1. Anisotropy and heterogeneity of the Earth's inner core
No talking … straight to next slide!
Arwen Deuss
Utrecht University

2. Why the Earth’s core …? Solidification heat is engine for mantle
convection
Now, why is the inner core so interesting and important?
Anisotropy and crystal
structure of iron
Thermal and chemical
core convection
drives magnetic field

3. (1) Seismic body waves N P = mantle P-wave K = outer core P-wave
I = inner core P-wave
i = inner core reflection
When we use body waves, we trays rays of waves through the Earth and this is the most easily visualized type of seismic data. The main wave of interest is called PKIKP, which travels the inner core. It is useful to compare with waves that only travel the outer core, called PKP and PKiKP. Let’s have a look at how the arrival times of the waves that travel the inner core, vary with the angle they make with the Earth’s rotation axis.
Useful for:
* measuring velocity
* studying boundaries
* illuminating small scale
structure
* short period data (~1 Hz)

4. (1) Seismic body waves Inner core Outer core 1D model Inner core
Here, two seismograms are shown. The top one is for a wave that has travelled along the equator, so the earthquake and the seismometer would both be on a plane parallel to the equator. The dashed lines show where the inner and outer core wave would arrive for an inner core without anisotropy. For an equatorial wave, they both arrive on time. However, for a wave that has travelled in the north-south direction, the inner core wave arrives up to 5 second earlier. This is anisotropy. The waves that travel north-south travel faster than waves that travel east-west. I often use these seismograms in practicals for students, who are always surprised that it is so easy to observe inner core anisotropy! They somehow expect it to be much more difficult …
1D model N S
Inner core
Outer core
1D model

5. (1) Seismic body waves isotropic anisotropic equatorial polar
Now, what we have done is measure several thousands of such waves, and we visualize them by plotting the travel time measurement against the angle. For small angle, the waves have travelled in the polar or north-south direction, and the larger angle is equatorial or east-west. The more the travel times vary with angle, the more anisotropy we have, and the less straight this line is. When we look at the top of the inner core, we find that the line is almost straight, so there is no anisotropy in the top 57 km. When we go deeper, we have just about 1.5%anisotropy. The deeper we go, the more anisotropy we get, with over 3% in the deeper part of the inner core. Now, let’s make figures to see how these arrival times vary as a function of location and depth in the inner core.
polar
isotropic
anisotropic
(Deuss, Annu. Rev., 2014)

6. Inner core hemispheres
One of the most striking observations has been that the inner core may have hemispherical structure: the western hemisphere may be slower than the eastern hemisphere.
When we look at those waves that travel fast in the north-south direction, then we find that they really only travel fast in the region under north and south america, which are the dark triangles here. It is as if we can slice the Earth’s inner core into two pieces …
Sharp boundaries
Real hemispheres
Mixed transition regions
Anisotropic hemisphere
(Deuss, Annu. Rev, 2014)

7. (2) Normal mode data Useful for: * illuminating large scale structures
26 December 2004
Sumatra, depth 35 km
The second data type are the normal modes. We observe normal mode by taking data for large earthquakes, such as the devastating Sumatra event of boxing day We typically take about one week of data, and do a simple Fourier transformation and all the peaks show up. For a spherically symmetric Earth, all these peaks are simple, but for the real Earth they are often split into two peaks.
data
1D model
Useful for:
* illuminating large scale structures
* complete theory (no approximations)
* long period data (1-10 mHz)

8. Isolated normal modes Data misfit = 0.34 Deuss et al, GJI, 2013
We find inner core anisotropy, which shows up as large positive frequency anomalies near the poles and negative frequency anomalies near the equator. This pattern is reproduced by a model containing inner core anisotropy. If we only take mantle structure into account, we would only get the ring around the Pacific, which is not what we find.
But how about the hemispheres? People had been making these observations ever since the first discovery of inner core anisotropy now almost 30 years ago.
Data misfit = 0.34
Deuss et al, GJI, 2013

9. Hemispheres in anisotropy
16S5-17S4 observed splitting function
Body wave observations
Inner core hemisphere structure
So, in agreement with the body waves, the normal modes also find the anisotropy in a small wedge region in the west. And we were just very lucky with the body waves, which were sampling in just the right region under north and south America.
THIS IS WHAT (WE THINK) WE KNOW … But there are lots of outstanding questions that still need answereing and which would benefit from CIDER type collaboration
Deuss et al, Science, 2010
Hemispherical structure?
anisotropic wedge in the West

10. Innermost inner core? Negative anisotropy – Tilted symmetry axis
Seen by Wang et al (2015)
Negative anisotropy –
N/S symmetry axis
Seen by Beghein & Trampert (2003)
Required (?) by normal modes N S N S N
Equatorial
plane:
isotropic N
Equatorial
plane:
anisotropic
Symmetry
axis
Symmetry
axis

11. What causes the anisotropy?
Asymmetric growth (Yoshida et al, 1996)
Solidification texturing?
(Bergman, 1997)
Deformation texturing?
* Thermal convection
(Jeanloz & Wenk,1988)
* Asymmetric growth
(Yoshida et al. 1996)
* Maxwell stress
(Karato, 1999, Buffet & Wenk, 2001)
Several ideas have been proposed. Mike Bergman suggested that the anisotropy freezes in at solidification. But that would give the largest anisotropy at the top, wile we actually find the top layer to be isotropic. Another idea would be thermal convection, but the most recent measurement of thermal conductivity make that very unlikely. So, we have two other deformation processes left. One, would be due to the fact that the inner core grows faster in the equatorial region, to keep the inner core being in hydrostatic equilibrium, there is a flow of material towards the pole which would align the anisotropic crystals. This idea is one of the much favored possibilities at the moment. Another one would be due to the Maxwell stress because of the magnetic field. I really like this idea, because it would suggest that the anisotropy may be related to where the magnetic field would be stronger or weaker.
Both of this two mechanisms requires the inner core to be able to deform under small stress, and this requires a low viscosity.
Maxwell stress (Karato, 1999)
radial anisotropy?

12. Radial anisotropy Fast parallel to inner core boundary
Fast perpendicular to
inner core boundary in
top 100 km
Lythgoe & Deuss, GRL, 2015

13. Attenuation anisotropy?
Velocity anisotropy
So, we set out to measure the attenuation anisotropy with normal modes. In fact, it turned out to be quite straightforward! So far, we had been measuring the elastic part of the splitting function, now we had to add the anelastic part. We find that the anelastic part shows the same zonal splitting as we had seen before, so normal modes show strong evidence of attenuation anisotropy.
Attenuation anisotropy
Fast direction is also the most attenuating
Velocity and attenuation
anisotropy are correlated
Origin?
(Makinen, Deuss & Redfern, EPSL, 2014)

14. What causes the hemispheres?
Frozen in at inner core boundary
Thermochemical flows couple
the Earth’s inner core growth to mantle heterogeneity
(Aubert et al (2008))
Inner core translation
lopsided growth of the inner core resulting in convective translation
(Alboussiere et al (2010)
Monnereau et al (2010))
So, how can we explain the existence of the hemispheres? Well, I think we are right at that point where earth science was after the second world war. Lots of data suggesting that there potentially was something like continental drift, but only until plate tectonics was discovered everything fell into the right place. I don’t think we have discovered the plate tectonics for the inner core just yet … Though there are two interesting ideas! One links the hemispheres to flow in the outer core, and thus to the magnetic field, with hemispheres frozen in at the inner core boundary. This would not explain the anisotropy, but at least the difference in velocity near the top. The other idea, proposes that the inner core is translating, by melting on one side and solidifying on the other side. There are several problems with this idea, not likely if thermal conductivity is too high, and actually requires a large viscosity, so cannot ever work in conjunction with any of the deformation processes to explain the anisotropy.
thermal conductivity too high
requires large viscosity

15. Inner core super rotation?
If we would go with the first idea, and assume that the hemispheres freeze in at the inner core boundary, and that this relates to colder and hotter regions at the base of the mantle, then how about inner core super rotation?
Song & Richards (1996):
Inner core spins faster than rest of the planet, with speed of up to 1o per year

16. Inner core super rotation?
Western hemisphere Eastern hemisphere
Inner core super rotation?
39-52km below ICB
Hemisphere boundary
moves east as a function
of depth
Hemispheres frozen in as
inner core solidifies over
time with +/- 1mm/year
Very slow super rotation of
less than 1o/Ma?
52-67km below ICB
Well, we found that the boundary between the hemispheres at the top of the inner core moves east as a function of depth. Assuming that the inner core solidifies with 1 mm/year, then we find that the boundary rotates with less than 1 degree per million year. So, we can actually reconcile inner core super rotation with the existence of hemispheres.
67-89km below ICB
Waszek, Irving & Deuss, Nature
Geoscience, 2011

17. Inner core super rotation
… or oscillation?
So, what we find is that reported values of inner core super rotation have been going down in the literature, so all is probably working out fine!
(Deuss, Annu. Rev., 2014)

18. Conclusions
The top 100km displays radial anisotropy, with cylindrical anisotropy in the deeper parts
what causes the anisotropy?
Hemispherical differences in velocity and anisotropy
how do we explain hemispheres?
Innermost inner core?
Attenuation anisotropy?
Superrotation?
So, to conclude …
Lots of potentially interesting CIDER projects!