Geico Corp. reported yesterday that its first-half net earnings have more than doubled from the same period last year, in large part because of an increase in gains from sale of securities. Second-quarter earnings were also up 27.5 percent from those of a year earlier.

Profits held steady, however, at another insurance company, Monumental Corp. of Baltimore, both in the second quarter and in the first half, compared to results last year, and LogEtronics Inc. of Springfield, Va. reported continued losses in its 1983 second quarter.

For the 1983 second quarter, Geico reported net income of $24.15 million ($1.13 a share), up from $18.95 million (92 cents) in 1982. The company reported profits of $74 million ($3.47) for the first half, compared with $35.9 million ($1.74) in 1982.

The first-half profits reflected a $28.5 million ($1.34) gain from securities sales--more than 28 times the $971,831 (5 cents) earned last year--even though Geico lost $459,592 from investment transactions in the second quarter. The company said it is common for its investment gains to fluctuate.

Operating earnings increased to $24.6 million in the 1983 second quarter from $19.2 million in 1982, and to $45.5 million in the first half from $34.9 million last year.

Monumental reported second-quarter net income of $3.6 million (56 cents), compared with $3.4 million (50 cents) last year. For the first half, the company showed profits of $6.98 million ($1.04), up from $6.78 million ($1.00) last year.

Operating income levels also remained close to those of last year. Monumental second-quarter operating income were $3.588 million, down slightly from $3.593 million a year ago. For the first half, operating income dipped to $6.76 million from $6.97 million in 1982.

LogEtronics, a maker of film processors, reported a second-quarter loss of $268,000 (20 cents), compared with a loss of $31,000 (2 cents) in 1982. In the first half, losses increased to $797,000 (59 cents) after a first-quarter loss of $529,000 (39 cents). Last year, LogEtronics had a net income of $182,000 in the first half.