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.

中文翻译：

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使用矩阵自回归的内核敏感模式概率估计结构系数及其不确定性

概要

正常模式结构系数是推断深地球内部速度，密度和衰减结构的关键观察结果，但是从地球正常模式光谱估算这些系数是一个非线性反问题。另外，对于大地震，完整的震源信息通常是未知的，并且在震源和衰减之间要进行权衡。因此，正确估计具有不确定性的弹性和非弹性结构系数变得具有挑战性。在这里，我们结合了矩阵自回归和完全非线性的概率抽样来解决现有的局限性。在使用具有噪声的合成数据成功进行可行性实验之后，我们将此组合方法应用于1994年至2016年地震测量的19种内芯敏感球体（S）模式的数据。我们进一步实施模型选择标准，以评估无弹性结构是否重要。我们的模型选择标准表明，仅对于内芯具有强剪切波能量的模式，才需要非弹性结构系数。反演结果还表明，这些模式的弹性和非弹性分裂函数之间具有很强的相关性。这表明地震波沿极路径传播的速度更快并且衰减很大，因此对于这些模式，m = 0单峰仍然很差。反演结果还表明，这些模式的弹性和非弹性分裂函数之间具有很强的相关性。这表明地震波沿极路径传播的速度更快并且衰减很大，因此对于这些模式，m = 0的单峰仍然很差。反演结果还表明，这些模式的弹性和非弹性分裂函数之间具有很强的相关性。这表明地震波沿极路径传播的速度更快并且衰减很大，因此对于这些模式，m = 0单峰仍然很差。