A New Method of Deriving Seismic Velocity Distributions from Travel-time Data

A law of the form gives a useful first approximation to the seismic velocity distribution in various parts of the Earth. A method is here devised of finding the corrections to numerical values given by the law which are needed to fit a given set of seismic travel-time data. The method provides an alternative to the classical Herglotz method of determining seismic velocity distributions, and can be specially powerful in regions where the proportionate deviations from the above velocity law are small or moderate. The method is exact in spite of the non-linear form of the first approximation. Auxiliary notes are given which facilitate computation in particular cases, for example when the form T = aΔ−bΔ3 has been used to represent part of the travel-time data. For purposes of illustration, the method is applied to determining the P velocity distribution for the whole region E of the Earth. The method incidentally illustrates anew the importance of the parameters ζ and α (defined below) in ray theory.