Normal-mode constraints on the structure of the Earth

We have analyzed the splitting characteristics of 75 spheroidal free oscillations excited by the Great 1994 Bolivia and Kuril Islands earthquakes. These spheroidal modes may be roughly subdivided in terms of 8 radial modes, 40 mantle modes, and 27 core-sensitive modes. The splitting of each mode is corrected for the effects of rotation and hydrostatic ellipticity. The remaining signal is due to lateral variations in the mantle and core and may be expressed in terms of so-called splitting functions, which represent a local radial average of the Earth's even three-dimensional heterogeneity. In the surface-wave limit, splitting functions are the equivalent of an even-degree phase velocity map. Each mode is uniquely sensitive to the Earth's structure. Some modes are predominantly sensitive to compressional velocities in the upper mantle, others to shear velocity variations in the lowermost mantle, and some modes ''see'' the inner core. As part of our analysis, we determine the center frequency and quality factor of each individual mode; these observations constrain the terrestrial monopole. Collectively, the normal-mode splitting observations presented in this paper put constraints on the large-scale, even structure of the entire Earth. We compare the observed splitting functions with predictions from three recent Harvard models: SH12WM13, SKS12WM12, and PS12WM13. These models are constrained by traveltime and waveform data but contain no normal-mode information. We demonstrate that large-scale, even structure is quite accurately represented in current Earth models, but that the splitting of some predominantly compressional modes is not satisfactorily explained. Although a distinct mantle signal is observed in the splitting functions of core-sensitive modes, a characteristic zonal degree 2 pattern is missing. This missing signal is believed to be the result of inner core anisotropy.