Amplitude, phase and path anomalies of mantle waves

Summary. The amplitude and phase anomalies observed in long period Rayleigh and Love waves (T> 150 s) show definite patterns of variation from orbit to orbit. In some cases the phase anomalies agree with the prediction of linear perturbation theory applied to a spherical reference model (Fermat's Principle), namely that each complete orbit of the earth in either direction corresponds to a constant phase anomaly increment. The corresponding approximation for amplitude anomaly is derived in this study; it is shown that orbits of one sense are amplified (or deamplified) by a constant factor for each complete orbit, and that orbits of the opposite sense are amplified (or deamplified) by the reciprocal factor. This amplification is due to partial focusing and defocusing of a ray bundle. The data often show such behaviour, establishing that the large observed anomalies are caused by focusing and defocusing due to heterogeneity. Some of the data, however, show substantial deviations from these approximations, indicating that lateral refraction is sometimes a large effect for high orbits. Evidence is presented for orbits which have paths deviating from the great circle by more than 1000km. A technique is outlined for making use of such data to constrain lateral variations in earth structure.