Hemispherical Transition of Seismic Attenuation at the Top of the Earth's Inner Core

Aimin Cao and Barbara Romanowicz

Introduction

The Earth's inner core is formed by a freezing process of iron as the liquid outer core gradually cools (Jacobs, 1953; Stacey, 1980). Because the outer core material is not pure iron, some of the light elements are excluded from the inner core during this dynamic process, to power the geodynamo, while the residual is likely kept within a mushy layer at the top of the inner core (Fearn et al., 1981). Thus, constraining the characteristics of the mushy layer at the top of the inner core, as revealed by seismic velocity and attenuation measurements, should give us important insights into the dynamics of the Earth's core.

The outer core $Q_\alpha$ is usually regarded as infinite ($\ge 10,000$) (Cormier and Richards, 1976), but the estimated $Q_\alpha$ in the inner core is constrained to be less than 450. This huge contrast indicates that a zone of decreasing $Q_\alpha$ with depth must exist beneath the ICB. However, this zone of decreasing $Q_\alpha$ should be confined to the top of the inner core, because multiple seismic observations confirm that $Q_\alpha$ increases with depth below a depth of approximately 100 km beneath the ICB (e.g., Souriau and Roudil, 1995). Therefore, the existence of a transition zone at the top of the inner core, where $Q_\alpha$ turns from decreasing to increasing with depth, seems likely.

In order to study the seismic structure at the top of the inner core, the most suitable body wave phases are PKIKP and PKiKP in the epicentral distance range from $120^o$ to $144^o$ (Figure 33.1). In this distance range, PKIKP samples the top 0-110 km of the inner core and PKiKP is reflected from ICB. The two phases have almost the same ray paths in the mantle and very close ray paths in the outer core. Hence the assumption that they experience almost the same heterogeneities in the mantle and outer core is valid in a first approximation. The differences in travel times and amplitudes can therefore be attributed to the vicinity of the ICB.

Unfortunately, these two phases present a great challenge. The separation of PKIKP and PKiKP is very small. For example, it is less than 1.3 seconds when the epicentral distance is less than $135^o$ (when referred to the seismic reference model PREM (Dziewonski and Anderson, 1981). On the other hand, the source time functions are usually longer than 3.0 seconds for events of $m_b\ge5.5$ (Cormier and Choy, 1986). Interference between the two phases seems inevitable. We have developed a direct, but arguably effective, approach to circumvent the complex issue of event source time functions and directivities.

Figure 33.1: Ray paths of PKiKP (reflected P wave from the ICB) and PKIKP (P wave passing through the inner core). The two phases may appear simultaneously as early as $120^o$, but we can only obtain well-separated PKIKP and PKiKP phases in the epicentral distance range from $135^o$ to $144^o$.
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Data, Method, and Results

We systematically downloaded both broadband and short-period vertical component seismograms from IRIS DMC, GRF, GRSN, Jarray, and F-net seismic networks corresponding to recordings in the epicentral distance range of $134^o-144^o$, for intermediate and deep earthquakes (focal depth $>$70 km, $M_w\ge 5.5$). These deeper events have shorter source time functions and higher signal-to-noise ratios than shallow events. To preprocess the seismograms, we employed a strictly narrow bandpass filter with corner frequencies of 0.7 and 2.0 Hz (corresponding to 1.5 and 0.5 seconds in period). The goal is to try to retrieve events whose 1.0 Hz energy was released in a short time and impulsively (within about 1.0 second), no matter how long their overall source time functions were. For this kind of events, we expect to observe pairs of well-separated PKIKP and PKiKP phases. In this paper, we directly measure amplitude ratios of PKIKP versus PKiKP in the time domain in order to estimate $Q_\alpha$ at the top of the inner core.

Our method requires to account for the phase shift of PKiKP with respect to PKIKP. Because PKiKP is a post-critically reflected wave at the ICB, the phase shift between PKiKP and PKIKP is approximately in the range of $142^o$ to $163^o$ (arguably close to $180^o$) in the epicentral distance range of our study. This means that if we reverse (that is multiplying the corresponding portion of the seismogram by -1) the PKiKP phase, the two phases should be very similar, as we verified using synthetic seismograms.

After data preprocessing, our data-picking criteria are as follows: (1) the signal-to-noise ratio before the identified PKIKP is $\sim 6$ or more; (2) the signal-to-noise ratio within about one duration of the waveform after the identified PKiKP is $\sim 3$ or more; (3) the identified PKIKP and PKiKP phases are well-separated; (4) the reversed PKiKP waveform is similar to the PKIKP waveform. Following the above criteria, we successfully selected 280 pairs of high-quality PKIKP and PKiKP phases.

This large dataset of well-separated and similar PKIKP and reversed PKiKP waveforms provides us a unique opportunity to explore the seismic structure at the top of the inner core. In order to study the P-wave velocity structure, we first measure the differential travel time between PKiKP and PKIKP by means of cross-correlation, and then calculate the differential travel time residuals between PKiKP and PKIKP with respect to the reference seismic model PREM. In order to study the $Q_\alpha$ structure, we first measure the peak-to-peak amplitude ratios of PKIKP to PKiKP, and then estimate $Q_\alpha$ from these amplitude ratios after applying corrections for geometrical spreading, transmission, and reflection.

For differential travel time residuals, our results show a striking hemispherical pattern in the epicentral distance range $135^o$ to $142^o$ (corresponding to depths of approximately 32 to 85 km beneath the ICB) (Figure 33.2a), in agreement with the observations of Niu and Wen (2001) and Garcia (2002). Beyond $142^o$, the robust hemispherical pattern is not as clear.

For quality factor $Q_\alpha$, our results also show a reliable hemispherical pattern almost in the same epicentral distance range ($135^o$-$141.5^o$) (Figure 33.2b). In the western hemisphere $Q_\alpha$ decreases as a function of distance. In the eastern hemisphere, $Q_\alpha$ increases as a function of distance. Beyond an epicentral distance of $141.5^o$, the hemispherical pattern in $Q_\alpha$ disappears, as does that in the differential travel time residuals.

The P velocity and $Q_\alpha$ variations are compatible with an interpretation in terms of small hemispherical variations of temperature at the top of the inner core (Sumita and Olson, 1999) and their influence on the morphology of porosity and connectivity of liquid inclusions in the mushy zone. The disappearance of the differences in $Q_\alpha$ beneath 85 km provide constraints on the likely depth extent of the mushy zone.

Figure 33.2: (a) Differential travel time residuals (referring to PREM). (b) $Q_\alpha$ with respect to the epicentral distance and depth beneath the ICB. High-lighted green squares show the data sampling offshore northwest of Africa. The event epicentral distances were all calibrated with a reference focal depth 100 km.
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Acknowledgements

We thank the following networks and data centers for providing the high quality data used in this study: IRIS-DMC, GRF, GRSN, J-array, and Fnet.

References

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