Spherical harmonic stacking for the singlets of Earth's normal modes of free oscillation

We extend the spherical harmonic stacking (SHS) method of Buland et al. (1979) for the radial (vertical) component in the seismogram to the transverse (horizontal) components of the displacement field. Taking advantage of the orthogonality of the spherical harmonic functions (scalar and vectorial), SHS isolates and accentuates the signals of individual singlets of the Earth's normal modes of free oscillation. We apply the SHS on the broadband Incorporated Research Institutions for Seismology (IRIS) seismograms from up to 97 IRIS seismic stations for the 2004 Sumatra-Andaman earthquake, in experiments targeted to spheroidal as well as toroidal modes(2)S(1), S-0(3), S-2(2), S-3(1), S-1(3), T-0(2), and T-0(3). We report the complete resolution of the singlet frequencies of these multiplets, some for the first time, and estimate the singlets' complex frequencies using the frequency domain autoregressive method of Chao and Gilbert (1980). The latter contain useful information to be used in inversions for the 3-D structure of the Earth's interior.