Inner core rotation: a test at the worldwide scale
Résumé
In order to determine the angular velocity Ω of a possible inner core differential rotation with respect to the mantle, we analyse travel times of waves sampling the inner core at the worldwide scale over a period of about 30 years. For situations in which the inner core heterogeneities are dominant with respect to the mantle heterogeneities, travel times of summary rays (i.e., bunches of seismic rays with the same geometry) must have smaller mean standard deviations when computed in the inner core reference frame than when computed in the mantle reference frame. Thus, we build summary rays by applying a backward rotation of the inner core at angular velocity - Ω, in order to sum residuals which sample the same inner core region at different times. The mean standard deviation of the summary ray residuals, computed for different values of Ω, should exhibit a minimum for the effective Ω-value. This method has been applied to absolute PKP(DF) residuals, in considering only polar paths, for which inner core heterogeneities are dominant with respect to mantle heterogeneities. The data used come from a high-quality file derived by Engdahl et al. [Engdahl, E.R., van der Hilst, R., Buland, R., 1998. Global teleseismic earthquake relocation with improved travel times and procedures for depth determination. Bull. Seismol. Soc. Am. 88, 722-743.] from the catalogs of the International Seismological Centre (ISC) for the period 1964-1995. The minimum standard deviation is obtained for the null rotation rate. A similar analysis on the absolute PKP(BC) residuals, which correspond to paths that do not sample the inner core, shows that mantle heterogeneities are not at the origin of the observed minimum. The same method has also been applied to a set of more than 1200 worldwide-distributed PKP(BC)-PKP(DF) differential travel time residuals, hand-picked by ourselves or gathered by different authors for specific core studies. Here again, the minimum standard deviation is obtained for the null rotation, implying a synchronous rotation of the inner core with the mantle. However, the limited number of very old data, and the geographic distribution of the paths, prevent us from obtaining a resolution better than 1°/year. In particular, a small super-rotation with Ω=1°/year cannot be ruled out with the presently available data. The problem of the level of the inner core heterogeneities compared to that of the mantle, which is another possible limitation of the method, is also discussed.