Constraining 1-D inner core attenuation through measurements of strongly coupled normal mode pairs

SUMMARY We measured inner core normal mode pair 10S2–11S2, which cross-couples strongly for 1-D structure and is sensitive to shear wave velocity, and find that our measurements agree with a strongly attenuating inner core. In the past, this mode pair has been used to try to resolve the debate on whether the inner core is strongly or weakly attenuating. Its large spectral amplitude in observed data, possible through the apparent low attenuation of 10S2, has been explained as evidence of a weakly attenuating inner core. However, this contradicted body waves and other normal modes studies, which resulted in this pair of modes being excluded from inner core modelling. Modes 10S2 and 11S2 are difficult to measure and interpret because they depend strongly on the underlying 1-D model used. This strong dependence makes these modes change both their oscillation characteristics and attenuation values under a small 1-D perturbation to the inner core model. Here, we include this effect by allowing the pair of modes to cross-couple or resonate through 1-D structure and treat them as one hybrid mode. We find that, unlike previously thought, the source of 10S2 visibility is its strong cross-coupling to 11S2 for both 1-D elastic and anelastic structure. We also observe that the required 1-D perturbation is much smaller than the 2 per cent vs perturbation previously suggested, because we simultaneously measure 3-D structure in addition to 1-D structure. Only a 0.5 per cent increase in inner core vs or a 0.5 per cent decrease in inner core radius is required to explain 10S2–11S2 observations and a weakly attenuating inner core is not needed. In addition, the 3-D structure measurements of mode 10S2 and its cross-coupling to 11S2 show the typical strong zonal splitting pattern attributed to inner core cylindrical anisotropy, allowing us to add further constrains to deeper regions of the inner core.