Data stacking methods for isolation of normal‐mode singlets of Earth's free oscillation: Extensions, comparisons, and applications

We review three data stacking methods developed for attaining the splitting parameters of normal modes of the Earth's free oscillation, namely, SHS (spherical harmonic stacking), OSE (optimal sequence estimation), and MSE (multistation experiment), that take advantage of the spatial orthogonality of the (scalar and vector) spherical harmonic functions. We further extend these methods to broader applicability as appropriate, in particular SHS extended to matrix-SHS (MSHS) to better accounting for the nonglobal distribution of recording stations, and OSE and MSE extended to transverse components and arbitrary harmonic degrees. We conduct synthetic numerical experiments and conclude that OSE and MSHS stackings yield superior results. Based on the lessons learned, we apply the methods on real global seismic records after the 2004 Sumatra earthquake and report the complete resolution of all singlets for 13 selected multiplets: 8 are mantle-sensitive (S-1(2), S-0(4), S-1(4), S-0(5), S-0(6), T-1(2), T-0(4), and T-0(6)) and 5 inner-core sensitive and of anomalous splitting (S-13(2), S-10(2), S-2(3), S-3(2), and S-11(1)), among them the singlet resolution of T-1(2), T-0(4), S-10(2), S-2(3), S-3(2), and S-11(1) are reported for the first time.