It is useful to be able to calculate synthetic primary reflection sequ
ences from which to generate synthetic seismic sections which can be u
sed for testing new processing algorithms. However, these synthetic re
flection sequences should closely match real properties found in recen
t studies. Using the ARMA(1,1) model resulting from such studies to de
scribe the correlation (or spectral) structure of the sequences, and b
y matching moments up to fourth order (since the sequences are non-Gau
ssian in practice), realistic sequences can be generated. A simple sch
eme is provided which also eliminates the necessity of throwing away l
arge numbers of simulated values at start-up. The procedure is illustr
ated on three real sequences and is seen to reproduce all the importan
t features.