The advent of broad-band seismology has meant that use is being made o
f a wide range of seismic phases, for many of which ellipticity correc
tions have not been readily available, In particular, when many seismi
c phases are used in location schemes, it is important that the system
atic effects of ellipticity are included for each phase. An efficient
and effective procedure for constructing ellipticity corrections is to
make use of the ray-based approach of Dziewonksi & Gilbert (1976), as
reformulated by Doornbos (1988), in conjunction with the rapid evalua
tion of traveltimes and slownesses for a given range using the tau-spl
ine procedure of Buland & Chapman (1953). Ellipticity coefficients hav
e been tabulated for a wide range of seismic phases and are available
in electronic form. The ellipticity correction procedures have been ex
tended to include an allowance for diffraction phenomena. for example
P-diff, S-diff diffracted along the core-mantle boundary. Corrections
for additional phases can be generated by building the ellipticity coe
fficients from suitable combinations of the coefficients for different
phase segments.