Conventional approximations of reflection traveltimes assume a small offset
-to-depth ratio, and their accuracy decreases with increasing offset-to-dep
th ratio. Hence, they are not suitable for velocity analysis and stacking o
f long-offset reflection seismic data. Assuming that the offset is large, r
ather than small, we present a new traveltime approximation which is exact
at infinite offset and has a decreasing accuracy with decreasing offset-to-
depth ratio. This approximation has the form of a series containing powers
of the offset from 1 to -infinity. It is particularly accurate in the prese
nce of a thin high-velocity layer above the reflector, i.e. in a situation
where the accuracy of the Taner and Koehler series is poor. This new series
can be used to gain insight into the velocity information contained in ref
lection traveltimes at large offsets, and possibly to improve velocity anal
ysis and stacking of long-offset reflection seismic data.