S$^{d}$S reflections and upper mantle anisotropy

The 16 available events recorded at the Tw~st array were examined for precursors to SS. To detect the precursors, 4th-root relative vespagrams for all stations of the array were calculated.
The relative vespagrams are computed by aligning the seismograms of the array stations on the SS onset for the R- and T-component. The R- and T-component are calculated by rotating the N- and E-component of the original 3-component seismograms with respect to the theoretical backazimuth. The anisotropic structure of the upper mantle beneath the station is taken into account using splitting parameters published by Kay et al. (1999) listed in Table A.2.
Only one of the 16 events shows clear precursors from the 410 and the Lehmann. A relative 4th-root-vespagram for the T-component of this event (14-oct-1997 09:53) is shown in Figure 6.11.

Figure 6.11: 4th-root relative vespagram for the event 14-oct-1997 09:53. Shown is the time window 300 s before the SS arrival. The SS slowness is 13.7 s/$^{\circ}$. The slowness step size is 0.3 s/$^{\circ}$. The theoretical travel times for SS and the 410 km and 210 km underside reflections are marked. Additionally, a phase with a theoretical travel time for S$^{300}$S is visible, which might be a result of sidelobes of the long-period S$^{410}$S and S$^{210}$S wavelets.

The slowness of the reference phase SS was set to 13.7 s/$^{\circ}$. The seismograms were filtered with a 4th order band-pass filter with cut-off frequencies of 20 s and 60 s prior to stacking. The vespagram shows strong S$^{410}$S and S$^{210}$S phases although the slowness resolution of the array for this event is poor, as a result of the backazimuth of $\sim$252$^{\circ}$. Additionally, a phase with a travel time appropriate for S$^{300}$S is visible between S$^{410}$S and S$^{210}$S. Whether this is an effect of the sidelobes of S$^{410}$S and S$^{210}$S, the result of a wrong backazimuth for this phase, or the real reflection from an unknown discontinuity at this depth is unclear. No reflection from the 660 is visible in this vespagram. The reflection point for this event is located $\sim$1000 km east of the Hawaiian Islands.

For the time windows around the S$^{410}$S and S$^{210}$S arrivals, the particle motions for the R- and T-components of individual stations are computed. Again, the data were corrected for the anisotropic structure beneath the station. The successful correction for the upper mantle can be controlled by the study of the polarization of the SKS wavelet. If this wavelet shows a linear polarization, the splitting time produced by the structures beneath the stations is removed from the data. The splitting time contribution of the mantle structure in the source region can be controlled by the S$_{diff}$ particle motion. The particle motion study for the station 5150 located approximately in the middle of the line array (compare Figure 4.3) is displayed in Figure 6.12.

Figure 6.12: Particle motion study for precursor time windows of the underside reflections detected in Figure 6.11.
a) Unfiltered and filtered R- and T-components of station 5150. The time window stretches from SKS to SS. The IASP91 theoretical travel times of different phases are marked.
b) SKS particle motion. The particle motion shows a linear polarization indicating no splitting of the SKS phase beneath the receiver.
c) Elliptical polarization of the SS wavelet. The SS phase travel through the anisotropic upper mantle at the reflection point.
d) Particle motion of the S$^{410}$S time window. The motion is mostly linear indicating that the anisotropic structure beneath the reflection point is located above the 410.
e) Particle motion of the S$^{210}$S time window. The amplitudes are too small for a clear identification of the particle motion. Nevertheless, a linear motion might be visible.

In Figure 6.12a) the R- and T-components of the time window from SKS to SS are displayed. The two traces at the top are unfiltered broad-band stations and the bottom traces are band-pass filtered. The travel times of standard phases using IASP91 are marked. Figure 6.12 b) - e) shows the particle motions for SKS, SS, S$^{410}$S and S$^{210}$S, respectively. A 30 s time window was selected for the calculation of the particle motion.
The linear polarization of the SKS wavelet is clearly visible. The correction for the upper mantle anisotropy is correctly applied. On the other hand, the SS phase shows a strong elliptical polarization. The anisotropic material of the upper mantle at the reflection point can be deduced from this splitting time (Wolfe and Silver, 1998).
The polarization of the precursors is not so easy to identify, most likely as a result of the small amplitudes. The S$^{410}$S wavelets seems to show a more linear polarization, comparable to SKS, which indicates that the anisotropic material is located above the 410. The S$^{210}$S signal is even smaller than S$^{410}$S and no obvious polarization can be identified, although it seems to be more linearly polarized compared to time windows without a dominant phase.
Most other stations show the same pattern for the polarizations of the different phases. Some stations, e.g. 5050, show S-wave splitting for SKS also, indicating an incomplete upper mantle correction for this phase.
Due to the small dataset and the small amplitudes of the precursors on single traces, a final conclusion about the depth structure of the anisotropy cannot be reached.