Standard Oil Co. of Ohio, benefiting from sharply higher crude oil prices, yesterday reported a 15 1/2 percent increase in first-quarter profits, but Standard Oil Co. of Indiana said its earnings declined 34.6 percent in the quarter.

Sohio's increase, which bucked the trend of lower earnings expected for most major companies, reflected the company's large profits from Alaskan oil production and relatively small refining operations.

Sohio said it earned $520.4 million ($2.12 a share), up from $450.7 million ($1.84) in the same period of 1980. Revenues rose to $3.12 billion in the first three months this year from $2.66 billion.

Standard of Indiana said it earned $376.7 million ($1.29), down from $576 billion ($1.95), in the 1980 first quarter. Revenues rose to $7.9 billion from $6.5 billion a year earlier.

"The large earnings decline primarily reflects the poor results of refining, marketing and transportation operations worldwide, which showed a loss of $208.5 million for the quarter, compared with a profit of $106.4 million in the first quarter of 1980," Amoco Chairman John E. Swearingen said.

AMAX Inc., a diversified mining and natural resources company, said its first-quarter earnings plunged 50 percent from a year ago, largely because of a drop in demand for minerals.

Profits for the three months ended March 31 sunk to $70.1 million ($1.04 a share) from $140.3 million ($2.45), in the comparable year-earlier period.

A $22.8 million gain from the exchange of convertible preferred stock for debentures brought first-quarter earnings of Lockheed Corp. to $2.33 a share, up from 71 cents a year ago, the company said.

New income for the three months increased to $36.3 million on sales of $1.3 billion compared with $12 million a year ago on sales of $1.1 billion. The debenture exchange also slashed the company's long-term debt by $86.3 million.

Operating earnings, hurt by a rise in interest expense, were 83 cents a share in the 1981 quarter.

Santa Fe Industries Inc. reported record first-quarter earnings of $68.1 million, up from $52.3 million a year earlier as a result of significant improvements in the company's rail and petroleum operations.

Chairman John S. Reed said revenues for the latest quarter rose 47 percent to $1.06 billion from $724 million in the first three months last year.