Abstract
SUMMARYWe 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.
Highlights
Inner core solidity was first observed using whole Earth oscillations or normal modes by Dziewonski & Gilbert (1971), it had already been predicted by a number of authors (i.e. Lehmann 1936; Birch 1940; Bullen 1946) before any direct observations were available
The Preliminary Reference Earth Model (PREM, Dziewonski & Anderson 1981), which was created using a combination of both normal mode and body wave data, has a strongly attenuating inner core with Qμ = 84 and has non-zero bulk attenuation with Qκ = 1328 mostly constrained using radial modes
We try a range of c20 values to test the best starting models, as it is usually not possible for inner core sensitive modes to converge to a solution by just starting from PREM, while all our c40 coefficients are started from PREM
Summary
Inner core solidity was first observed using whole Earth oscillations or normal modes by Dziewonski & Gilbert (1971), it had already been predicted by a number of authors (i.e. Lehmann 1936; Birch 1940; Bullen 1946) before any direct observations were available. Inner core solidity was first observed using whole Earth oscillations or normal modes by Dziewonski & Gilbert (1971), it had already been predicted by a number of authors The main issue is the incompatibility between body waves and normal modes based models of shear attenuation Qμ. The Preliminary Reference Earth Model (PREM, Dziewonski & Anderson 1981), which was created using a combination of both normal mode and body wave data, has a strongly attenuating inner core with Qμ = 84 and has non-zero bulk attenuation with Qκ = 1328 mostly constrained using radial modes. Body waves still prefer an even more strongly attenuating inner core than normal modes. Two possibilities have been suggested to overcome the disagreement either (i) non-zero inner core bulk attenuation Qκ in order to explain strong compressional wave attenuation, or (ii) frequency dependent Qμ in
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