LETTERS PUBLISHED ONLINE: 20 FEBRUARY 2011 | DOI: 10.1038/NGEO1083
Reconciling the hemispherical structure of Earth’s inner core with its super-rotation Lauren Waszek *, Jessica Irving and Arwen Deuss a
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Earth’s solid inner core grows through solidification of material from the fluid outer core onto its surface at rates of about 1 mm per year1 , freezing in core properties over time and generating an age–depth relation for the inner core. A hemispherical structure of the inner core is well-documented: an isotropic eastern hemisphere with fast seismic velocities contrasts with a slower, anisotropic western hemisphere2–4 . Independently, the inner core is reported to super-rotate at rates of up to 1◦ per year5–7 . Considering the slow growth, steady rotation rates of this magnitude would erase ’frozen-in’ regional variation and cannot coexist with hemispherical structure. Here, we exploit the age–depth relation, using the largest available PKIKP– PKiKP seismic travel time data set, to confirm hemispherical structure in the uppermost inner core, and to constrain the locations of the hemisphere boundaries. We find consistent eastward displacement of these boundaries with depth, from which we infer extremely slow steady inner core super-rotation of 0.1◦ –1◦ per million years. Our estimate of long-term superrotation reconciles inner core rotation with hemispherical structure, two properties previously thought incompatible. It is in excellent agreement with geodynamo simulations8,9 , while not excluding the possibility that the much larger rotation rates inferred earlier5–7 correspond to fluctuations in inner core rotation on shorter timescales10 . The Earth’s solid inner core was first discovered by the observation of PKiKP, a seismic wave which travels through the mantle and outer core before reflecting from the sharp inner core boundary (ICB; ref. 11). The inner core is composed mostly of iron, growing through solidification of outer core material onto the ICB surface as the Earth cools, resulting in deeper structure being older. Although the thermal history of the inner core is debated12,13 , its uppermost structure results from processes occurring in the recent past, of which we have greatest understanding; these mechanisms are unlikely to have changed in the last 100 Myr. This resulting time–depth variation of the upper inner core is key to investigating any changing environment at the ICB region associated with inner core super-rotation. Hemispherical variation in the velocity, anisotropy and attenuation structure of the upper inner core have been investigated repeatedly and, although there is still much uncertainty regarding the detailed characteristics, these properties are consistently reported in previous studies2,14,15 . Velocity anisotropy was originally determined as present throughout the entire inner core, through both body-wave and normal-mode observations16–18 . Following these discoveries, a layered structure was found in the uppermost inner core: an isotropic layer of debated thickness atop deeper anisotropic structure3,19 . Concurrent investigations observe large regional differences: strong anisotropy in the western hemisphere, with little to none in the east4,20,21 . The eastern hemisphere shows a higher velocity than the western
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Figure 1 | Ray paths, travel time curves and an example of the seismic phases PKIKP and PKiKP. a, Ray paths of PKIKP (blue) and PKiKP (red) for an event at 100 km depth. b, Travel time curves of PKIKP and PKiKP. The earthquake–receiver epicentral distance range of 130◦ –143◦ avoids both interaction between the phases and interference from the outer core sensitive phase PKP (black). c, A seismogram from the Peru event of 5 September 2009, station AAK, epicentral distance 139◦ . PKiKP arrives just under 2 s later than PKIKP with opposite polarity and a slightly larger amplitude.
hemisphere22 ; these differences are present to depths of at least 800 km (ref. 23). Several mechanisms have been proposed as responsible for imprinting texture which results in hemispherical structure. It has been suggested to arise from thermochemical coupling of the inner core with the core–mantle boundary (CMB) region8 , in which more heat is extracted in the eastern hemisphere, creating a localized increase in inner core growth rate. This variation in freezing rates may also explain seismic texture throughout the inner core. More recent studies propose that the differences are a consequence of melting in the eastern hemisphere and freezing in the west, resulting in a lateral translation of the inner core eastwards12,13 . Here, the uppermost inner core is studied with PKIKP, which travels through the Earth’s mantle, outer core, and inner core, and a reference phase PKiKP, which has a similar path but reflects off the ICB (Fig. 1a). PKIKP and PKiKP can be observed as individual arrivals for earthquake–receiver epicentral distances of 130◦ –143◦ (Fig. 1b), whereby PKIKP samples up to approximately 90 km deep into the inner core. From every suitable event between 1990 and 2010, a total of 2,497 acceptable seismograms were obtained, making this the most extensive PKIKP–PKiKP study to date.
Bullard Laboratories, Department of Earth Sciences, University of Cambridge, CB3 0EZ, UK. *e-mail:
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NATURE GEOSCIENCE DOI: 10.1038/NGEO1083
LETTERS
West
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Figure 2 | Map showing all PKIKP–PKiKP differential travel time residual data collected. Thin lines indicate PKIKP ray paths through the inner core, and the locations of the circles correspond to the turning points of the rays. A clear hemispherical difference can be observed, with predominantly positive residuals (red circles) in the east due to faster velocity structure here, and negative residuals (blue circles) in the west indicating slower velocity. Hemisphere boundaries as a function of ray turning depth are indicated: Solid line 39–52 km, dashed line 52–67 km, and dotted line 67–89 km below the ICB.
Arrival times of the phases are picked using cross-correlation and hand-picking techniques (Fig. 1c). The PKIKP–PKiKP differential travel time is compared with that predicted by the seismic reference model AK135 (ref. 24) to obtain the PKIKP–PKiKP residuals. The paths of these two phases diverge only at the top of the inner core, thus any variation in the differential travel time residuals indicates a departure in inner core velocity structure from the 1D Earth model. Our data set confirms that the velocity structure of the upper inner core comprises two distinct eastern and western hemispheres (Fig. 2). Positive travel time residuals (shown as red circles) in the eastern hemisphere indicate faster velocity structure than AK135, whereas the west contains mostly negative residuals (blue circles) and hence is slower than the model. Also present in the western hemisphere are faster paths (red circles) orientated in the polar, north–south, direction. Polar paths have ζ < 35◦ , where ζ is the angle between the PKIKP ray path in the inner core and Earth’s rotation axis. These paths have residual values comparable to those in the eastern hemisphere, and reveal anisotropy aligned with Earth’s rotation axis, in good agreement with known anisotropic structure17,18 (Supplementary Fig. SI1). Similar anomalous polar travel time residuals are not observed in the east, indicating isotropic velocity structure. Previous studies have not led to well-defined limits on the longitude of the hemisphere boundary locations, which range from 40◦ to 60◦ for the eastern boundary, and from 160◦ to 180◦ for the western boundary2,3,21 . The uncertainty may be due to lack of data or uneven sampling; this is avoided here through our considerably larger data set, which provides extensive coverage to constrain the boundaries to the most accurate locations yet.
To explore the temporal changes in the upper inner core we partition the data by PKIKP turning depth below the ICB. We separate the residuals into three turning depth ranges: 39–52 km, 52–67 km and 67–89 km below the ICB (Fig. 3). The western hemisphere (blue data points) has predominantly negative residuals and the eastern hemisphere (red data points) has positive residuals. The hemisphere boundaries are determined to be located at the longitudes (or range of longitudes) which separate the negative and positive residuals. Some of the boundaries are constrained by only one or two data points, which have been checked for accuracy; the corresponding seismograms for all points which constrain the boundaries are contained in Supplementary Fig. SI2, in which the clarity of the phases can be clearly observed. Anisotropy in the deep western hemisphere results in positive residuals for polar paths, which may then be erroneously identified as sampling the eastern hemisphere. To prevent misinterpretation, we omit from Fig. 3 all western polar paths with PKIKP turning points deeper than 69 km below the ICB when we determine the hemisphere boundary locations, relying solely on paths with ζ > 35◦ at this depth. As negligible anisotropy is observed in the eastern hemisphere, and serves to make the residuals more positive, we need not remove any points from the east. We find that both boundaries separating the hemispheres exhibit a consistent eastward shift with increasing depth (Fig. 3). The change in hemisphere boundary locations with depth are listed in Table 1, and correspond to an average shift of ∼20◦ over the 50 km thick layer. If the inner core rotates faster than the mantle, and hemisphere differences result from frozen-in structure at the ICB, then it is expected that the location of these boundaries will change over time. The eastward shift of the hemisphere boundaries with depth may be explained by an eastward displacement of the ICB
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NATURE GEOSCIENCE DOI: 10.1038/NGEO1083
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Figure 3 | PKIKP–PKiKP differential travel time residuals as a function of PKIKP turning point longitude, separated according to PKIKP turning depth. a, 39–52 km below the ICB. b, 52–67 km. c, 67–89 km. Anomalous anisotropic polar paths in the west are omitted. Vertical dashed lines indicate the hemisphere boundaries, which are determined as the longitude where the travel time residuals change from predominantly negative to positive. Red points and blue points represent eastern hemisphere and western hemisphere data respectively. With increasing depth, the boundaries show a consistent westward shift.
over time, entrained by a very slow steady rotation of the inner core. Thermal evolution investigations calculate the age of the inner core as between 1.0 and 3.6 Gyr, the most likely value being at the younger end of this range25,26 . Assuming uniform growth, the ∼50 km layer of inner core sampled takes up to 150 Myr to grow. Taking the possible shifts of 12◦ –29◦ to have occurred over this time, this equates to an extremely slow steady inner core super-rotation of 0.1◦ –1◦ Myr−1 (Table 1).
Most recently, temporal changes of the inner core structure have been explored using either scattering27 or doublet earthquakes6,7 , events occurring in the same location with similar mechanisms but separated in time by a period of up to a few decades. As a result, steady inner core super-rotation rates of 0.1◦ –1.0◦ yr−1 have been proposed5–7,27 . However, these seismic studies provide only a snapshot of the current inner core super-rotation. Considering the slow growth of the inner core, rotation rates of this magnitude would completely erase any regional differences frozen in by the evolving environments at the ICB; this is incompatible with our observations of hemispherical structure. Conversely, normalmode studies and other body-wave investigations find little to no rotation28,29 . Our observed steady rotation rate of 0.1–1◦ Myr−1 is far too slow for any doublet earthquake to observe. This suggests that previously observed rapid temporal changes of the inner core may be a result of fluctuations occurring on timescales too short to allow freezing-in of the properties, including the movement of small scale topography at the inner core surface6 , a layered mosaic structure comprising patches of solid and fluid30 , or short timescale fluctuations in inner core rotation9,10 . Examining hemisphere boundaries, a recent normal-mode study4 finds transition zones between the hemispheres, rather than sharp boundaries, located in approximately the correct vicinity were the eastward shift to continue with depth. These indistinct locations may result from a depth-average of the shifting boundaries. Body-wave investigations in the same study locate the hemisphere boundaries using anisotropy within a depth range of 170–1,090 km below the ICB, finding values of −151◦ ± 61◦ and 14◦ ± 34◦ ; the large error bounds are compatible with a further eastward shift with depth. The study uses the anisotropy of the western hemisphere to locate the boundaries, whereas here we use the difference in isotropic velocity structure. The isotropic velocity structure at the top of the inner core is most likely frozen in at the ICB. Anisotropy only appears at a depth of 69 km below the ICB, indicating that anisotropy could result from texturing after solidification, and therefore the isotropic velocity and anisotropy structures may not coincide. Geodynamo simulations which combine the effects of gravitational coupling of the inner core to the lower mantle with viscomagnetic torques find a small differential rotation of a few degrees per million years9 . The much faster rotation rates inferred in other seismic studies5–7 may then be a result of inner core oscillation or fluctuations on shorter timescales (∼100 yr), superimposed on this much slower, steady rotation10 . Compared with previous seismic observations, our rotation rate of 0.1◦ –1◦ Myr−1 is much more consistent with the geodynamo calculations; the slower rate would permit the freezing in of regional structure at the ICB. This may be generated from asymmetrical heat flows at the CMB, and subsequent faster growth rates in the eastern hemisphere8 . Conversely the hemispheres may arise from convection within the inner core, resulting in melting in the eastern hemisphere and freezing in the west, accompanied by an eastward lateral translation of the entire inner core12,13 . The proposed eastward translation of the inner core in addition to steady super-rotation might result in an eastward shift with depth of the boundaries; we find that the east boundary experiences a greater shift than the west (∼27◦ compared
Table 1 | Longitude of the hemisphere boundary locations with increasing depth below the ICB. Depth below ICB (km)
West boundary
East boundary
Average eastward shift with respect to upper layer
Inner core rotation rate for growth rate 0.3 mm yr−1
39–52 52–69 69–89
−173◦ −169◦ to −160◦ −161.5◦
8◦ to 14◦ 21◦ 35◦ to 41◦
– 9◦ ± 6◦ 22.25◦ ± 10.75◦
– 0.1 ± 0.07◦ Myr−1 0.15 ± 0.07◦ Myr−1
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NATURE GEOSCIENCE DOI: 10.1038/NGEO1083 with ∼11.5◦ ), in good agreement with this idea. However, further modelling is required to conclusively reconcile these two properties. As our inner core super-rotation rates is derived from the observed constant shift of hemisphere boundaries with depth, the observed hemispherical structure is inherently compatible with this extremely slow steady rotation. Furthermore, our observation does not rule out the possibility of short timescale oscillations or wobbles of the inner core, superimposed on a much slower, steady superrotation9,10 , nor does it exclude the possibility of a lateral translation of the inner core in addition to steady rotation and oscillations12,13 .
Methods The ideal event to obtain robust PKIKP–PKiKP travel time residuals must generate observable PKIKP and PKiKP phases, well separated both from each other and their crustal reflections. This criteria requires impulsive ruptures, with 5.2 < Mw < 6.3, and a source depth of greater than 15 km. Broadband vertical seismic data was filtered between 0.7 and 2.0 Hz to centre on the dominant phase frequency of 1.0 Hz. A total of 1,162 events were used, resulting in 38,361 seismograms before processing.
Received 7 October 2010; accepted 13 January 2011; published online 20 February 2011
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Acknowledgements The research was funded by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement number 204995. We thank M. Dumberry and V. Cormier for their constructive and helpful comments.
Author contributions L.W. compiled and analysed the data and produced the manuscript and figures. J.I. wrote the cross-correlation code. J.I. and A.D. supervised the analysis. All authors discussed the results and implications at all stages.
Additional information The authors declare no competing financial interests. Supplementary information accompanies this paper on www.nature.com/naturegeoscience. Reprints and permissions information is available online at http://npg.nature.com/reprintsandpermissions. Correspondence and requests for materials should be addressed to L.W.
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