Subsections

A Brief Review of Observation of the Slichter Mode

Shan Dou, Robert Uhrhammer, Barbara Romanowicz

Introduction

Slichter mode ${_1}{S}{_1}$, which is caused by the translational oscillations of the solid inner core about its equilibrium position at the center of the Earth, was named after the seismologist Louis Slichter when he first claimed the detection of this mode from the data of the Chile Earthquake in 1960. The preliminary estimation of its period made by Louis Slichter proved to be too short (around 86 min). Up to now, the generally-accepted interpretation was that the frequency of the Slichter mode is principally controlled by the density jump between the inner and outer core, and the Archimedean force produced by the fluid outer core. According to theoretical calculations based on perturbation theory, its period is thought to be in the range of 4$\sim$8 hours, and it splits into 3 singlets because of the Earth's rotation. As this translational mode can offer important information about the density jump at the ICB (Inner Core Boundary), much effort has been made to detect it. However, there are large uncertainties on its attenuation.

Review on the Detection of the Slichter Mode

Although the Slichter mode is crucial in determining the density difference across ICB, its detection is very challenging. The difficulties mainly come from the following aspects: (1)The largest displacement of the Slichter mode occurs at great depth (at ICB, see Figure 2.40), and its displacement is strongly attenuated as it goes through the liquid outer core. When the motion finally propagates to the surface of the Earth, it is too weak to be easily observed. For example, for an event as big as the 1960 Chile Earthquake($M_w$ 9.5), the theoretical estimation of its amplitude on the Earth's surface is only on the order of a nanogal; (2) As the period of the Slichter mode is very long (4$\sim$8 hours), it sits in the ``subseismic band'' (i.e. frequency lower than 0.03mHz) that has very strong background noise; (3)The period of the Slichter mode is also very similar to that of Earth tides, which means that a precise tide model is needed to do the tidal correction. However, as tidal phenomena are quite complicated, it is very difficult to perform this correction with adequate confidence; (4) Q estimates vary by up to several order of magnitude.

Figure 2.40: normalized theoretical sensitivity kernel of the displacement of ${_1}{S}{_1}$.Left: c00; right: c20(c00 and c20 are splitting coefficients). We use PREM model here.
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Although the exact excitation mechanism of the Slichter mode is still unclear, many detection efforts were undertaken with the assumption that the Slichter mode is continuously excited. Therefore, very long time series can be used to analyze this ultra low frequency signal, but a flat instrumental response (in the frequency domain) is then required to avoid amplifying low frequency noise. Superconducting Gravimeters (SGs) can therefore facilitate the observation, as their response in subseismic bands is very flat and stable. Over 20 SGs are installed around the world, which make it possible to extract of global signals by stacking.

The first claim of the detection of the Slichter mode after L. Slichter was made by Smylie et al (1992, Science). They used 4 long records from SGs in Europe: Brussels (1982$\sim$1986), Brussels (1987$\sim$1989), Bad Homburg (1986$\sim$1988), Strasbourg (1987$\sim$1991). They found out three singlets with periods of $3.5820\pm0.0008$, $3.7677\pm0.0006$, and $4.015\pm0.001$ hours, as well as Q values of 116,141 and 115, respectively. These frequency values are very close to the theoretical calculation based on 2nd order perturbation theory (Dahlen and Sailor, 1979). However, this promising observation was put into doubt when Hinderer et al. (1995) failed to reproduce Smylie's (1992) results. They used 2 simultaneous records at SG stations in Canada and France, and analyzed both the product spectra and cross-spectra. The whole process was optimal, as the phase information could be kept in this way, but the results were disappointing, as they could not detect the triplet in their spectra. They argued that cross-spectra should enhance coherent signals and interpreted the null observation as indicating that the triplet of Smylie was not the Slichter mode. Later, Ochi et al. (2000) designed a method to utilize the spatial dependency of the 3 singlets to obtain a better spectral estimate for each of them. They used 6 records from different observatories but covering the same time period. They then confirmed the presence of the triplet using an analysis based on product spectra. The mode showed up in the data from both Europe and outside of Europe, but with slightly different periods for both groups of stations. Again, Rosat et al. (2006) failed to reproduce Ochi's result. Rosat et al. developed a detection method based on predictions from theoretical models, which were similar to those used by Ochi et al. (2000), and applied it to one-year datasets of SG gravity using product spectra, but they were unable to observe the triplet. Many other attempts to observe the Slichter mode through SG data are not listed above, but they all have negative answers. Detection of this special mode is still a challenge.

Motivation and Future Work

SG data has played a key role in the study of the Slichter mode, but the disadvantages of these instruments are also apparent: (1) Since SGs are very expensive and have strict site condition requirements, they are still sparsely distributed globally; (2) Only a small part of SG data are directly shared on-line, and these data always have a delay of 6 months; (3) the SG data format is not used by seismologists, and the transfer function is not always known. Compared with SGs, STS-1 seismometers also have good performance at ultra low frequency (Figure 2.40), and the wide distribution of the STS-1 makes it an optimal instrument for global stacking. Also, the transfer functions are well known. For these reasons, we are trying to develop a standard procedure to search for the Slichter mode using STS-1 data.

Acknowldgements

We thank David Dolenc, David Crossley, and Ichiro Kawasaki for their help on tidal corrections.

References

Dahlen, F.A. and Sailor, R.V., Rotational and elliptical splitting of the free oscillations of the Earth, Geophys. J. R. Astron. Soc. 58, 609-623, 1979.

Hinderer, J., Crossley, D., and Jensen, O., A search for the Slichter triplet in superconducting gravimeter data, Phys. Earth Plan. Int., 90, 183-195, 1995.

Ochi Y., K. Fujita, I. Niki, H. Nishimura, N. Izumi, A. Sunahara, S. Naruo, T. Kawamura, M. Fukao, H. Shiraga, H. Takabe, K. Mima, S. Nakai, I. Uschmann, R. Butzbach, E. Forster, N. Courtier, B. Ducarme J. Goodkind, J. Hinderer, Y. Imanishi, N. Seama, H. Sun, J. Merriam, B. Bengert, D.E. Smylie D.E, Global superconducting gravimeter observations and the search for the translational modes of the inner core, Phys. Earth and Plan. Int., 117, 3-20, 2000.

Rosat, S., Y. Rogister, D. Crossley, J. Hinderer, A search for the Slichter triplet with superconducting gravimeters: impact of the density jump at the inner core boundary, J. Geodynam., 41, 296-306, 2006.

Slichter, L.B., The fundamental free mode of the Earth's inner core, Science, 47, 186-190, 1961.

Smylie, D.E., The inner core translational triplet and the density near Earth's center, Science, 255, 1678-1682, 1992.

Smylie, D.E., J. Hinderer, B. Richter and B. Ducarme, The product spectra of gravity and barometric pressure in Europe, Phys. Earth and Plan. Int., 80, 135-157, 1993.

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