On the convergence of the time-domain bremmer series

The frequency-dependent Bremmer series for wave propagation in a plane stratified medium has been well studied. It is known that the series converges if the variations in the medium are not too large. Less well-known is the fact that the series is more likely to converge in a medium with large variations if the frequency of the incident wave is high than if it is low. Here we show that if the variations in the medium remain finite, a frequency-independent (Fourier transformed) version of the series converges. We obtain exponential bounds for the series, which can often be improved.