Buried under a 700-foot granite mountain just outside Salt Lake City is a vault with a massive steel door engineered to protect the treasures in case of a nuclear bomb blast.

The treasures thus secured are neither gold nor precious jewels, but rolls of microfilm - more than a million of them - which the Momon church has collected to aid in geneological research.

Since televising of Alex Haley's "Roots" - and particularly since Haley's mention Mormon genealogial facilities last month on the Jonny Carson Show - Mormans in Salt Lake City are being flooded with appeals for help from ancestor-seekers of all creeds at the rate of one out-of-state telephone call a minute, a church spokesman said.

For most of those inquires, checking out one's family tree is only a pastime, albeit an increasingly popular one. Geneological reasearch is reportedly the third most popular hobby in the country, ranking after coin and stamp collecting.

But for members of the Mormon faith, known more properly as the Church of Jesus Christ of Latter Day Sainus, it is an important tenet of their religion.

Mormons searcah out their ancestors in order that the living may serve as proxies in carrying out certain rites of salvation for dead relatives who for whatever reason, neglected such rites in their lifetimes.

The church teaches that family ties do not end in death but continue in the afterlife if "sealed for time and all eternity" in sacred temple rites.

Mormons hold that happiness, in both this world and the next, is a big family. They believe that attaintment of the most preferred status in eternity is dependent on carrying out the obligation placed on them by their religion to perform the proxy ordinances for their ancestors.

The church requires that the identity of any dead person for whom proxy work is done be fully documented; hence the church's establishment of genealogy research facilities not only in the master library in Salt Lake City but in 231 branch libraries around the world.

There are three such branches in the Washingto n area: in Annandale, Oakton, Va., and Silver Spring, Md.

"Anyone can fill out a form and borrow any microfilm from Salt Lake City for 50 cents for a two-week rental," explained Lt. Bryan R. Elkins, volunteer head of the Annandale repository.

Elkins, a hospital administrator for the Navy, who is assigned to the Navy's Bureau of Medicine and Surgery, explained that the facilities are open to non-Mormons as well as to church members. "In fact we encourage non-Mormons to use the library," he said. Local Mormon libraries are listed in the telephone directory under Church of Jesus Christ of Latter Day Saints.

Elkins has traced his ancestry back 35 generations, to the year 970. He is quick to credit his father and grandmother for doing a large part of the work - and knows first-hand both the pitfalls and the rewards of ancestor-tracking.

"You can start with name gathering, and you get all the names that are identical or similar," he said, pointing out that in earlier times, in hand-written documents, consistency in spelling was a virtue pursued by few at a time when most of the population was illiterate.

"We've found 23 different ways to spell 'Elkins.' In one will, a man mentioned his name three times and spelled it a different way each time," he said.

The Nordic system of patronymics, in which fathers' first names became their sons' last names, offers a special kind of puzzle to genealogists. Elkins explained "With patronymics, a son born to Hans Jenson was named not 'Jenson,' but 'Hanson,' just as Jenson's father would be named not 'Jenson,' but 'Jens Anderson,'" Elkins explained.

High infant mortality rates occasioned another custom that makes trouble for genealogists. "It was the custom to give children Biblical names. If the first child died, then the next child might be given the same name. One of my ancestors had three sons named Moses and none of them lived. There were 11 children born to the family, but only four names were used."

One "wierdo" in his family tree, Elkins said, "had four sons and he gave all of them the same name as his - and they all grew to adulthood."

"Since we as Mormons believe we exist after this life," said Elkins with a grin, "there are several individuals I just can't wait to meet!"

Published geneologies, Elkins said, are not always the most reliable records. "The accuracy may depend on why the record is needed. If they feel they just have an ancestor who came over on the Mayflower, they may take some short-cuts," he said. Even some of the genealogies recorded in the Bible, he added "cut out th black sheep."

Elkins says the Washington area is the "best in the country" for genealogical research, largely because of church member, June Andrew Babbel, has put together a comprehensive 135-page "Guide to Genealogical Research In the Nation's Capital."

It is complete down to floor plans of institutions for such research and even instructions for getting there by Metrobus. It's available from local Mormon genealogical libraries for $5.

According to Elkins, Mormons rely heavily on all kinds of government records for tracking down ancestors: tax, army, pension, census, register and transfer of property and wills - even poorhouse and prison records. Parish church records of baptisms, marriages and funerals are also considered highly reliable.

"England," said Elkins of the land of his ancestors, "is especially noted of keeping reords."

The Mormon library in Salt Lake City not only keeps records of all the persons whose existence has been verified for proxy rites - "We have more than a billion names on record," an official in Salt Lake City said last week - but is recording other material as well.

"The church has had a program of copying down all the headstones in cemeteries through the South and New England," Elkin said. "The Salt Lake City library has crews out microfilming records all over the world - not only in England and western Europe but in Japan, Indonesia . . . "

"Many records are the only copy in the world that's in existence. So many records were destroyed in World War II. The faster we get these records microfilmed the better," he said.

A full roll of microfilm, Elkins said, may contain "as many as eight volumes." The Utah library has more than a million rolls and is producing new ones at the rate of 4,000 a month. It is the third largest user of microfilm in the country.

Mormons believe all mankind has a common ancestor, the Bilblical Adam, and that in heaven, as Elkins explains, "Father Adam will be the head of the eternal family and his lovely wife will be by his side."

They haven't been able to push the genealogical charts back quite that far. But they're working on it.