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
b
PKP
1,180
PKiKP
Inner
PKIKP
core
Event
Outer core
Travel time (s)
140°
Mantle
c
1,160
PKiKP
1,140
PKIKP
125 130 135 140 145 150
Epicentral distance (°)
PKiKP
Amplitude
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
0
PKIKP
1,140
1,141
1,142 1,143 1,144 1,145 1,146 1,147 1,148 1,149 1,150
Travel time (s)
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: [email protected].
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NATURE GEOSCIENCE DOI: 10.1038/NGEO1083
LETTERS
West
¬1.0
East
¬0.5
0
0.5
Differential travel time residuals (s)
1.0
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
LETTERS
a
West
East
Residual (s)
1.0
0.5
0
¬0.5
39¬52 km
¬1.0
¬160
b
¬120
¬80
¬40
0
40
Longitude (°E)
80
120
160
Residual (s)
1.0
0.5
0
¬0.5
52¬67 km
¬1.0
¬160
¬120
¬80
¬40
0
40
Longitude (°E)
80
120
¬160
¬120
¬80
¬40
0
40
Longitude (°E)
80
120
160
c
Residual (s)
1.0
0.5
0
¬0.5
67¬89 km
¬1.0
160
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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© 2011 Macmillan Publishers Limited. All rights reserved.
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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