Detected discontinuities

The evidence for two separated discontinuities at shallow depths (h < 100 km) has been discussed in chapter 6.1. As a result of the polarity study, the two discontinuities were identified as Hales and Gutenberg discontinuities with average depths of 60 km and 99 km, respectively. The depth of the H is in good agreement with depths reported by Revenaugh and Jordan (1991b). They found depths of $\sim$ 60 km using ScS reverberations.
The depth found in this study also corresponds well to depths of 45 - 55 km found in high-pressure laboratory experiments for the spinel $\rightarrow$ garnet transition (Jenkins and Newton, 1979; Webb and Wood, 1986). The difference between the laboratory experiments and the seismological data can be explained by the dependence of the transition depth on temperature and the major element composition of the mantle material (Wood and Yuen, 1983; MacGregor, 1970). Both effects would increase the depth of the discontinuity some 10 km (Revenaugh and Jordan, 1991b). Due to these influences, the depth of the H beneath continents is much larger, e.g. Australia and North America $\sim$ 90 km (Green and Hales, 1968; Simpson et al., 1974).
This study contradicts the studies by Gaherty et al. (1996) and (1999) in oceanic regions. They detect a strong and shallow G (h < 80 km) in their ScS reverberation profile but do not find the H. However, a shallow and pronounced G could obscure the H, as they have similar travel times. This effect could explain the apparent lack of the H in the studies by Gaherty et al. (1996, 1999) in the oceanic regions studied there.
The mean depth of the G of h = 99 km differs from other studies by some ten kilometres. The oceanic models PHB3 (Philippines) and PA5 (Pacific) show the beginning of the low velocity layer at depths of $\sim$90 km and $\sim$68 km, respectively (Gaherty et al., 1999). The depth of $\sim$100 km for the G is in better agreement with depths of the discontinuity beneath continents, where studies report 90 km - 120 km (Thybo and Perchu$\acute{c}$, 1997) or even deeper (Nielsen et al., 1999). In better agreement with the depth reported in this thesis for oceanic regions than the results by Gaherty et al. (1999) is a decrease of velocity between 70 km and 80 km, that has been found beneath Oahu (Hawaii) using S $\rightarrow$ P conversions (Bock, 1991).
The depths of the G reported by others show great scatter and no detailed picture of the G in oceanic regions exists, due to the lack of long range seismic profiles. Despite the divergence of the results presented here from previous studies, the polarity study supports the interpretation of this reflector as the upper boundary of the LVZ.

Figure 7.1: Depth variation of the discontinuities between $\sim$50 km and $\sim$150 km. The depth variations of the Hales and the Gutenberg discontinuity are indicated by the dashed lines. The dot-dashed line marks the discontinuity at intermediate depths. The lines are fitted to the data by eye. Topography of $\sim$20 km on wavelengths over more than 1000 km exist on both discontinuities. The depths of the Hales and the Gutenberg discontinuity (dashed lines) are correlated.

In Figure 7.1, the depth variation of the H and the G are shown along the profile (see also Figure 6.2). The dashed lines are the approximated depth tendencies of the discontinuities. The dot-dashed line indicates the intermediate reflector at a depth between the G and the L. Both discontinuities, the G and the H, show similar depths near the subduction zone. The reflector can only be separated by the polarity of the reflections. The deepening of the H in this region, where lower than average temperatures are expected due to the influence of the cold subducting slab, supports the theory of a phase transition origin of this discontinuity. A phase transition with a negative Clapeyron slope is depressed, if colder material is present.
Both discontinuities show topography of $\sim$20 km over scalelengths larger than 1000 km along the profile. The depths of both discontinuities seem to be correlated. The data have been tested for any correlation of the source parameters with the reflector depths. Only strong P-wave velocity variations in the source region of these events relative to the other source regions used can explain a bias of the reflector depths. The ray paths at the receiver side cross the mantle beneath the Canadian shield where only small lateral variations are expected. High resolution tomography models of the source region with a horizontal resolution of $\sim$2$^{\circ}$ and a vertical resolution of $\sim$50 km show no increase of velocity perturbations (Widiyantoro and van der Hilst, 1997; Karason and van der Hilst, 2000). There is no influence of the possible Hawaiian plume near the Hawaiian Islands visible in the shallow reflections.
The depth variation of the H can be explained by temperature variations of the mantle material, but the topography of the G contradicts previous studies (Gaherty et al., 1999; Thybo and Perchu$\acute{c}$, 1997; Revenaugh and Jordan, 1991b). These studies interpret the reflector as the upper boundary of a region of partial melt, or the boundary between dry and water-saturated mantle material with little topography. Gaherty et al. (1999) propose a compositional boundary where the G reflects the depth of melting at the ridge and the compositional boundary does not deepen with increasing age of the lithosphere. The topography existent on this discontinuity contradicts this hypothesis. On the other hand, the correlation with the H indicates a temperature dependent mechanism for the G.
The other model for the G, the onset of partial melt, can explain the topography on the reflector. The onset of partial melt is controlled by the geotherm and the solidus curve of the perioditic mantle material (Anderson, 1989). If the geotherm intersects the solidus, melting at grain boundaries starts. Temperature variations of the mantle material, as detected by seismic tomography, shift the intersection of geotherm and solidus and thereby influence the melting depth. This mechanism is also able to explain the depth discrepancy between the results by Bock (1991) and Gaherty et al. (1999), with greater reflector depths beneath Hawaii being found by Bock (1991). The deeper reflector beneath Oahu indicates higher temperatures than along the Pacific path studied by Gaherty et al. (1999). The higher temperatures beneath Oahu may result from underplated hotter material supplied by the suggested Hawaiian plume. Slightly higher temperatures in this region are indicated by high-resolution tomography (Widiyantoro and van der Hilst, 1997; Karason and van der Hilst, 2000).
In the compositional boundary model (Gaherty et al., 1999) the topography cannot be explained as the result of temperature variations at the ridge. Depth variations result from temperature variations of the mantle material at the ridge. Temporal temperature variations during time periods of $\sim$50 million years at a fixed point at the ridge are too small to explain the detected topography on the G.
In Figure 6.7, the possible signature of a low velocity lamella between the mean depths of the G and the L was described. The polarity study indicates the upper and lower boundaries of the lamella lie at 135 km and 170 km, respectively. A laminated structure of the LVZ or small scale velocity variations in the upper mantle have been discussed to explain seismic data (Thybo and Perchu$\acute{c}$, 1997; Tittgemeyer et al., 1999). Some of these variations may be large enough to generate P$^d$P phases.

The detection of the L shown in chapter 6.2 is the first direct evidence for this discontinuity beneath oceanic regions, and the L is not included into current Earth models. Figure 7.2 shows a comparison of vespagrams.

Figure 7.2: 4th-root vespagrams calculated using synthetic seismograms for different radial Earth models and the YKA recording of one event beneath North Halmahera (04-jun-1993 10:49). The arrivals of P, PP and upper- and underside reflections from the upper mantle discontinuities are marked. All seismograms were filtered with a 4th-order band-pass with cut-off frequencies of 0.5 Hz and 1.4 Hz and the amplitudes of the seismograms were normalized to PP.
a) Synthetic seismograms were calculated using model IASP91 with a source depth of 5 km, an epicentral distance of 100$^{\circ}$ and a backazimuth of 270$^{\circ}$. The reflections from the 410 and 670 are visible.
b) For this seismogram the model ak135 (Kennett et al., 1995) was used to compute the seismograms. The same source parameters as for a) were used. The crustal structure of ak135 was simplified to obtain sharper onsets of PP. The vespagrams of IASP91 and ak135 are quite similar.
c) A combined model of ek1 (Estabrook and Kind, 1996) and PREM (Dziewonski and Anderson, 1981) was used. Down to depths of 271 km the velocity and density structure of PREM was used to incorporate the Lehmann discontinuity. Below that depth the model of ek1 was used. The reflection from the L are clearly visible in the vespagram, whereas the 660 underside reflection is absent.
d) Vespagram of real event (04-jun-1993 10:49) with a depth of 26.4 km, a distance of 98.6$^{\circ}$ and a backazimuth of 295.5$^{\circ}$. The vespagram resembles strongly the vespagram in c).

The vespagrams in 7.2a)-c) were calculated using synthetic seismograms. The synthetic seismograms were computed using the reflectivity method (Müller, 1985) and the radial Earth models IASP91 (Kennett and Engdahl, 1991)  (7.2 a), ak135 (Kennett et al. 1995) (7.2 b) and a combination of PREM (Dziewonski and Anderson, 1981) and ek1 (Estabrook and Kind, 1996) (7.2 c). The combined model was constructed with the velocity and density structure of PREM down to depths of 271 km and the structure of ek1 for greater depths. Figure 7.2 d) shows the vespagram of one event (04-jun-1993 10:49) recorded at YKA. All seismograms were filtered with a 4th-order band-pass filter with cut-off frequencies of 0.5 Hz and 1.4 Hz and the amplitudes were normalized to PP.
The IASP91 and ak135 models do not show upper- and underside reflections from the Lehmann discontinuity, which is not included in the models. The upperside (Pp$_d$p) and underside reflections (P$^d$P) from the 410 and 660 are clearly visible. The different P and PP signals are the result of different crustal structures of the models. The vespagrams in Figure 7.2a) and b) are quite different from the vespagram in d) showing real data. The real seismograms show reflections from the L and the 410, but no phase reflected from the 660. The combined model in 7.2 c) shows many details of d). Pp$_d$p and P$^d$P from the Lehmann and the 410 are visible, whereas P$^{670}$P is absent. The upperside reflection Pp$_{670}$p can be identified. But amplitudes of the upperside reflection are overestimated, because the source- and receiver-side upperside reflections for surface events have the same travel time and correlate positively at the receiver. Therefore, the amplitude of the upperside reflection for this shallow event and the radial Earth model is overestimated.
Comparing 7.2c) and 7.2d) the 410 and 210 upperside reflections can be identified within the P-coda of the real seismograms. The structure of the 660 in the model used for 7.2d) does not fit the upper mantle near the receiver ( $\Delta \approx$ 3$^{\circ}$), because Pp$_{660}$p cannot be seen in the data. The receiver side reflection point of Pp$_{660}$p at the 660 is $\sim$2.6$^{\circ}$ away from YKA beneath the Canadian shield. The difference between the real attenuation (Q-structure) beneath Canada and the PREM Q-model used for the modelling can explain discrepancy between model and data. Because the upper mantle Q-structure beneath the Canadian shield is not the focus of this thesis, the Q-model was not changed.
These synthetic examples show that the global Earth models ak135 and IASP91 are not able to explain the data recorded at YKA, especially regarding the 660 and the Lehmann discontinuity and that the Earth models must be altered at least in the region of the Pacific studied here.
This evidence for the L in this region is the first time that the L is undoubtedly detected beneath oceanic lithosphere.
The detections of the L using ScS reverberations are dubious because the impedance contrast is close to the minimum resolution and is a result of the limited modelling parameterization used. The detection using pP precursors of deep earthquakes (Vidale and Benz, 1992) was located in subduction zones. The lack of occurrence of the L in oceanic regions can be a result of a lack of data, because most studies reporting the L used seismic refraction data. The use of PP precursors offers an ideal tool to study areas not covered by stations or earthquakes.
In previous studies, the depth of the L varied strongly for different tectonic regions, but the mean depth of the L in this study (h = 200 km) is in good agreement with studies by Vidale and Benz (1992) who find a mean depth of 211 km. The depth of the L, as well as the depth of the H and the G discussed previously, corresponds well with depths found for this discontinuity along the Hawaiian swell by Rayleigh wave studies (Woods et al., 1991). The reflector detected in this study shows depth variations larger than the estimated depth error of $\sim$8 km even within the first Fresnel zone. This effect can be observed even when the events have similar great-circle paths. The similarity of the great circle paths exclude lateral velocity heterogeneities along the path as a possible error for the different apparent depths. Although the sources are located in a small region, the strong heterogeneity of the slab can generate significant travel time disturbances (Weber, 1990). Furthermore, the Fresnel zone is the projection of the Fresnel volume on a horizontal plane. The influence of small undulations of reflector depth on the structure of the Fresnel zone has not been studied yet. These aspects complicate the interpretation of the detected small scale topography.
The strong topography on the L is unexpected. The scattered reflections shown in this study are not able to prove the existence of a continuous discontinuity at $\sim$200 km depth. The different depths of the reflectors can also indicate a layer of normal mantle material with embedded heterogeneities. The scale of the heterogeneous bodies must be several wavelengths of the short-period waves, but smaller than the wavelengths for periods of 15 - 20 s used in long-period studies. Larger heterogeneities would produce reflections also in long-period data, which is not observed. This estimate indicates scalelengths of less than 20 km for the heterogeneities. The detected P$^{210}$P show very large amplitudes. Either, the impedance contrast of the heterogeneities is large, or constructive interference of the different reflections at the isolated bodies generate the large amplitudes. Different models of the discontinuity have been tested and are discussed later in this chapter.
The mechanism producing the hypothetical heterogeneities and their existence over long periods of time is unclear and must be tested using numerical simulations. The ''embedded bodies'' hypothesis cannot finally confirmed nor declined by this study, but some evidence on the nature of the Lehmann discontinuity can be given using synthetic seismograms.
The topography of the reflector is very steep with amplitudes of $\sim$40 km on wavelengths of 4$^{\circ}$, and can hardly be explained by temperature variations. A temperature induced mechanism for the L cannot be supported. The small-scale topography can explain the lack of a 210-km discontinuity in long-period studies. The long-period waves smooth the topography of the discontinuity and stacks of recordings with adjacent reflection points do not stack coherently. The underside reflections are sensitive to the presence of topography on the discontinuity (Chaljub and Tarantola, 1997; Davis et al., 1989). The topography breaks the symmetry of the ray-paths of the underside reflections and as a result the wavefield is focused or defocused at the receiver. The three-dimensional small scale structures found here studied with high frequency waves cannot be modelled using numerical methods for the computation of synthetic seismograms due to computer limitations, and the influence of the small-scale topography on the short-period waves cannot be modelled. However, the results for larger wavelengths of topography and seismic waves can qualitatively be adapted. The effects dependent on the curvature of the topography (Chaljub and Tarantola, 1997), and therefore should be strong for the steep topography detected on the L.
Comparing the results of long-period PP underside reflections with the outcome of this study, the lack of the L in the long-period studies is striking, because the L is such a dominant feature in this study. Besides the topography on the reflector, a lamination of the reflector could result in a small long-period signature (Vidale and Benz, 1992). This hypothesis is tested using synthetic seismograms.

Figure 7.3: Synthetic seismograms computed for laminated models of the Lehmann discontinuity. The width h and the distance d between the single lamellae were varied. Most seismograms were computed with a dominant period of 1s. The top trace was computed for a width h and a distance d of 4km for a dominant period of 15s. No clear signal from a discontinuity is visible. The different models produce precursor with different amplitudes. The highest amplitude can be achieved for a distance and a thickness of half a wavelength, i.e. $\sim$4km.

Figure 7.3 shows synthetic seismograms calculated with the reflectivity method for different laminated models of the Lehmann discontinuity. The thickness h and the distance d between the single lamellae was varied. The models consist of 4-6 layers with a 1% velocity and density increase. All seismograms except the first one at the top have a dominant period of 1 s. The long-period (T$_{dom}$ = 15 s) seismogram does not show a signal from a layered stack of discontinuities with a thickness and a distance of 4 km. This result indicates that a laminated discontinuity generates only small long-period signals. The different models indicate that a layer thickness of 4 km and a distance between the lamellae of 4 km is able to generate large precursor amplitudes (amplitude ratio A$_{PP}$/A $_{P^{210}P} \approx$ 8%). The large precursor amplitude for the small impedance contrast is the result of constructive interference. The reflectivity results can be used only qualitatively, but they show that models of a laminated reflector exist which are detectable by 1 Hz short-period data, whereas they are invisible for longer periods. The model producing the largest amplitudes has a thickness and a distance of approximately half a wavelength ( $\lambda \approx$ 8 km). The reflectivity method allows only one dimensional variations of the seismic parameters. Therefore, these tests cannot distinguish between a continuous laminated discontinuity and localized embedded bodies.
A linear regression computed for the data points indicates that the discontinuity shows a slight depression of 20 km from the Hawaiian Islands to the deepest point beneath the subduction zone. As a result of the superimposed small scale depth variations the correlation coefficient is small. The deepening is only slightly larger than the error of the individual depth estimates and this slight trend is probably not significant.
Figure 7.4 shows a detail of the reflector depths near the Kurile subduction zone.

Figure 7.4: Reflection points of events showing a 210 discontinuity near the subduction zone. The depth of the reflector is coded in gray scales. The size of the circles indicates the size of the first Fresnel zone. The thin lines mark 50 km depth isolines of the subducting slabs (Gudmundsson and Sambridge, 1998). The 200 km depth isoline is marked as a thick line.

The depth of the reflector is shown at the location of the geometrical reflection point, and the depth of the reflector is coded in grey. The thin lines give 50 km depth isolines of the subducting slab. The 200 km depth isoline is marked as thick line. Only few points sample the area where the slab intersects the L. No depth variation correlated with this possible intersection is visible. This confirms the hypothesis that the L is not formed by a temperature controlled mechanism.
The fk-analysis does not allow an easy conclusion on the velocity contrast across the reflector. To give estimates on the velocity change forward modelling was used. For different models synthetic seismograms were computed using the reflectivity method (Müller, 1985). Two parameters were varied: (i) the velocity change across the discontinuity and (ii) the thickness of the discontinuity. Most PP studies use the h $\approx$ $\lambda$ / 2 estimate derived for P'P' precursors (Richards, 1972) to relate the maximum thickness h of a discontinuity with the wavelength $\lambda$, respectively the frequency, used to study the discontinuity. The transfer of the results of P'P' studies to PP produces wrong results of the thickness due to the different incident angles of the waves at the discontinuity. P'P' has nearly vertical (90$^{\circ}$) incidence at the discontinuity, whereas PP shows only angles of $\sim$50$^{\circ}$.
The effect of a gradient zone with changing velocity and density over a depth interval on the underside reflection from the L is shown in Figure .

Figure 7.5: Effect of increasing width of a gradient zone of the L on the amplitude of the underside reflection. The right hand side shows three seismogram traces with increasing width from a sharp discontinuity (1st-order) to a 10-km gradient. The corresponding velocity models used to compute the synthetic seismograms are shown on the left hand side. The velocity and density changes of PREM were used. The arrivals of PP, P$^m$P (Moho reflection), P$^{410}$P, Pp$_{410}$p, Pp$_{660}$p, and P$^{220}$P are marked atop the traces. The P$^{220}$P onset is clearly visible for the 1st-order discontinuity, but invisible on the trace for the 10 km gradient.

The models used for the calculation of the synthetic seismograms (right hand side) are shown on the left hand side. The discontinuity structure is varied from a sharp discontinuity (1st-order discontinuity) to a 10 km wide gradient zone. The velocity change corresponds to the 220 km discontinuity in PREM. The seismograms are short-period seismograms with a dominant period of 1 s. The seismograms are filtered with a 4th-order band-pass with cut off frequencies of 0.5 Hz and 1.4 Hz and normalized to PP. The arrivals of PP and some under- and upperside reflections are marked. The underside reflection from the L is clearly visible in the seismogram trace calculated for a sharp discontinuity. The amplitude in the trace for a 4 km gradient is reduced but still visible. No underside reflection from the L can be detected in the seismogram computed for a 10 km gradient.
A more detailed study of the influence of the thickness gradient and impedance change of the L is shown in Figure 7.6a) and b), respectively.

Figure 7.6: a) Synthetic seismograms computed to test the influence of the gradient thickness on the precursors amplitudes. The same model as for Figure 7.2c) was used. All synthetics seismograms are band-pass filtered and the amplitudes are normalized on PP. The thickness of the discontinuity is varied between 0 km and 20 km. The visibility of the Lehmann discontinuity underside reflection vanishes between gradient thicknesses of 8 km - 10 km.
b) Synthetics with varying impedance contrast. The impedance contrast is varied from 0.93% to 9.58%.

The seismograms were processed as described in Figure b). The impedance was varied from 0.93% to 9.58% and the gradient thickness from 0 km to 20 km. The influence of both parameters on the P$^{220}$P reflection is obvious.
Figure 7.7 shows amplitude ratios of P$^{210}$P versus PP as a function of gradient thickness (7.7a) and impedance contrast (7.7b) for synthetic seismograms calculated using the reflectivity method.

Figure 7.7: Amplitude ratios of the synthetic seismograms computed with the reflectivity method. For the computation a combined model of PREM (Dziewonski and Anderson, 1981) and ek1 (Estabrook and Kind, 1996) was used. Above a depth of 271 km, the model PREM and below model ek1 was used. To estimate the thickness of the discontinuity and the P-wave velocity jump across the discontinuity these parameters were varied. The amplitude ratio of P$^{220}$P relative to PP versus the variable parameter is displayed. The mean noise level of the data set is marked by the horizontal dashed line.
a) Variation of gradient thickness of the L. The horizontal solid lines mark the 50% - 60% level of the data noise level. This resolution level below the noise level was found by the synthetic resolution tests (compare chapter 5.4). This synthetic test indicates a thickness of less than $\sim$5 km - $\sim$7 km for the L.
b) Variation of the impedance change across the L. The impedance change is in given in %. The horizontal lines mark the 50% - 70% level of the data noise level. This test indicates a minimum impedance contrast of 5% to 6.5% across the L relative to PREM.

The amplitude ratio was determined using the mean amplitude ratios of the seismograms of 18 stations in YKA configuration for a distance of $\Delta$ = 100$^{\circ}$. The amplitude ratios are used to estimate the thickness and the impedance contrast of the discontinuity. This is done by comparing the synthetic amplitude ratios with the maximum resolution of the fk-analysis. For the resolution, the amplitude ratios of the precursor time window and the PP arrival are calculated from real YKA recordings. This amplitude ratio is marked by the dashed line. The resolution tests in chapter 5.3 showed that the sliding-window fk-analysis is able to resolve a coherent signal with amplitudes of 50% - 70% compared to the noise. These thresholds are marked by the solid horizontal lines. The minimum values of the impedance change and the maximum for the gradient thickness are indicated by the vertical dashed lines. The flattening of the amplitude ratio curve for larger gradient thicknesses is a result of the coherent signals buried in numerical noise. For Figure 7.7a) the impedance contrast was fixed at the PREM value for the L ($\Delta$v$_p$ = 7.12% and $\rho$ = 2.2%) and for Figure 7.7b) a sharp discontinuity was assumed and the impedance change was varied. This analysis indicates that a discontinuity thinner than $\sim$7 km and a minimum impedance change of $\sim$5% - 6.5% is required to produce reflections observed by the sliding-window fk-analysis. This is equivalent to a velocity change of $\sim$4.3% assuming the PREM density change.
The velocity change of $\sim$4.3% is bracketed by the values found by ScS reverberations ($\sim$2%) (Gaherty and Jordan, 1995) and the velocity jump proposed by PREM ($\sim$7.1%) (Dziewonski and Anderson, 1981). It is also in good agreement with the 3.5% - 4.5% change across the L reported for direct P waves (Anderson, 1989).
Only one estimation of the thickness of the L has been given previously. This estimate of $\sim$15 - 25 km is based on long-period data and in contradiction to the relatively sharp discontinuity found here. The mineralogical model of the L with a change from anisotropic to isotropic material as source of the discontinuity predicts a thickness of $\sim$20 km due to the change of the creep mechanism from dislocation to diffusion creep (Karato, 1992). This thickness is based on mineralogical observations only and contains a large error as a result of the uncertainty of the activation volume of the two deformation processes and might also be temperature dependent (Karato and Wu, 1993). Additionally, the unknown grain size of deformed rocks influences the transition width (Karato, 1992). Nevertheless, it is uncertain whether a sharp discontinuity can be explained by the change of creep mechanism or by the onset of partial melt.
The region studied is mostly homogeneous with lithospheric age and the reflection points sample old oceanic lithosphere. Therefore, a dependency of the discontinuity on lithospheric age cannot be studied. As shown in Figure the backarc basin of the Sea of Okhotsk and the subduction zone are not sampled densely enough to study the influence of the subducted slab in detail. However, the results indicate no strong influence of the slab on the discontinuity depth. No detailed answer on the nature of the discontinuity can be given by this study. Either the bottom of the LVZ with partial melt or the boundary between two regions with different anisotropy structure are consistent with present data.


The 410 has been the focus of several studies and the global existence of the 410 is not questioned. Nevertheless, the fine structure and especially the thickness of this discontinuity is still under discussion.
This study reveals evidence for a small-scale structure of the 410. In chapter 6.1.3 the discontinuity depths have been presented. The mean depth of 404 km found in this study is in good agreement with other studies. The long-period global study by Flanagan and Shearer (1999) gives a depth of 400 - 405 km south of the Kuriles and of 410 - 415 km near Hawaii in fairly good agreement with the mean values for these regions found here. Studies using short period waves (pP and P'P') in different regions showed similar depths of $\sim$410 km (Indian Ocean: Benz and Vidale, 1993; continental USA: Melbourne and Helmberger, 1998). The mean values of the long-period studies which smooth out the small scale structure are in good agreement with the average values for the whole corridor studied.

Figure 7.8: Location of the reflection points (circles) of events showing a reflection from a depth of $\sim$410 km depth near the subduction zone. The size of the circles indicate the approximated size of the Fresnel zone. The thin lines mark the slab contours in different depths (Gudmundsson and Sambridge, 1998). The interval between the lines is 50 km each. The thick line marks the depth contour of 400 km. Only one event is able to map the influence of the dipping slab on the discontinuity. This event shows an unusual shallow depth of 330 km.

The structure of the discontinuity near the subduction zone cannot be studied in detail, because the reflection points of the events showing 410-km reflections are mostly southeast of the subduction zone. The reflection points and the slab contours are displayed in Figure 7.8. The reflection points are at least 300 km away from the region where the slab crosses the 410. The reflection points near the subduction zone do not show an elevation of the 410. This indicates that the temperature disturbance of the slab decays within this distance and does not influence the structure of the discontinuity south of the subduction zone. Shearer (1991) on the other hand concluded from long-period studies that the undulations of the discontinuities in the Kuriles extend to distances as large as 500 km away from the slab piercing point, although he states, that uncorrected upper mantle heterogeneities could produce these results. This result is not supported by this study. If depth variations of the 410 exist in the region where the slab intersects the 410, this disturbance does not extend to distances of $\sim$300 km to the south-east. The reflection point within the back-arc basin which is able to measure the depth of the 410 in the region where the slab intersects the discontinuity shows a very shallow depth of 330 km. The elevation of 80 km is very large compared to other studies in this region (Flanagan and Shearer, 1998). Assuming a Clapeyron slope of 2.9 $\frac{MPa}{K}$ (Bina and Helffrich, 1994) the elevation corresponds to a temperature difference of $\sim$1000 K. Estimates of slab temperatures for 100 - 130 million year old oceanic lithosphere subducting in the northwest Pacific (Jarrard, 1986) show temperature differences relative to the surrounding mantle of 800 K - 1000 K at 400 km depth (Schubert et al., 1975, Creager and Jordan, 1986; Castle and Creager, 1998; Deal and Nolet, 1999). Taking into account the uncertainty of the Clapeyron slope of the Olivine $\rightarrow$ $\beta$-Spinel transition this is in very good agreement with the elevation found here. The elevation of 80 km for the 410 is much larger than those found elsewhere (Shearer, 1991; Flanagan and Shearer, 1999). The Fresnel zone of the waves used here is very small. The Fresnel zone of the 1 Hz waves samples only the elevated region of the discontinuity, whereas long-period reflections reduce the topography by averaging elevated and normal discontinuity depths. The slab thickness for the Kuriles subduction zone is estimated to be 84 km (Deal and Nolet, 1999). Taking into account, that the temperature anomaly of the mantle material, produced by the subducting slab, is larger than the slab itself, the short axis of the 1 Hz Fresnel zone samples only the elevated part of the discontinuity. Therefore, no smoothing between elevated and normal discontinuity depths occurs. The great circle path and the dipping slab are roughly parallel, and the reflection point is located exactly where the slab intersects the discontinuity. Therefore, the reflection samples the elevated 410 along the strike of the slab. An asymmetric reflection from the dipping slab can be ruled out, because the waves recorded at YKA arrive along the great circle path. Any wave reflected from the westward dipping slab would be deflected from the great circle path southward, an effect not found in the data. The shallow reflection point shows the elevation of the 410 due to the transition of the cold subducting slab. Unfortunately, no other reflection points are located in that region which makes a more detailed interpretation of the influence of the subducting slab on the 410 impossible.
A depression of the 410 has been noticed north-northeast of Hawaii (Figure 6.10). This might indicate the piercing point of the postulated mantle plume through the 410. Assuming a Clapeyron slope of 2.9 $\frac{MPa}{K}$ a 100K change in temperature produces an approximated change in 410 topography of 8 km. The deepening of $\sim$30 km can be correlated with a temperature change of 300K - 400K and is in good agreement with plume excess temperatures found in numerical experiments (Ribe and Christensen, 1994). The width of the elevated zone of $\sim$350 km is larger than the plume radius, but the temperature disturbance extends to distances of about 150 km. There is no agreement about the location of the Hawaiian plume conduit in the upper mantle in the literature. The location of the possible piercing point north-northwest of Hawaii is in agreement with diffraction tomography studies (Ji and Nataf, 1998). The results of the diffraction tomography study are weak, therefore the study of Ji and Nataf (1998) cannot be taken as a support for the results of this study, but the results should nevertheless be reported. Studies by Wessel and Kroenke (1997) and Corrieu-Sipahalamani (1995) locate the plume conduit in the same region north-northwest of Hawaii. Recent receiver function studies near Hawaii (Li et al., 2000) detect a narrowed transition zone south-southwest of the Island of Hawaii, indicating the piercing point of the rising mantle plume originating in the lower mantle in this region. However, numerical studies including mantle wind, plate motions and different viscosity models of the upper mantle place the plume conduit south-southeast of Hawaii (Steinberger and O'Connell, 1998).
This list of studies locating the Hawaiian plume at nearly every possible location around the Islands indicates that there is no consensus about the location of the Hawaiian plume. The depth variation of the 410 north-northeast of the Hawaiian islands is dominant enough to be considered. However, the result presented here is based on only five data points and should not be over interpreted. The depression of the 410 may also be a result of slow velocities in the upper mantle above the 410 reflection points in this region. Smaller P-wave velocities above the discontinuity enlarge the differential travel times resulting in a deeper apparent discontinuity depth. The PP - P travel time study by Woodward and Masters (1991) shown in Figure 5.9 and the tomographic results by Karason and van der Hilst (2000) propose only small relative variations of the velocity around the location of the Hawaiian islands. Therefore, rays sampling the southwest and rays sampling the northeast would show the same depth deviation, but the relative depression of the discontinuity would be still detectable in the right order of magnitude. Nevertheless, these two studies use long-period waves with a small resolution and the velocity variations near the Hawaiian islands can be on a smaller scale not detectable for these studies, but changing the differential travel times on scales important for short-period waves.
The lack of reflections from the 410 between the Hawaiian Islands and the bend of the Hawaii-Emperor seamount chain is a prominent feature in Figures 6.8 and 6.9. The lack of reflections in this region could be by chance or could be correlated with some source effects, but the existence of reflections from shallower depths (e.g. the G, H, and L) in this region precludes source effects. Nevertheless, the possibility of a non-detection by chance cannot be ruled out due to the restricted size of the data set. In the following some mechanisms which could destroy the reflections from the 410 in this region are discussed.
In Figure 7.9, the global long-period structure of the 410 is displayed (after Flanagan and Shearer, 1999).

Figure 7.9: Global results for the long-period structure of the upper mantle discontinuities studied with PP underside reflections (after Flanagan and Shearer, 1999).
a) Smoothed structure of the 410 km discontinuity. The depth variations are given as colours. The location of the Hawaiian Emperor seamount chain is marked by the white line. Note the depression of the 410 north-northwest of the Hawaiian Islands at the tip of the Hawaiian chain.
b) Raw depth estimates for the 410 plotted at the centroid location of the bounce points for each cap. Crosses indicate depressions and diamonds indicate elevations relative to the mean discontinuity depth. The Hawaiian chain is marked as a black line. Near the Hawaiian islands the discontinuity shows nearly its mean depth. The large depression visible in a) is marked by the large region containing crosses indicating a depression of $\sim$20 km.

In Figure 7.9a) the smoothed structure of the discontinuity is displayed. Figure 7.9b) shows the mean depth of all reflection points within a cap of 10$^{\circ}$ radius plotted at the centroid location of the reflection points. The cap radius corresponds roughly to the Fresnel zone of the long-period data. The strike of the Hawaii-Emperor seamount chain in Figure a) and b) is marked as white and black line, respectively. The depression to more than 430 km depth north-west of the Hawaiian Islands perfectly fits the gap of the short-period P$^{410}$P reflections. A deepening of the 410 can be related to higher temperatures of the mantle material in this region. It has been demonstrated that the sharpness of the 410 is temperature dependent (Helffrich and Bina, 1994). However, the width of the two phase field ($\alpha$+$\beta$-spinel phases existing simultaneously) defining the transition thickness narrows for higher temperatures. This effect produces a sharper discontinuity for hotter mantle material which is easier to detect with short-period data and is unable to explain the lack of 410 reflections from this region in the YKA dataset. The sharpness of the 410 is also controlled by other parameters, e.g. the water content of the material (Wood, 1995). The $\beta$-phase of (Mg,Fe)$_2$SiO$_4$ can hold large amounts of H$_2$O, since the replacement of one of the O atoms in Mg$_2$SiO$_4$ by an OH group is energetically favoured. Therefore, the $\beta$-phase could be a host for large amounts of H$_2$O below the depth of 410 km. Normal olivine at 410 km depth contains maximally 200 ppm H$_2$O. A content of as little as 500 ppm of H$_2$O at this depth broadens the transition from olivine to the $\beta$-phase from $\sim$7 km to 22 km. In addition to the broadening effect, thermodynamical calculations show that the 410 should also be elevated in H$_2$O-rich regions. The content of small portions of H$_2$O in the mantle may explain the lack of reflections from the 410 as well as the depression of the 410 found by Flanagan and Shearer (1999), but the mechanism delivering the 'wet' material to this place remains unsolved.
The influence of the gradient thickness and the impedance contrast of the 410 are displayed in Figure 7.10.

Figure 7.10: a) Synthetic seismograms as in Figure 7.6 but with a thickness variation of the 410. For the calculation of the seismograms the IASP91 model was used. The effect of the gradient thickness on the underside (P$^{410}$P) and the upperside reflection (Pp$_{410}$p) is unambiguous. The crustal reverbarations are the result of reflections from shallow discontinuity (35 km) in the source region.
b) Variation of the 410 impedance contrast in model IASP91. The traces show seismograms with impedance contrast ranging from 0.89% to 9.03%.

For the computation of the seismograms the IASP91 model was varied. The discontinuity thickness was varied from 0 km to 18 km (Figure 7.10a) and the impedance contrast from 0.89 % to 9.03 % (Figure 7.10b). The influence of both parameters on the amplitudes of the upperside and the underside reflection is obvious. The P$^{410}$P amplitudes for gradients thicker than 6 km become very small, whereas the impedance contrast can be divided in half compared to IASP91 and the reflection is still visible. Note the smaller amplitudes of P$^{410}$P in comparison to P$^{660}$P. The 410 in the IASP91 model is a weak discontinuity. More conclusions from the synthetic results can be obtained by comparing P$^{410}$P amplitudes with the maximum resolution of the sliding-window fk-analysis (Figure 7.11).

Figure 7.11a) shows a part of a synthetic test on the discontinuity thickness. The thickness of the gradient zone is varied while keeping the P-wave velocity change $\Delta\alpha$ = 3.6 % and the density change $\Delta\rho$ = 5.2 % fixed. The velocity jump across the 410 corresponds to IASP91 and is rather small. As a result of the small velocity change the amplitudes of P$^{410}$P are small. This indicates a thickness from a sharp (1st-order) discontinuity to a maximum gradient thickness of $\sim$5 km. The P$^{410}$P amplitudes in Figure 7.11a) are close to the minimum resolution of the sliding-window fk-analysis. Even the sharp discontinuity might not be resolvable. Seismological studies report at least a locally sharp 410 (Neele, 1996; Nakanishi, 1988; Benz and Vidale, 1993). The estimate of a discontinuity thickness of less than 5 km conflicts with studies of the equilibrium thermodynamic behaviour of an olivine mantle chemistry. For any reasonable mantle composition, the $\alpha$-Olivine $\rightarrow$ $\beta$-Spinel transition is expected to occur over a few tens of kilometres in the vicinity of 400 km depth. But the large transition thicknesses found in experiments might be an artifact, due to the presence of small amounts of H$_2$O in the sample cell (Wood, 1995).
Figure 7.11b) shows the variation of the impedance for a sharp discontinuity. An impedance contrast of more then 6.5% is resolvable for very good signal-to-noise conditions. The existing Earth models predict a very small impedance contrast across the 410. The synthetic tests show that the resulting amplitudes of IASP91 are very small, close to the resolution of the sliding-window fk-analysis.
The recent model for the 410 by Shearer and Flanagan (1999) for $\Delta\alpha$ = 7.3%, $\Delta\beta$ = 9.7% and $\Delta\rho$ = 0.9% show similar amplitudes compared to IASP91 due to the small density change. This model cannot explain the detected reflections as well as IASP91, but a larger density contrast in combination with the larger P-velocity change reported by Shearer and Flanagan (1999) produces P$^{410}$P amplitudes which can easily be detected by the sliding-window fk-analysis.