A. Souriau , Toulouse
The inner core of the Earth has a major importance in most of the physical and chemical processes which affect our planet, in particular its thermal evolution and its global dynamics; it also plays an important role for stabilizing the magnetic field. A better knowledge of inner core structure is thus quite important. It may help to understand the Earth's differenciation process and to specify the chemical and mineralogical nature of the iron alloy which constitutes the center of our planet.
The seismology of the inner core covers many different aspects. We will focus on a few aspects for which important advances have been made during the last few years.
Anisotropy and heterogeneities
The presence of anisotropy inside the inner core is well established from the travel time anomalies of PKIKP, a P-wave transmitted through the inner core, and from the splitting of inner core sensitive normal modes. Path parallel to the Earth rotation axis are about 4s faster than those parallel to the equatorial plane. Proposed explanations are either preferred orientation of anisotropic iron crystals (possibly the hexagonal closed-packed form, e.g. Stixrude and Cohen, 1995), or orientation of non spheroidal fluid inclusions (Singh et al., 2000). Liquid inclusions are proposed, at least in the external part of the inner core, to account for the low value of the quality factor (Spies, 1991; Bhattacharyya et al., 1993, Souriau and Roudil, 1995).
The exact geometry of the anisotropy is an important information for understanding its physical nature and its origin. The early observations led to propose that the anisotropy has a cylindrical symmetry, with possibly a slightly tilted symmetry axis (Creager, 1992; Su and Dziewonski, 1995). The tilt of the axis is however uncertain (Souriau et al., 1997). This image has been modified in an important way by the observation that the two hemispheres exhibit different anomalies (Tanaka and Hamaguchi, 1997). The "western" hemisphere, between 180°W and 40°E, is strongly anisotropic (3.5%), whereas the "eastern" hemisphere, between 40° and 180°E, has only a week anisotropy (0.5%). This asymmetry concerns mostly the uppermost few hundreds of kilometers of the inner core (Creager, 2000).
It is important to estimate the relative contributions of heterogeneities and anisotropy in the travel time anomalies of the inner core phases. The isotropic average of P-wave velocity seems almost invariant for scale lengths larger than 200 km (Creager, 2000; Garcia and Souriau, 2000), indicating a chemical lateral homogeneity of the inner core. Thus anisotropy is predominantly responsible for the observed travel time anomalies of PKIKP. Their inversion leads to a very simple model in which a homogeneous central body with a 3% uniform anisotropy is asymmetrically surrounded by a homogeneous isotropic layer with a thickness of 100-200 km on the western hemisphere, increasing to 400 km on the eastern hemisphere (Figure 1).
It would be crucial to know whether the radial transition from the isotropic layer to the anisotropic deeper structure occurs gradually, or if it is a first order discontinuity. In the first case, it could correspond to a progressive disorientation of the crystals, whereas in the second case, it may reveal a mineralogical or chemical transformation. Observations of waves possibly reflected at this discontinuity have been reported (Song and Helmberger, 1998), but waves refracted or diffracted at short wavelengths heterogeneities (Bréger et al., 1999; Vidale and Earle, 2000) may probably provide an alternative explanation to these observations.
Figure 1: Shematic structure of the inner core. Meridian (a) and equatorial (b) cross-sections. A central body with 3% uniform anisotropy (with fast axis parallel to the Earth rotation axis) is asymmetrically surrounded by a homogeneous, isotropic layer.
The inner core model described above, with a strong anisotropy, a hemispherical pattern and an uppermost isotropic layer, explains most of the seismological observations. Some doubts remain however concerning a possible bias due to the heterogeneties in the D" layer at the base of the mantle: an inner core model with a 1% uniform anisotropy and strong heterogeneities in the lowermost mantle may also explain most of the seismological observations.
The rigidity of the inner core
The observation of S-waves propagating through the inner core (PKJKP for example) would be a direct proof of its rigidity. There are many indirect evidences of the solid nature of the inner core: Both the P-velocity jump (Müller, 1973, Song and Helmberger, 1992; Kennett et al., 1995) and the density jump (Souriau and Souriau, 1989, Shearer and Masters, 1990) suggest that the inner core is solid. An additional evidence is given by the S-velocity required to fit the eigenmode periods (e.g. Gilbert and Dziewonski, 1975; Tromp, 1993). However, direct observations of S-waves would allow to build an S-velocity radial model, which would be very informative about the composition of the inner core.
Several attempts to detect PKJKP have been made in the past, none of them leading to uncontestable results. Recently, two studies leading to different results have reported possible observations of inner core shear waves. Okal and Cansi (1998) analysed a Flores Sea deep event recorded at short period French stations, whereas Deuss et al. (2000) reported observations in the frequency domain 0.01-0.1 Hz for the same event, and for a Bolivian earthquake. In both studies, different stacking methods were used to enhance the signal.
The difficulty to identify inner core S-phases is partly due to the very low amplitude of the signal to be detected. But a more severe problem is the lack of strong constrains concerning this phase. The distance at which it has its maximum amplitude, and this amplitude itself, depends drastically on the incidence angle and transmission coefficients at ICB, thus on the S-velocity immediately below the ICB, which is poorly known. It could be close to zero (Choy and Cormier, 1983). If such is the case, the absence of a sharp discontinuity in S-velocity at ICB would prevent the generation of a PKJKP phase, at least at short period.
Another difficulty comes from the possible confusion of PKJKP with an other phase, PKKP. These two phases have nearly the same phase velocity, and they may arrive nearly at the same time, depending on the inner core structure. Thus, they may be very difficult to discriminate, even with stacking methods.
The differential rotation of the inner core
The possible existence of a differential rotation of the inner core with respect to the mantle was first suggested from results of dynamo modelling. Attemps to detect it from seismological observations are based on differents methods: The detection of a travel time anomaly varying with time along a particular path, or the detection of an apparent evolution in the worldwide heterogeneity pattern, either from body waves, or from eigenmode splitting. The first observation (Song and Richards, 1996) reports a variation of PKIKP anomaly of 0.3s in 30 years along the path from South Sandwich Island (SSI) to station COL in Alaska. The interpretation, based on a tilt of the anisotropy symmetry axis, leads to a very fast rotation rate, of the order of 1.1°/yr. A still larger rate (3°/yr) is obtained from the absolute PKIKP travel times processed at the worldwide scale (Su et al., 1996). The SSI to COL data, reinterpreted in considering the drift of an heterogeneity beneath this path (Creager, 1997), lead to rotation rates between 0.05 and 0.3 °/yr, depending of how much of the signal is ascribed to mantle heterogeneities. All the paths other than SSI to COL fail to detect large rotation rates, or lead to results which are poorly statistically significant (e.g. Souriau, 1998). A doublet analysis of the core phases, which allows to discriminate between earthquake mislocations and inner core rotation, shows that the SSI to COL residual time variations mostly reflect mislocation of the SSI events (Poupinet et al., 2000).
Another evidence of the absence of differential rotation (or possibly of a very low rotation rate, 0 ± 0.2 °/yr) is provided by the splitting functions of the inner core sensitive modes: their pattern remains almost unchanged during 15 years (Laske and Masters, 1999). A method based on the temporal change of scattered waves also gives a low rotation rate, of the order of 0.15°/yr (Vidale et al., 2000).
To summarize, a rotation rate of 0 ± 0.2 °/yr seems compatible with most of the seismic observations. A recent geodynamo model including gravitational coupling between inner core and mantle predicts a mean rate of 0.02°/yr (Buffett and Glatzmaier, 2000), but it requires some parameters which are poorly known. More accurate seismological observations may help to constrain such models.
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