Bayesian inversion of free oscillations for Earth’s radial (an)elastic structure

• A Bayesian inversion of spheroidal mode data for radial (1-D) Earth structure using neural networks.
• The method is flexible and allows us to assess the robustness of features in existing models.
• The data prefer an inner–outer core boundary (ICB) that lies deeper than in existing reference models.
• The density contrast at the ICB is probably larger than in PREM and ak135f.
• The jump in VP and VS at the 220 km discontinuity is probably overestimated in PREM.

We perform a Bayesian inversion of degree-zero spheroidal mode splitting function measurements for radial (1-D) Earth structure, in terms of the Voigt averages of P-wave (VPVP) and S-wave (VSVS) velocities, density, bulk and shear attenuation, using neural networks. The method is flexible and allows us to assess the robustness of features in existing reference models, such as PREM. The Bayesian framework provides a means for quantifying uncertainties in the model parameters and for measuring the information content of the data. The analysis of the information content suggests that the free oscillations constrain most parameters better than body wave travel time data.Our most important findings can be summarised as follows. The data prefer an inner–outer core boundary (ICB) that lies in the depth range 5154.7–5165.7 km, i.e. deeper than in existing reference models; the effect on the travel time of inner-core-sensitive seismic phases is comparable to the estimated noise in such measurements. The density contrast at the ICB (0.73 g cm−3) is larger than in PREM (0.60 g cm−3) and ak135f (0.56 g cm−3), but our range including uncertainties (0.52–0.94 g cm−3) encompasses all previous estimates in the literature. The average VPVP and VSVS in the D″ region are smaller than in PREM, whereas the mean density is probably larger. The data cannot uniquely determine whether this density excess is restricted to the D″ region or distributed throughout the lower(most) mantle. The data cannot determine with certainty the presence or absence of a discontinuity at 220 km depth for VP,VSVP,VS and density. If present, the jump in both velocities is likely smaller than in PREM. Shear attenuation parameters in the mantle deviate from PREM in a similar fashion to results from more recent studies. We find a non-homogeneous shear attenuation in the inner core, reinforcing the hypothesis that a distinct ‘innermost inner core’ may exist. The bulk attenuation in the mantle and the outer core is stronger than in PREM.We investigate the influence of radial anisotropy on the inversions and analyse possible trade-offs between (anisotropic) parameters. The largest trade-offs are observed in regions that are believed to be anisotropic, such as the D″ region. This illustrates the need to constrain anisotropy in the (deep) mantle.