Theory of Inner Core Super-Rotation: An Analysis

Theory of Inner Core Super-Rotation: An Analysis Andrew Brown Introduction This article investigates the various thought processes behind, and controversies surrounding, the theory of Inner Core super-rotation. The Inner Core of the Earth is composed predominantly of soli iron, and lies at the centre of the planet, surrounded by a liquid Outer Core (again, predominantly composed of iron). It is a region that has long been known for having a profound influence in the processes that maintain convection within the liquid Outer Core. Understanding the workings of the Inner Core could be key in the understanding of dynamo theory, the Earth’s magnetic field (from its origins, through to the present day), heat-flow, core-history, core-composition, and possibly effects on the Earth’s gravity field. In recent years, many seismic studies have indicated that the Inner Core contains large-scale anisotropy in its velocity structure. It was discovered that there was evidence of systematic changes in the travel-time of waves travelling through the Inner Core. These changes (changing over long time periods) were interpreted as indications of the Inner Core rotating at a different rate than that of the other material within the Earth. It was suggested that the Inner Core is rotating in an Eastward direction relative to the Mantle and Crust, at a rate measurable within human time-scales. This finding was initially dismissed as being either too slow a rotation-rate, or considered to be physically impossible. However, additional evidence, displayed in recent studies into the matter, is found to support the hypothesis that the Inner Core is, in fact, super-rotating. Despite this finding, the topic of Inner Core super-rotation, along with discussions about the rate at which it is rotating, i s still considered a controversial area of research. Research History The first suggestion of a super-rotating mass at the centre of the Earth was brought on by analysis of the interaction between the solid Inner and liquid Outer Core. The viscosity of the Outer Core is very low, and is thought to convect at a rate of approximately 1cms-1. It could be thought that this might result in the appearance that the Inner Core was moving with respect to the mantle. In order to investigate this phenomenon further, Glatzmaier Roberts (1995) modelled a numerical solution for 3D convection dynamo motions within the Outer ore. This model successfully reproduced observed magnetic field strength and reversal behaviour. However, in the model, the Inner Core was free to rotate, and what was found was that it naturally super-rotated in an Eastward direction. From this is was then hypothesised that seismic reflections, rebounding off the Inner/Outer Core boundary, could show evidence of this modelled rotation, but it was later found that a more efficient data set would be to examine seismic waves that are transmitted through the Inner Core (Song Richards, 1996). Using this technique, along with others (such as analysis of geodynamo processes and shear-wave conversions within the Inner Core), there is more evidence supporting a super-rotating Inner Core, than not. However, even upon agreeing that this idea is both plausible and probable, there is still a large level of uncertainty surrounding the rate at which the Inner Core is rotating with respect to the Mantle. There have been suggestions in recent studies that it is rotating at a rate of less than 1à ¢Ã‚ Ã‚ °yr-1, but equally, there have been suggestions of rotation rates of over 1à ¢Ã‚ Ã‚ °yr-1, and even suggestions recently of no discernable difference in rotation. Evidence for Super-Rotation Our current theories of the origins of the Earth’s magnetic field rely on the understanding of the geodynamo processes occurring within the core. Differential rotation is a requirement for the geodynamo to exist. It is this differential rotation that drives the dynamo action by generating toroidal magnetic fields from poloidal. Initially, there are poloidal field lines, which are then ‘wound up’ by the differential rotation (shown in figure 1). Only a small amount of diffusion is needed to break these poloidal lines and form a toroidal loop, and these new toroidal field lines then amplify the original poloidal field, and the process repeats. It can be observe that the core surface appears to drift in a westward direction. If the Inner Core is, indeed, differentially rotating, then it would suggest an eastward drift at the Inner Core boundary. This predicted eastward drift agrees with the eastward drift observe in geodynamo simulations. In addition to this, it is well understood by electromagnetism, that Inner and Outer Core are well coupled, and thus would suggest that the Inner Core should be super-rotating, and drift east. Although a super-rotating Inner Core is consistent with current geodynamo theories, such a controversial subject area requires more actual, observable evidence in order to validate these assumptions. This evidence comes from analysis of Inner Core seismology. P-waves are found to travel through the Inner Core approximately 3 or 4% faster in a direction almost parallel to the north/south axis, than in directions along the equatorial plane. (Poupinet et al., 1983; Morelli et al., 1986; Song Helmberger, 1993). In addition to this, analysis of the free-oscillations of the Earth that contain significant energy within the Inner Core shows evidence of shear-wave splitting (Masters Gilbert, 1981; Sharruck Woodhouse, 1998), another indication of a variation in velocity between planes. Both these phenomena are show Inner Core anisotropy, with the ‘fast axis’ tilted approximately 10à ¢Ã‚ Ã‚ ° from the rotation axis (figure 2). This fact can be used to the advantage of research ers, as if the Inner Core is super-rotating then it should be possible to observe this ‘fast axis’ precessing over long time periods. In other words, if the anisotropic Inner Core rotates about the north/south axis at a different rate to that of the Mantle, then the observed travel-times will change in a systematic fashion for repeated seismic signals passing through the Inner Core. Interpretations of the relative (rather than absolute) timings are use in order to reduce the methods sensitivity to errors in source locations. The method uses a combination of source and receiver pairs that allow for seismic rays through the Inner Core, that also have an orientation that will be sensitive to the effect of the hypothesised rotation on the ‘fast axis’. The differences in travel-times are analysed for three different ray path phases: AB, BC and DF (shown in figure 3). Ray paths through the Earth are very close together, hence the need to analyse relative travel-times. Mantle convection is slow, and the Outer Core is well-mixed, and thus the travel time of the BC phases should remain relatively constant over time. It should, therefore, be safe to assume that any variations observed over time will have an Inner Core origin. Each of these phases travel through different sections of the Earth’s Mantle and Core, and thus contain different information, therefore, changes between phases are unlikely to be due to event mislocation. The contrast between AB and BC phases are mostly just scattered; however, the difference between BC and DF phases show a systematic increase over time. However, interpretation of the differences in travel time, alone, is not sufficient to detect super-rotation. It is the effect on the parameter, ÃŽ ¾ (the angle of the ray with respect to the Inner Core ‘fast axis’), that is sensitive to the changes in ray paths that would be observed if the Inner Core were differentially rotating. Figure 4 shows two curves: the percentage velocity perturbations with ÃŽ ¾; and the derivative of this curve, with respect to ÃŽ ¾, which illustrates the sensitivity to changes in velocity with ÃŽ ¾, which is what would be expected with super-rotation. Studies of these core-phase relative travel times have indicated a definite eastward Inner Core rotation rate of approximately 1à ¢Ã‚ Ã‚ ° per year (Song Richards, 1996), although further studies have produced varying results for this rate. Ovtchinnikov et al. (1998), again, used BC-DF travel-time differences brought on by nuclear explosions, thus reducing the error in source location. The result of this study, produced through the analysis of long time-series data over decades, was consistent with a cylindrically symmetric Inner Core which is moving in an eastward direction. It was found that it rotated at a rate of 0.3-1.1à ¢Ã‚ Ã‚ °yr-1. Another, different, approach by Vidale Earle (2000) was to use short-period seismic waves, or ‘coda’, that are reflected back from the Inner Core (PkikP phase). This method is particularly affective (in comparison to previous techniques) as it allows for the measurement of changes in Inner Core rotation rates. They found that, over a period of around 3 years, the western hemisphere of the Inner Core appeared to be moving towards the recording station, and the eastern, away. This is what would be expected for an eastwardly super-rotating Inner Core, and the rate of this rotation was estimated to be around 0.15à ¢Ã‚ Ã‚ °yr-1. Controversies Surrounding Super-Rotation Although many studies agree on an eastwardly rotating Inner Core with respect to the Mantle, research using only slightly different methodologies and phase combinations has produced vastly varied results. Researchers have dismissed the variations in the findings as being due to the methodology producing the results being inadequate, and that the data is insufficient. All of the methods described rely on the use of data over a time period which could be up to decades. Seismogram quality has improved greatly over time; therefore arrivals will end up being picked earlier in the more accurate, modern seismograms. In addition to this, the rays being analysed have to 1st travel through local source, receiver and deep mantle structure before then passing through the area of interest (Inner Core). These have greater effects on the velocity variations than that of the Inner Core anisotropy, which reduces the accuracy at which the effects of the Inner Core can be interpreted. All initial studies, although successful in providing ‘proof’ of Inner Core super-rotation, rely on the assumption of a homogeneous, cylindrically symmetric model for the distribution of Inner Core anisotropy, with a north/south tilted fast axis. On top of this, the assumption of the Inner Core as essentially a rigid rotating rigid body, forces a potentially unrealistic framework. Instead, a ductile Inner Core is more plausible, which would deform as rotates. Recent studies into mode splitting functions have shown that there are complex patterns of inhomogeneity in anisotropy within the Inner Core. These must be included in the base-model because of the effects of Inner Core lateral velocity variations on the observed travel times as the body rotates. Therefore, work is still needed to be done to understand these heterogeneities, in order to interpret the changes in travel times for a more precise estimation of the rotation-rate. In addition to heterogeneities within the Inner Core, the effects on seismic velocities brought on by artefacts (such as subducting slabs) at the base of the mantle must be understood, as they could lead to misinterpretation of ‘evidence’ for temporal brought on by the rotation. Thus there is some-what of a trade-off between the rotation rate, and the lateral change in velocities when interpreting the travel-times. It is found that a non-zero rotation rate of approximately 0.2à ¢Ã‚ Ã‚ °yr-1 is required to explain the temporal variations in observed relative travel times between the BC and DF phases. Finally, â€Å"the Inner Core is far less accessible to us than the surface of any planet in the solar system†. The Inner Core lies at the very centre f the Earth, inside a highly variable 3000km of solid mantle and a convecting liquid Outer Core. This results in poor, restricted sampling locations and reduced number usable of ray-paths, resulting in biased results, as there are only limited locations for source receiver pairs that can collect information on the key phases (see figure 3) used in the interpretation. Conclusions In conclusion, although there is increasing evidence supporting the theory of Inner Core super-rotation, it is clear that there is still a lot of work and research needed to be done. In addition to this, even if the theory of a super-rotating Inner Core is viewed as not only plausible, but necessary, a further understanding of the dynamics and structural influences of the Outer and Inner Core is still required to correctly determine a precise rate for this rotation It is for these reasons that the topic of Inner Core super-rotation, along with discussions about the rate at which it is rotating, is still a very active and controversial area of research. References Glatzmaier, G. A. and Roberts, P. H. 1995. A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle.Physics of the Earth and Planetary Interiors, 91 (1), pp. 6375. MAkinen, A. M. and Deuss, A. 2011. Global seismic body-wave observations of temporal variations in the Earths inner core, and implications for its differential rotation.Geophysical Journal International, 187 (1). Masters, G. and Gilbert, F. 1981. 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