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The article presents the theory of stationary regularly varying random fields. In this context, we prove a new compound Poisson approximation theorem under appropriate dependence conditions, and demonstrate a couple of effective methods for checking its conditions. The main result is based on an extension of the Grigelionis' Poisson convergence theorem and a novel concept of anchoring of the tail process of regularly varying sequences and fields. We apply these theoretical results to shed entirely new light on the classical problem of evaluating local alignments of biological sequences.

Compound Poisson approximation for regularly varying fields with application to sequence alignment