An explanation of the systematic error in the Jeffreys-Bullen Travel-time table

Abstract

Plotting the seismic travel time from a point as a function of azimuth and distance yields a surface called a "chronoid". The chronoid for the standard eart h is a surface of revolution, termed the ·'standard chronoid". Local anomalies are defined as the set of coordinate transformations required to bring the local chronoid into least-square coincidence with the standard chronoid. In general, this is accomplished by mea ns of two mutually orthogonal translations, plus one rotation in an azimuthal plane. These operations giw rise to three distinct components of the local anomaly. One of these. the "skew anomaly'', introduces a hias in the travel-time residual as defined by J effreys. It is shown that the expected value of the residual is greater tan zero. The assumption that the mean residual is zero leads to a systematic overestimation of the standard travel time.