THE ELLIPTICITY CORRECTION TO TRAVEL‐TIMES OF P AND S EARTHQUAKE WAVES.

The importance of the effect of the Earth's ellipticity on the traveltimes of earthquake waves was recently brought into prominence in a paper by Gutenberg and Richter,* and Jeffreys -ihas since given a theoretical analysis of the general effect. I t is proposed in this paper to examine in detail the effect on P and S waves. I . Jeffreys 1 defines a standard sphere of reference such that each internal surface of equal velocity for any pulse is spherical and encloses the same volume as the corresponding surface of equal velocity within the actual Earth. Now let E be the epicentre of any given earthquake and 0 a given observing station, and let their geocentric co-latitudes be a, y respectively. Let the angular distance between E and 0 be A (computed using geocentric latitudes). Take r as the distance from the Earth's centre of any point P on the path of a ray that travels from E to 0, and T 6 ~ as the distance of the corresponding point from the centre of the standard sphere. Let c be the velocity of the ray at P, 9 the angle subtended at the Earth's centre by EP, and s the length of path of the ray between E and P. As usual, p is defined by the equation d% pc z 7' Then if T' is the actual travel-time of the ray between E and 0, and T the time between the two corresponding points on the surface of the standard sphere, Jeffreys shows that to the first order in Srlr [ I dr 1: 1; ( d 2 I I ) r2 dtl d f P r Y T ' T = p --6r + p 6~ -+-d%.