Archive Corp. of Costa Mesa said it expects to report a 72% jump in earnings and a 37% increase in revenue for its 1988 fiscal year ended Sept. 30. The manufacturer of computer tape drives said earnings are expected to reach $10.5 million, up from $6.1 million in 1987. Revenue should climb to about $122 million from $88.8 million a year ago. The company attributed the improved financial results to strong market demand for its products, which are used to store data in personal computers. Archive expects to release its final 1988 results during the next few weeks.