Short Wavelength Topography on the Inner Core Boundary

Aimin Cao, Yder Masson, and Barbara Romanowicz

Introduction

The ICB separates the liquid outer core from the solid inner core and is the site of important dynamical processes, as the core freezes and light elements are expelled to power convection in the outer core (Glatzmeier and Roberts, 1995). Significant long wavelength topography of the ICB is ruled out by dynamical considerations (Buffett, 1997). While hemispherical variations in the seismic properties at the top of the inner core have been documented, seismological investigations indicate that the ICB is, to a good approximation, quite spherical. However, the observation of significant PKiKP coda, likely due to multiple scattering (Poupinet and Kennett, 2004), indicates that the structure of the ICB is more complex at short wavelengths. There is also evidence for significant scattering near the top of the inner core (Vidale and Earle, 2000). Recently, in a study of amplitudes of ICB reflected phases (PKiKP), Krasnoshchekov et al. (2005) have proposed that the ICB is ``patchy'' in its reflective properties at scales of  10-200km laterally. Because their data were obtained at sub-critical distances, these authors could not constrain the precise nature of the variability in the measured PKiKP amplitudes.

In their efforts to constrain the rate of differential rotation of the inner core previously estimated using PKP(DF-BC) differential travel times on paths to Alaska stations in the epicentral distance range $147-155^o$, Zhang et al. (2005) found several high quality earthquake doublets in the South-Sandwich region, separated in time by a decade or more. The high waveform similarity at many stations indicates that the two sources are located within a wavelength for compressional waves. One of the earthquake doublets reported in the Zhang et al. study is of exceptional quality (Dec 1, 1993/ Sep 6, 2003). Highly similar waveforms for both events were recorded at 102 stations with a broad coverage of epicentral distances and azimuths, and the hypocenter separation of the two events was inferred to be  100 m vertically and less than 1.0 km horizontally.

Data, Method, and Results

We found that this doublet was also well recorded on the short-period Yellowknife Seismograph Array (YK) in northern Canada, which is located in an optimal position for the study of mantle phases PP as well as both refracted (PKIKP) and post-critically reflected (PKiKP) core phases. Indeed, these phases are emitted near the maximum in the lobe of the doublet's radiation pattern (Figure 34.1), at an epicentral distance of $137.8^o$, where the two core phases are well separated and where the PKiKP undergoes total reflection. High signal-to-noise seismic waveforms were recorded for both events at eighteen of the nineteen YK stations. In a 50-second time window around the PP phases of the doublet, unfiltered waveforms are very highly similar at all stations of the array, with cross-correlation coefficients larger than 0.97. The amplitudes of PP for both events differ only by a factor of 1.05. This provides strong additional confirmation of the high quality of this doublet. We therefore expect the waveforms of other phases to be very similar in shape and amplitude for this special doublet.

Figure 34.1: (A) Yellowknife Seismic Array (YK) and the doublet. The 19 stations of the array form two arms, one along a lake (shore indicated) and one orthogonal to it. Its aperture is 25 km with a station interval of 2.5 km (upper-right inset). The doublet consists of two South Sandwich Islands (SSI) events at an epicentral distance of $137.8^o$ : Dec 1, 1993, $m_b$=5.5, depth=33 km according to the PDE catalog; and Sept. 6, 2003, $m_b$=5.6, depth=33 km according to the PDE catalog. According to Harvard CMT (http://www.seismology.harvard.edu), scalar moments and depths are ($M_o$=3.53x1024 dyne-cm, h= 45 km) and ($M_o$=4.02x1024dyne-cm, h= 44km), respectively. The lower-left inset is the P-wave radiation pattern of the doublet based Harvard CMT moment tensors. Black triangles and dots are entry (exit) points of PKIKP at the ICB and the CMB, respectively. (B) Ray paths of PP, PKIKP(df), and PKiKP(cd) phases used in this study.
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Figure 34.2: (A) Original waveform profile of PKIKP and PKiKP phases. For each event, waveforms are highly similar at most of stations except YKR1, YKR2, and YKR3 stations. These three stations are close to the lake, and they have a common feature for both events: site-related filtering of higher frequencies. (B) Bandpass filtered waveform profile of PKIKP and PKiKP phases (from 1.0 to 2.0 Hz). In this frequency range, waveforms of PKIKP and PKiKP are highly similar at all stations (including YKR1, YKR2, and YKR3) for each event. Also, waveform shapes of PKIKP and PKiKP for the 1993 event are more similar to those of the 2003 event. In this profile, it is obvious that phase shifts between PKiKP and PKIKP are close to $180^o$ as predicted theoretically. (C) Linearly stacked waveforms of PKIKP and the reversed PKiKP phases after bandpass filtering (1-2Hz) showing the similarity of shape. Vertical broken line indicates place where the PKiKP waveform has been cut and reversed. The amplitude of PKIKP for 2003 event is  1.5 times larger than that for 1993 event; the amplitude of PKiKP for 2003 event is  7.2 times larger than that for 1993 event. Amplitude ratios of PKIKP to PKiKP are  2.3 (1993 ) and  0.7(2003) event. (D) Theoretical phase shifts of PKiKP with respect to PKIKP based on PREM, IASPEI91, and AK135 reference models. In this study, the phase shift is $\sim 145^o$. (E) Theoretical amplitude ratios of PKIKP to PKiKP. Dashed lines are assuming that the inner core $Q_\alpha = \infty $ (i.e., no seismic attenuation in the inner core) based on the above three reference models. Solid lines are using $Q_\alpha =445$ provided in PREM model. The black dot and square are observed amplitude ratios of PKIKP to PKiKP for the 1993 and 2003 events, respectively.
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However, the first two arrivals (PKIKP and PKiKP) in the individual unfiltered YK seismograms, which are well separated for both events, have significantly different waveforms (Figure 34.2A). For the 2003 event, the waveforms of PKiKP are simply reversed in polarity with respect to those of PKIKP as theoretically predicted for post-critical reflections (Figure 34.2D). For the 1993 event, the amplitudes of PKiKP are much reduced (by a factor of  3.0). The later part of the PKIKP waveform also shows some change. In the frequency range 1-2 Hz, PKIKP and PKiKP waveforms of both events are simpler (Figure 34.2B), so that reversed waveforms of PKiKP are similar to those of PKIKP for both events (Figure 34.2B,C). In this frequency range, where the amplitude ratios can be determined more robustly, the amplitudes of PKiKP for 2003 and 1993 events differ by a factor of 7.2. Given the striking similarity of the PP waveforms and their coda, and the other evidence for the quality of the doublet, we infer that both phases (especially the PKiKP phase) have undergone temporal changes within 10 years.

This observation, complemented by data from several other doublets, indicates the presence of topography at the inner-core boundary, with a horizontal wavelength of about 10 km. Such topography could be sustained by small scale convection at the top of the inner core, and is compatible with a rate of super-rotation of the inner core of $\sim $0.1-0.15 deg/year. In the absence of inner core rotation, decadal scale temporal changes in the ICB topography would provide an upper bound on the viscosity at the top of the inner core.

Acknowledgements

We thank the operators of Yellowknife Seismic Array and Canadian National Seismograph Network. This work was partially supported by the NSF.

References

Glatzmeier, G.A., P. H. Roberts, A three-dimensional self-consistent computer simulation of a geomagnetic field reversal, Nature, 377, 203, 1995.

Buffett, B.A., Geodynamic estimates of the viscosity of the earth's inner core, Nature, 388, 571, 1997.

G. Poupinet, B.L.N. Kennett, On the observation of high frequency PKiKP and its coda in Australia, Phys. Earth Planet. Inter., 146, 497, 2004.

J.E. Vidale, P.S. Earle, Slow differential rotation of the Earth's inner core indicated by temporal changes in scattering, Nature, 404, 273, 2000.

D.N. Krasnoshchekov, P.B. Kaazik, V.M. Ovtchinnikov, Seismological evidence for mosaic structure of the surface of the Earth's inner core, Nature, 435, 483, 2005.

Zhang, J., et al., Inner core differential rotation confirmed by earthquake waveform doublets. Science, 309, 1357 2005.

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