Fairfax County, already the fastest-growing jurisdiction in the metropolitan areas, is in the middle of a population surge that could continue indefinitely, according to a newly released county study.

Despite attempts by the county to slow its growth, almost 48,000 people will be added to the county's present population - 567,600 - this year and in 1979, according to the study by the county's Office of Research and Statistics.

The projected growth rivals earlier surges in the mid-1960s, when Fairfax and the entire surburban ring round Washington were experiencing an unprecedented construction boom. For example, from 1965 to 1967 Fairfax's population grew from 347,100 to 403,500, an increase of 56,400.

Most of growth in Fairfax is occurring in the county's distant southern and western sectors - areas that don't have enough public services and roads to absorb population surges.

The lightly populated Pohick region southwest of Springfield, for example, is expected to be the site of more than 40 percent of the total growth projected in the county in 1978 and 1979.

All this growth in the newly developing areas means that more schools, police and fire stations and other facilities will be pressure to improve the network of rural roads, laid out on farm land long before commuter rush hours were imaged.

These improvements will require millions of dollars in public funds, much of which will have to be sought from voters in bond referendums. In recent years, county residents, upset over their increasing real estates tax burden, have rejected proposals to build new schools and fire stations.

Though the Fairfax study follows the surge only through 1979, it says there is a "long-term potential of increased residential development activity."

Fairfax officials, who in 1975 launced a widely publicized plan (called "PLUS" for Planning and Land Use System) to bring their county's development under control, have been hoping that growth would fall off - to 12,000 to 14,000 a year - at least in the 1980s. But the study offers no evidence of a coming slowdown.

One of the prime indicators of what is likely to happen is the so-called "pipeline," which includes new houses and apartments ready for occupancy, those under construction and those planned to be built. The study by the Office of Research and Statistics reports that the pipeline has gotten bigger - "for the first time in three or four years," according to county demographer David Sheatsley.

Last year, in arguing that growth was "moderating," ORS said "pipeline growth is down." But new figures show the pipeline has risen 12.2 percent - from 91.212 units to 102.330.

Another indicator of growth - building permits, which are authorizations to begin construction - also attests to Fairfax's continuing capacity to grow faster than all the other jurisdictions in the area. During 1977, Fairfax issued more than 40 percent of all permits granted in the metropolitan area, Sheatsley said.

Road improvements in the county have been held up by a lack of state funds, time-consuming planning and, sometimes, opposition from residents trying to preserve a rural atmosphere as the county relentlessly urbanizes.

The county's number one priority - construction of the Springfield bypass to link the Pohick region to I-95 - may not be completed for eight years, state officials have estimated to the dismay of county leaders promoting the project.

The full impact of the growth occuring in the Pohick and other rapidly developing areas, such as Herdon-Reston and Great Falls, is partially disguised in the new Fairfax study. While the study says about 48,000 people will be added this year and in 1976, actually more than 60,000 people are expected to move into new houses and apartments in those two years.

But Sheatsley said the declining household size in older parts of the county closer to the Beltway will mean a net population increase that will be smaller - 48,000.

Any declines in the settled areas, however, will not greatly reduce the demand for services from the people who will be moving to less urbanized areas.

In hoping for slower growth, county officials have been heartened by the declining size of the average household, especially in apartments and town houses. But the emphasis in the recent construction has been on single-family houses, which still are home for the statistical family of two adults and 1 1/2 children. The ORS study says future construction will continue to emphasize single-family houses.

The Fairfax study also reported that the median value of houses in the county has risen from $64,000 in 1977 to $68,200 in 1979 - an increase of 5.6 percent. The increase since 1970 when the median value was $35,300,has been 93.2 percent.