Non-detected discontinuities

In chapter 2, two discontinuities deeper than the 410 were discussed. These discontinuities, i.e. the 520 and the 660, are not detected in the dataset used for this study.
The 520 is an enigmatic discontinuity which has been detected by some studies (Hales et al., 1980; Shearer, 1990; Revenaugh and Jordan, 1991a), but has not been detected by others (Benz and Vidale, 1993; Bock, 1994). The phase transition from the $\beta$-phase $\rightarrow$ $\gamma$-spinel of the olivine component of the mantle material results in a very small velocity change distributed over a $\sim$25 km broad region (Katsura and Ito, 1989). A sharp discontinuity is not expected. Therefore, it is not surprising that no signals have been found from this discontinuity here. The non-detection of the 520 in this study supports the hypothesis that the 520 is either too small (in impedance contrast) and/or too diffuse (in thickness) to reflect 1 Hz data.


The results on the P-wave structure of the 660 are quite inconsistent. The 660 is absent in long-period PP stacks (Shearer, 1991; Estabrook and Kind, 1996; Shearer and Flanagan, 1999), but can be seen in recent P'P' studies (Xu et al., 1999) and pP investigations (Benz and Vidale, 1993). Nevertheless, often the P'P' studies of the 660 do not show P'$^{660}$P' reflections in the direct vicinity of reflection points with a detected P'$^{660}$P' phase (Davis et al., 1989). The phase transition $\gamma$-spinel $\rightarrow$ perovskite + magnesiowüstite predicts a sharp discontinuity which should easily be detected by P'P', but the other perovskite forming transition (garnet $\rightarrow$ perovskite) at similar depths occurs over a larger depth interval and has a broadening effect on the transition. This broader transition can explain the lack of the signals from the 660 in short-period studies. The non-detection of the 660 in long-period investigations cannot be explained by this mechanism. Estabrook and Kind (1996) showed, that the velocity gradient at the 660 must be as broad as 100 km to explain the missing P$^{660}$P reflections in 15 s period P-wave stacks. Such a large depth interval cannot be explained by mineralogical data. The problem of the missing P reflections was tried to be solved by changing the existing velocity models with respect to the bulk modulus, the P-wave velocity and the density (Estabrook and Kind, 1996; Shearer and Flanagan, 1999). All these models kept the criterion of a first order discontinuity.
This short period study offers the possibility to set constraints on the minimum thickness and the maximum impedance contrast of the 660, although no reflections have been found from the 660. For this purpose synthetic reflectivity seismograms for different models of the thickness and the impedance contrast have been calculated. Seismograms of the numerical calculations are displayed in Figure 7.12a) and b).

Figure 7.12: a) Same as Figure 7.10a) for the 660 discontinuity.
b) Same as Figure 7.10b) for the 660. Note the different effect of the impedance change on the upperside and underside reflections.

Again, the gradient thickness (Figure 7.12a) and the impedance contrast (Figure 7.12b) have been varied. The seismograms have a dominant period of 1 s and were band-pass filtered with the filter described earlier. The epicentral distance for this test is 100$^{\circ}$. The variation of the amplitudes of the upper- and underside reflections is clearly visible for both parameters varied.
The variation of the impedance contrast reduces the amplitudes of the underside reflection much stronger than the upperside reflection, whereas the discontinuity thickness has roughly the same effect on both reflected phases. The maximum impedance change and the minimum thickness of the 660 can be tested, as shown before, by a comparison of the P$^{660}$P amplitude and the PP amplitude ratios with the fk resolution.
The amplitude ratios of P$^{660}$P to PP of the synthetic seismograms are compared with the detection threshold of the sliding-window fk-analysis. An undisturbed model IASP91 (Kennett and Engdahl, 1991) was chosen as reference model. The density structure was taken from PREM (Dziewonski and Anderson, 1981).
Figure 7.13 shows the results for a variation of the impedance change for a first order discontinuity and different thicknesses of the velocity gradient.

The combined IASP91/PREM model proposes a very strong discontinuity with an impedance change of $\sim$16%. The resulting amplitudes are very high. These tests indicate a depth interval for the 660 of at least 15 km or a maximum impedance contrast of 10%. Assuming the PREM density models this corresponds to a velocity change of less than 1%, indicating that the proposed density change by PREM is too large. Larger values for the impedance contrast or a sharper discontinuity would produce reflections detectable by the sliding-window fk-analysis.
A certain trade-off exists between the impedance change and the thickness. Therefore, a grid search has been performed, testing different velocity models and gradient thicknesses.
The results for this grid search are shown in Figure 7.14.

Figure 7.14: Grid search for gradient thickness and impedance change across the 660. A + denotes a combination where the precursors are detectable and a - denotes a non detected precursor. The boundary between detected and non-detected discontinuities is marked by the dashed line. For comparison the impedance parameters of three models assuming a sharp discontinuity are added. The black circle at the right hand side marks the IASP91 model, which would produce clearly observable precursors. The models SF99 and ek1 (squared circles) are within the non-detected domain predicting precursor amplitudes too small to be detected by the sliding-window fk-analysis.

The gradient thickness h is varied from 0 - 25 km and the impedance contrast, $\Delta$I, from $\sim$4.5% to 16.1%. Models which varied both, h and $\Delta$I, were also computed. The parameter range producing positive results is shown by the + signs, i.e. the P$^{660}$P phases are detectable. Non-detections are indicated by the - sign. The 70% threshold was used for this classification. The boundary between both areas is marked by the dashed line. The IASP91 impedance contrast (using the PREM density model) for a sharp discontinuity is shown as the black circle with the white cross in the lower right corner. This model is clearly within the parameter range producing visible P$^{660}$P. The models SF99 (Shearer and Flanagan, 1999) and ek1 (Estabrook and Kind, 1996) for the 660 are marked by the squared circles left to the region boundary. Both models were derived to explain the absence of P$^{660}$P from long-period P-wave stacks. But they assume a sharp discontinuity, because the studies were performed using long-period data which cannot resolve the difference between a first-order discontinuity and a 30 km gradient zone. The method presented here has the advantage that velocity and density gradients over finite depth intervals can be resolved.
The results of both studies (Shearer and Flanagan, 1999; Estabrook and Kind, 1996) can be supported by the synthetic test shown in Figure 7.13 and the YKA dataset. The models produce non detectable P$^{660}$P phases. The EK1 model is very close to the regime boundary. Due to the rough estimate of the resolution threshold, these precursors might nevertheless be detectable. The SF99 model with a smaller impedance contrast clearly predicts unresolvable precursors.
A comparison of the results with recent thermodynamic models of the 660 (Weidner and Wang, 1998) indicates that the pyrolite model with a chemical composition of 45 weight % SiO$_2$, 4.5% Al$_2$O$_3$, 8.0% FeO, 38% MgO and 3.6% CaO cannot explain the reflection amplitudes found here, because it overpredicts the density and velocity change. The thickness of the 660 is very sensitive to the amount of Al in the mineral system (Weidner and Wang, 1998). The results of a maximum thickness of the 660 of 12 km can be interpreted in terms of Al-content. Since an Al cation percentage of 5% at 1700 K results in transition widths of more than 20 km, the Al content must be less (Weidner and Wang, 1998).
Due to the different phase transitions at depths around 660 km and the still unknown transition dynamics, a further estimation of temperature and mineral content at this depth is not possible.