"The Deep," scheduled to open Friday at nine area theaters, is to a considerable extent the creation of three men called Peter. Derived from the best-selling adventure novel about treasure diving by Peter Benchley, who acquired fame and fortune as the author of "Jaws," the movie was directed by Peter Yates and produced by Peter Guber, whose chief deputy happened to be an experienced diver and underwater photographer named Peter Lane. When the five-month shooting schedule began in July 1976, that production was based, inevitably, on Peter Island in the British Virgin Islands.

In recent conversations in New York and Washington, the direction and producing Peters recalled some of the problems they encountered and solutions they found in the processing of transposing "The Deep" to the screen. Yates, 48, a pot-bellied but sturdy Englishman with as an easygoing disposition and a winning gap-toothed smile, regards the picture as "virtually the first underwater film ever shot.

"There have been other fiction films with underwater sequences, of course, but I don't believe any were as extensive or varied as ours, nor as photogenic and exciting. I was very pleased by the look we achieved. The light diffusion makes shooting underwater difficult, but you'd never know it from the quality of our images. The whole screen looks pin-sharp."

Yates came to the United States a decade ago to make his fourth feature, and biggest hit to date, the Steve McQueen police thriller "Bullitt." He now resides in Connecticut with his wife and their two children. Although he's physcially active and generally regarded as a superior action director, Yates began "The Deep" with no diving experience to speak of and no burning desire to submerge.

Like almost everyone on the production, including co-stars Robert Shaw, Jacqueline Bisset, Nick Nolte and Lou Gossett, he got on-the-job training from Al Giddings and Stan Waterman, the veteran underwater cameramen hired to photograph the diving sequences. As things transpired, director of cinematography Christopher Challis also spent more time underwater than anyone had originally planned, a development that evidently helped Yates achieve a more consistent visual style than he had dared hoped for.

"I wanted Chris in the first place because he's great cameraman," Yates said, "and in the second place because he sails and has had experience with seagoing pictures. He worked on both 'H.M.S. Defiant' and 'Sink the Bismarck.' I knew that he wouldn't do all the usual inexperienced things that waster time when you have to shoot at sea, like lash a raft next to the ship and then look puzzled when the waves wash all the equipment off it. He learned to dive too and established wonderful rapport with Al and Stan.

"I had gone down several years ago for a movie called 'Murphy's War.' I hadn't liked it a bit. I was wearing all sorts of cumbersome equipment that had since became obsolete. That was a nuisance, but I also developed earaches that hurt like bloody hell. I was dreading a recurrence of the ear trouble when I started 'The Deep,' but in some guilt-ridden Presbyterian way, I suppose, I was prepared to endure it. And, in fact, the earaches returned the first few times I dived. But thank god for Al Giddings, and people who know what they're going in general! When I complained about my ears, he had me describe the feeling and immediately deduced that I was breathing incorrectly. He showed me the proper way to breathe and the trouble ended."

Although Yates prefers driving, sailing and particularly skiing to deep sea diving, the lure of "the deep" got to him. "You discover that it's a totally different environment down there," he said. "Once you've adjusted to the change and begun to feel relatively comfortable, you're aware of new sensations and intrigued at the prospect of communicating them on film. One of the most fascinating things to me, after I'd learned to relax and listen, was the quality of sound underwater. At first you're only conscious of the general rush of pressure singing in your ears, but then you begin to apprehend a variety of sounds, all very distinctive - bubbles, respirators, the echoes off wrecks.

"We spent several weeks in post-production working to recreate and stylize those sounds in a pool at the Burbank Studio. It was very difficult at first getting the authentic spooky resonance you hear underwater, but I think we've done it. There are five diving sequences which add up to about 30 minutes of running time. In addition to varying the kinds of action going on underwater, we've tried to alter the sound slightly with each descent. In some dives we add music, in others we go with sound effects only. We wanted a mix that would be surprising and suspenseful. John Barry, our composer, worked on frequencies that Fred Brown, our post-recorder, wasn't using for his metallic and rumbling and other sounds."

Yates estimated that the finished film would consist of about 25 per cent underwater scenes and 75 per cent surface scenes. Naturally, the former took much longer to shoot, requiring almost 12 weeks of production while the surface footage took about eight weeks. There were two principal underwater locations: the site of the wreck of H.M.S. Rhone, a mail ship that sank in 1867 near Salt Island in the Virgin Islands, and an enormous underwater set constructed by the company on a hillside in Bermuda.

Benchley's story concerns a vacationing couple, played by Bisset and Nolte in the movie, who happen upon two layers of buried treasure - a cache of morphine ampules lost during World War II on top of coral-encrusted jewels lost by a Spanish galleon. The Rhone was used for establishing shots, photographed at depths of 80-100 feet. The man-made set was designed to establish control over the intimate, detailed underwater action.

Production designer Tony Masters, who was also called upon the build a lighthouse and a 100-foot elevator tower to accommodate highlights from the book, scooped a saucershaped pool 30-feet deep and 120-feet in diameter out of the coral, then sealed it with cement and 15,000 pounds of urethane spray. It look four pounds of urethane spray. It look four months to build this giant outdoor studio tank, which was then filled with sets representing the wreck of the Rhone and a million gallons of ocean water. The set was stocked with fish indigenous to the British Virgin Islands, and 200,000 gallons of fresh ocean water were pumped into it daily to assure maximum clarity, while the old water was diverted over a spill wall and back to sea.

Giddings designed a new waterproof housing for three 35mm Panavision cameras that reduced their surface weight from 225 to 75 pounds. Below the surface, the cameras weighed 8 ounces. Yates found that by holding the legs of a cameraman he could guide his motion in ways that approximated dolly or cran shots on the surface. Underwater Yates was singled out by wearing a yellow wet suit. His face mask was also rigged with a microphone which allowed him to transmit instructions to the surface which then relayed by an assistant into a submerged public address system. "Between takes we'd have music piped in," Yates recalled."You can't imagine how frightening it is to be underwater and suddenly hear Strauss' 'Zarathustra' surrounding you."

Benchley, who did the first draft of the screenplay, which was then revised by Tracy Keenan Wynn and augmented by additional dialogue from Tom Mankiewicz, seems to have anticipated some of the problems the filmmakers might face. "The Deep" is a better written book than "Jaws," and a more movie-wise book as well. The action shifts from land to sea to underwater and back again with an urgency and variety that indicates the writer recognized the melodramatic liabilites in prolonged submersion.

Guber, 35, a delightfully energetic and enthusiastic young entrepreneur making his debut as an independent producer after several years as an executive at Columbia, the company distributing "The Deep," expressed the problem succinctly: "Underwater pictures have a way of going lugubrious on you."

About $8.5 million was invested in this new and possibly innovative underwater adventure movie in the hope that it would prove anything but lugubrious. Another $5 million has been earmarked for the advertising campaign. Although "The Deep" will performance of "Jaws" or the pace currently being set by "Star Wars," it is Columbia's big hope for the summer. It will have to compensate for costly write-offs like "Nickelodeon" and keep the studio in contention as a major at least until the arrival of Steven Spielerg's "Close Encounters of the Third Kind" next winter.

Columbia recruited Guber right out of New York University Law School, and he spent three years as an exceptionally young executive vice president in charge of worldwide production before switching to the more lucrative and apparently satisfying role of independent producer. It's obvious that Guber viewed "The Deep" as a deliverance from desk work and relished every moment as a "working producer" on location.

"I always thought I'd end up in Washington as a government lawyer," Guber said. "Not that my family frowned on movies. They were just something other people did. Even now I have trouble making what I do sound socially repectable. Do you know what I mean? I love what I'm doing, but it doesn't seem as real as other professions. It's not like being in agriculture or the steel industry. My kids are still too young to grasp precisely what my job entails, so I tend to say, 'Daddy tells stories for a living.' It sounds a little nebulous, huh?

"But as a matter of fact, this business is important to the economy. American movies are significant balance-of-payments asset, and they're probaby one of our most effective sources of propaganda, especially when they don't make propagandistic noises.

Guber's only worry about "The Deep" is that it may be measured against "Jaws." According to Yates, the preview reactions in San Francisco were highly encouraging: "People seemed to find it a rousing story. They were alerting the good guys to look out behind them and cheering when the bad guys got it, which is what we intended. I hope it revives the kind of feelings I had going to the movies before I got professionally interested. At that time I was looking for good stories that allowed me to forget about my problems. That's the way Benchley writes: good entertainment that doesn't insult you intelligence."