Note on Cusps in Seismic Travel‐times

Summary When there is triplication in travel‐time curves, it is often assumed that the cusps in the curves are necessarily associated with large wave amplitudes. Models which give a good representation of various types of seismic velocity variation are here set up to show that there are important cases in which this assumption does not apply. The analysis, which is facilitated by use of the variable α= 2d log r / d log |Gh, shows fairly directly that dΔ / dp , where Δ and p are the angular length and parameter of ray, is sometimes discontinuous, sometimes continuous, at a cusp.