This booming little town, until five years ago a stagnating way station on the Union line, sits literally in the middle of the nation's hottest oil and gas territory.

North, south, east and west of Evanston in extreme southeastern Wyoming or across the border in Utah, nearly 100 drill rigs have been scattered at times this year, piercing the complex geology of an area known as the Western Overthrust Belt. And they are scoring big.

Geologists for Amoco Production Co., the domestic production arm of Standard Oil Co. (Indiana), officially estimate that at least 8.5 trillion cubic feet of natural gas and 674 million barrels of oil have been located so far in the area around Evanston known fondly as "the fairway." They are fully confident, much more will be found.

"We are in the billion-barrel kind of thing," says J.W. Vanderbeek, manager of Amoco's Denver region. "It's gross out there."

The Overthrust Belt -- so named because massive forces long ago pushed older rocks westward over younger rocks, in the process creating many geological traps in which oil and gas accumulated -- runs all the way from Alaska to Mexico and is productive in many areas. Some of Mexico's fabulous oil finds lie along it, as do many of Alberta's to the north.

At least one geologist estimated this year that the area from Montana to Arizona probably could produce 15 billion barrels of oil and 100 trillion cubic feet of gas. Today wildcat wells are being drilled in Montana, Idaho, central Utah and Arizona, in addition to all the activity here.

For comparison, total proved reserves in the United States, including Alaska, last year were put at 28 billion barrels of oil and 200 trillion cubic feet of gas. In 1979 the United States consumed 20.2 trillion cubic feet of gas and 6.7 billion barrels of oil.

As is so often the case, success in the search for oil and gas was preceeded by repeated failure. About 500 dry holes were drilled in the general vicinity of the fairway before an independent concern, American Quasar Petroleum Co., hit oil in 1974 in the Pineview field in Utah about 23 miles southeast of here.

That same year, Amoco discovered its Ryckman Creek field about 15 miles to the northeast of here, and the boom began.

Amoco, Champlin Petroleum Co. which is a subsidiary of Union Pacific Corp., and Standard Oil Co. of California (Chevron) have had the greatest successes so far, though dozens of other comnpanies are active in the area, including Exxon and Anschutz Corp., which also operates a huge ranch along the state border.

Amoco, on the basis of strikes so far, has the lion's share of the reserves, but Champlin, by virtue of the Union Pacific's land holdings, has a piece of almost every Amoco well in addition to some of its own.

To encourage construction of a transcontinental railroad at the end of the Civil War, the federal government granted the Union Pacific alternating sections of land in a swath 20 miles wide on either side of its right-of-way. Each section was one mile square, creating a checker-board pattern, with the government owning the intervening squares.

The fairway lies almost precisely within the boundaries of the land grant area, a fact of enormous significance for the future of Union Pacific, which even last year had more revenues from oil and gas ($2.06 billion) than it did from transportation ($1.79 billion.)

Champlin has participated in 15 of the 17 discoveries made in the Overthrust Belt since 1975, and in 7 of the 8 made in 1979 and 1980. Its interest ranges from 9.5 percent to 30.3 percent, the company says. Moreover, it has a share in 13 of the 25 wildcats now being drilled in the area, with an interest running as high as 41.25 percent in one.

Back in 1969, Amoco Production got from Union Pacific exploration rights on 7.5 million acres of land grant territory. That agreement terminated in late 1977, but Amoco continues to hold rights on 12-section groupings on which it had made strikes or was still drilling.

Chevron, on the other hand, leased from the federal government many of the intervening squares of the checkerboard. And all of the companies also leased some of the privately held land, much of which had been sold by the railroad. Few of the buyers, however, had purchased mineral rights along with the surface rights. Champlin is giving such owners a 2 1/2 percent royalty nevertheless, though some of the ranchers still are quite bitter about their circumstances.

The key to the recent successes in the fairway has been vastly improved information from seismic work, says Amoco's Vanderbeek, himself a geologist. To get information about subsurface geology, shallow holes are drilled and a small explosive charge set off. Some distance away, other apparatus records the shock waves that radiate in all directions from the explosion as they are transmitted through the ground.The waves radiating downward are reflected as they encounter different types of rock and different structural features.

The geology in the Overthrust Belt -- which in many ways is similar to that of the Eastern Overthrust Belt running from New York State to Alabama in which oil and gas discoveries now are being made -- is so complex that the same rock formation may be encountered three separate times as a well is drilled.

"We have to massage the seismic data" with computers, Vanderbeek explains. It helps the interpretation greatly if the shot holes are in a straight line, something that in the rugged country of parts of the fairway is all but impossible using truck-mounted drills and recording devices.So the companies have turned to helicopters. "That costs $30,000 a mile," he continues.

Once a drilling site is picked, the battle is only beginning. Typically, the wells encounter zones of salt that are sufficiently plastic so that the hole quickly flows shut again. Other rock conditions regularly deflect drill bits, leaving the wells with doglegs that can make deeper drilling impossible.

A deep gas well that is 12,000 to 15,000 feet deep, can cost $6 million "if we have no trouble," Vanderbeek estimates. But because trouble usually is encountered, the average cost is about $8 million. The oil wells typically are shallower, as well as less costly to make ready for production, so cost only about half as much.

Last month Amoco had 18 rigs working in the fairway. Five were drilling wildcats and 13 were drilling development wells or completing wells for production, according to Martin Zimmerman, Amoco's district production superintendent.

As he drove over the bumpy network of dirt and gravel roads linking the various fields of the fairway. Zimmerman discussed the drilling problems, and the social and economic problems, of the Overthrust Belt:

"Our ability to find porous rocks is getting better. Our geology and our seismic work is better, but the drilling is still pretty rough. Making 100 to 125 feet a day is pretty good, and that costs us, typically, $20,000 to $25,000. . . .

"The Cave Creek discovery has cost us more than $10 million to complete, and we still need a plant to process the sour (high-sulfur-content) gas. We've had the application for the plant in for 10 months, and there's some question about getting the environmental permits. If all goes well, it will still take two years to build and cost several hundred million dollars. . . .

"Evanston was a railroad town with about 4,000 people. When we moved in in a big way, it went to 7,000 or 8,000. People here were aghast. Now housing prices are outrageous . . . One trailer court wants a 10-year lease at $200 a month for a space. . . ."

Whatever the costs, and whatever the problems, the payoff will be huge. Today, only about 60 million cubic feet of gas and 29,000 barrels of oil are produced daily from the Overthrust Belt. At least another 50,000 cubic feet of gas can be sold as soon as the Federal Energy Regulatory Administration gives the go-ahead.

The big production, however, will have to wait until new pipelines are built and Amoco and Chevron complete several gas processing plants. On top of the one 8,000-foot "hill," Amoco is pushing hard to get a $200 million plant sufficiently under cover that work can continue through the often-bitter winter weather. The plant had to be located there so that any emissions would be dispersed over a wide area.

And this small town, which itself sits on the edge of the Yellow Creek field, will bear the brunt of a boom it never sought and still doesn't care for.