Data, Method, and Results

We use the high quality data from the broadband Gr$\ddot a$fenberg Seismic Array (GRF) in Germany. With an aperture of $\sim 100$km x 50km, GRF provides continuous high quality records at all of its 13 stations since 1980. Its geographical location with respect to frequent large events ($Mw > 7.0$), which occur in the south Pacific Ocean at distances around $140^o$, make it an ideal broadband seismic array to study PKJKP. We systematically examined large events from 1980 to 1999 and found $\sim $ 20 large events in the vicinity of Tonga and Santa Cruz islands in this time interval. One of them (Mw=7.3, depth=76 km, 02/06/1999) is unique for PKJKP observation. We choose the 0.06 to 0.1 Hz band for our analysis.

After aligning the seismograms with respect to the origin time of the event and making an array-sided travel time correction band-pass filtering, normalizing with respect to the first arrival (PKIKP+PKiKP), and stacking using the Phase Weighted Stack (PWS) technique (Schimmel and Paulssen, 1997), we computed a vespagram (Figure 13.43a), which corresponds to the predicted window for PKJKP based on the PREM mode. In the negative slowness range, the slowness of the energy maximum is $\sim -1.6 s/deg$, close to the PREM prediction of -1.43 s/deg. The arrival time is also compatible with PREM (1695 sec for the maximum energy, compared to a prediction of 1690 sec for the high frequency onset of the pulse). We also observe a clean stacked waveform corresponding to the energy maximum in the PKJKP window (Figure 13.43b). We verified that this phase arrives within $5^o$ of the great circle path from the source, ruling out a scattered near source phase (Figure 13.43c). We further verified that this phase is not a mantle, outer core, or even crust phase (Figure 13.43d). In the negative slowness region there is no energy maximum corresponding to the observation in Figure 13.43a. For this, the introduction of the concept of liquid inner core, as was done by Duess et al. (2000), is helpful. If the inner core were liquid, there would not be a PKJKP phase. Therefore, we constructed a synthetic vespagram for an assumed liquid inner core in the relevant time window, using the Direct Solution Method (DSM) to generate complete synthetic seismograms (Takeuchi et al. 1996).

The clear PKJKP waveform (Figure 13.43b) allows us to estimate the shear wave attenuation in the inner core. We use the envelope function of PKJKP in the synthetic differential seismogram between the solid inner core and the 'pseudo-liquid' inner core, to constrain the $Q_\beta$ in the inner core. We process the synthetic differential seismograms in the same way as the observed seismogram and compare the envelope amplitude to the observed one for different values of $Q_\beta$ in the inner core (Figure 13.44), obtaining a value of $Q_\beta \sim 320$, with an error of $\pm 150$, accounting for various uncertainties in the measurement. This is significantly higher than obtained from normal mode measurements. Normal modes mainly sample the shallow portion of the inner core, whereas PKJKP samples the central part. Thus, we find that $Q_\beta$ increases with depth in the inner core, just as $Q_\alpha$ does (Souriau and Roudil, 1995). The envelope function modeling also suggests that the observed PKJKP is about 9.0 seconds faster than the synthetic PKJKP. It means that the constrained shear wave velocity in the inner core is $\sim 1.5\%$ faster than that for the PREM model, also in agreement with previous results if one allows for a slight increase in shear velocity with depth in the inner core.

Figure 13.44: Envelope function modeling. The solid black line corresponds to the observed PKJKP, and dashed lines denote synthetic PKJKP with respect to different shear wave quality factors assumed in the inner core.
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