Mobil Oil Corporation began digging in Fairfax county yesterday. No, it was not oil exploration, but the county may strike it rich.

Mobil formally broke ground for its U.S. Marketing and Refining Division headquarters, which will be located on Gallows Road, just off the intersection of Interstate 495 and Route 50.

Prior to the official ground-breaking, Mobil Chairman Rawleigh Warner Jr. and Gov. John Dalton addressed a group of 200 state and county officials, Mobil executives and press, under two yellow and white striped plastic tents while the Falls Church High School 23-piece band entertained.

It was perhaps appropriate that one of the tunes played by the band was "Who Sorry Now?", since the new facility will bring some 1,300 new employes to Northern Virginia from financially beleaguered New York City.

Warner denied that Mobil was abandoning New York. In an interview after the groundbreaking, he said. "We are leaving 2,600 employes there, and we have just bought the building we have been renting there for years."

But he would not state flatly that more Mobil divisions would not relocate outside of New York. He said discussions on such matters are always going on, and "I don't know what the future will dictate."

Dalton appeared particularly happy to be at the groundbreaking. For his and Virginia's sake, the band played, "Sing, Sing, Sing."

"We are going all out to bring companies to Virginia," Dalton said in an interview. "We have several attractions, including the very significant factor of being located near the nation's capital. And we have other attractions like a 5 3/4 percent maximum income tax and a Right-to-Work law."

Warner agreed, emphasising the attraction of being near the capital.

"It has become a fact of business life that our activities involve increasing interfaces with government and government regulation," Warner said in his speech. "From here, U.S. Division managers will have easy access to the various federal offices with which they must deal . . . this proximity to Washington will continue to grow in importance."

He also cited easy accessibility to Dulles Airport, attractive nearby housing, and "reasonably complete cultural and recreational amenities," as reasons for choosing Virginia over such possible relocation sites as Maryland, Connecticut and other spots on the eastern seaboard.

Warner also said Mobil enjoyed excellent relations with state government officials while developing the move.

Mobil official Bill Richardson, who headed up the relocation project, praised the "integrity and financial stability of the state and local governments," as a major factor easing the move here.

Both officials praised Fairfax county Board of Supervisors Chairman John Herrity for his work in getting Mobil to move to his county.

Herrity presented Warner with a silver shovel and a plaque showing the shovel to be a gift from the people of Fairfax County. In his remarks before the groundbreaking, Herrity said that the business tax base in Fairfax county had slipped from 16.5 percent of the total county tax base in 1971 to 14 percent in 1975.

Pointing out that the figures meant that residential users were paying higher portions of the county tax bills in recent years, Herrity added, "We did not think that trend should continue."

Mobil is one of several operations moving major facilities into Fairfax County recently, including American Telephone and Telegraph Co. and Boeing.

As part of the festivities, Dalton presented Warner with a "stock certificate" for a share in the Virginia Company, the first corporation in America, which was set up in 1607 in Virginia to foster trade between Virginia and England.

The Mobil facility will consist of two buildings. One is an eight-story office building, consisting of two wings and a cylindrical core. It will house the basic administrative services and a heliport on the roof of one wing.

The second building will have three stories and contain an employe services and training center, as well as an atrium. The buildings will be linked by a glass-enclosed pedestrian walkway.

There will be underground parking facilities in the building, which was designed by architect Gyo Obato, of the St. Louis firm of Hellmuth, Obato & Kassabaum.

The complex, located in the center of a heavily wooded area, and is scheduled for occupancy in the summer of 1980.