Probabilistic estimation of structure coefficients and their uncertainties, for inner-core sensitive modes, using matrix autoregression

Abstract

SUMMARY Normal-mode structure coefficients are crucial observations to infer the velocity, density and attenuation structure of the deep Earth interior, but estimating these coefficients from Earth's normal mode spectra is a non-linear inverse problem. Additionally, complete source information is typically unknown for large earthquakes, and there is a trade-off between the earthquake source and attenuation. Therefore, proper estimation of elastic and anelastic structure coefficients with their uncertainties becomes challenging. Here, we combine a matrix autoregression and a fully non-linear probabilistic sampling to address existing limitations. After successful feasibility experiments using synthetic data with noise, we apply this combined approach to the data for 19 inner-core sensitive spheroidal (S) modes measured for earthquakes from 1994 to 2016. We further implement a model selection criterion to assess whether anelastic structure is significant. Our model selection criterion indicates that anelastic structure coefficients are required only for modes with strong shear-wave energy in the inner core. Inversion results also show a strong correlation between elastic and anelastic splitting functions for these modes. This indicates that the seismic waves travel faster and strongly attenuate along polar paths such that the m = 0 singlet remains poorly observed for these modes.