Mobil Corp. said yesterday that rising crude oil prices and sharply improved profits on refined products overseas allowed the company to earn $651 million, or $1.58 a share, in the fourth quarter of 1990, up 45.6 percent from $447 million, or $1.08 a share, in the 1989 period.

The nation's second-largest oil company said revenues rose 30.5 percent in the quarter, to $19.15 billion, from $14.67 billion in 1989.

The figures easily topped most predictions on Wall Street, helping lift the company's stock 37.5 cents, to $56.75 a share, in trading on the New York Stock Exchange.

Analysts noted that earnings would have been even better but for a number of special charges, includ

ing $112 million to write down the value of various exploration properties, a $105 million write-down in the value of coal deposits, and $54 million to pay for future environmental remediation projects.