunity to the economic woes of the rest of the country, a perception the current recession has nearly wiped out.

Today, people here acknowledge that the growth rates of recent years--6 percent annually in the labor force--were too large to be sustained. The local economy still may add 50,000 new jobs in 1982, but that is far below the average of about 85,000 new jobs added each year recently.

In the future, energy will continue to be a vital part of the Sunbelt economy, but energy industry experts and regional economists said there is little on the horizon to suggest another rapid increase in exploration activity of the kind just experienced.

"We must be near the bottom, but we don't see the industry bouncing back to the levels of the fourth quarter of 1981," said J.C. Grindal, coordinator of strategic planning for Exxon.

Joblessness is now a staple in the Houston newspapers. The unemployment rate here rose to 5.6 percent in May and is expected to increase further when the June figures are calculated. Last year the June rate was 6.2 percent, and local labor market analysts believe it could hit 7 percent this year. The statewide rate hit 7 percent in June, believed to be the highest rate since the 1930s.

Houston's 5.6 percent rate in May is still well below the national average of 9.5 percent, but what concerns labor market experts here is that the rate rose sharply at a time of the year when it historically has not.

Initial claims for unemployment compensation jumped from 7,328 in February to 13,420 in May, according to the Texas Employment Commission. Continued claims for unemployment insurance have risen from 44,770 to 73,218 during the same period.

"It's quite significant," said Ron McMonagle, a labor market analyst for the state. "It's larger than any trend that we've seen."

Rising unemployment has afflicted other cities along the Texas gulf coast, which is home to refineries and petrochemical plants that are operating far below capacity. Hardest hit is the industrial triangle in the southeast corner of the state. Unemployment in Orange County was 12.9 percent in May. In Port Arthur, it was 11.4 percent.

In part, Texas is a victim of its own success. Unemployment is rising because the labor market can no longer easily absorb the influx of out-of-state workers, who continue to see Texas as a job mecca and are still pouring in. Also, the national recession has affected manufacturing firms here and throughout the state.

But the decline in the oil drilling industry was so unforeseen that Texans have concentrated on it. In the past two years, the domestic energy industry, spurred by full decontrol of oil prices and the worldwide price increase that resulted from the Iranian crisis, grew almost giddy with the expectation of continued profitability. Drilling activity grew at a rate of 30 percent a year.

But the decline in world oil prices and other factors have made oil exploration far less attractive this year. Drilling capital has declined by about 50 percent, and the cost of starting new wells has made many operators wary.

The 36 percent drop in drilling activity has brought a wave of bankruptcies among thousands of small oilfield servicing companies, with more expected.

Some energy analysts said they believe the next six months will see a dramatic shakeout of smaller independent oil and oilfield servicing companies. "You haven't seen the impact yet," said Geoff Hertel of the investment firm of Rotan Mosle, Inc. "Most of the companies who are having trouble just now know it. I haven't seen the bloodletting yet."

An official of one company that recently filed for bankruptcy said, "Sales in the oilfield equipment business are nil." Others report equipment selling for 10 cents on the dollar. When business does rebound--and many industry experts believe the decline may be over--it will be at a much slower pace than in the past two years.

Not even the largest and strongest oil companies are immune to the problems brought on by the recession, the worldwide excess of crude oil and the accompanying drop in prices.

Exxon, the world's largest oil company, has revised its internal forecasts and recently instituted a program of voluntary retirements and incentives for separation that will pare its 30,000 member staff.

"We, like a lot of other major oil companies are undergoing a tightening process," Grindal said. "We don't have the opportunities we had a year ago."

Remarkably, things in Houston are far from gloomy. For one thing, even after the sharp drop in drilling, 1982 could end up as one of the highest years on record.

In addition, energy industry experts, perhaps imbued with an incurable faith in the free enterprise system, said the shakeout is overdue and will result in healthier, more productive companies.

"We grew too fast the last two years," said George P. Mitchell, president of Mitchell Energy & Development Corp. "There was some fat in there."

The fat included inexperienced and unproductive crews in the oilfields and a sharp rise in drilling costs. "It was frightening the incompetency in the oil field the last 12 months," one industry analyst said. "What was going on out there would singe your hair."

Daily rig costs in the Anadarko Basin in Oklahoma rose from $5,500 to $12,000 within three years, and today have fallen back to about $8,000, according to Olson.

Many of the companies that are going bankrupt will not even be noticed, testimony to the fragmented nature of the domestic oil industry. "In Houston, the losers are dots on the landscape," an oil economist said. "They're not a Ford or a Chrysler--the very foundation of Detroit. They're very tiny suppliers."

Perhaps of most significance is the fact that Houston can experience such a dramatic tailoff in the energy industry and remain as healthy as it is. In some ways, the drilling slump has shown that the city's reputation as the energy capital of the world may be misleading.

"If the influence of energy on Houston paralleled the auto industry's influence on Detroit, the decline in oil activity over the last six months would have brought this economy to a standstill," said Francis J. Magrino, vice president and economist at Texas Commerce Bank. "We've slowed down, but we're continuing to gain."