1. Translating Tomographic Images into a Physical State of the Upper Mantle
Ulrich Faul and Ian Jackson
Research School of Earth Sciences
The Australian National University
This is work done in collaboration with Ian Jackson who built the attenuation apparatus and John Fitz Gerald who does the TEM work.

2. Outline
Review of experimental data and grain-scale mechanisms
Calibration: Oceanic and continental lithosphere
Vs, Q (T, To, gs, p)
Application to subduction zones: Tonga

3. Structure of the upper mantle: Seismologists’ version
Vp, km/s
Vs, km/s
Depth, km
As background to the following, what we are trying to do is not only address lateral variations in velocity relative to a reference model, but to explain absolute velocities in the upper mantle. This includes velocity variations with depth as shown here in an early paper by Gutenberg, who, alongside with Press first described the low velocity zone. The low velocity zone was speculated later to be due to melt, and more recently, due to water.
Gutenberg, 1959; Press, 1959

4. Relative Shear Wave Velocity Variation at 200 km Depth
Possible Causes of Velocity Variations
Relative Shear Wave Velocity Variation at 200 km Depth
Temperature
Grain Size
Fluids/Melt
Dislocations
Composition
Besides the velocity variations as a function of depth in the upper mantle, there are of course also large lateral variations as shown in this image of Australia and surrounding oceans at 200 km depth. The magnitude of the velocity variations in this image of up to +/- 8% is typical of regional and as well as global models.
I have listed here the main causes of velocity variations which you have already seen discussed. As you saw from the experimental data that Ian presented, temperature is the primary variable to explain the first order structure in the upper mantle both laterally and with depth. If velocity variations due to temperature are not properly accounted for, misinterpretation of other variables are possible. This is why we have concentrated a lot of effort so far to properly measure the temperature variations of shear modulus and attenuation. Accordingly I will mostly talk about applications of our measurements of temperature and grain size.
Fishwick et al., 2004

5. Model rocks for measurement of shear modulus (G)
and attenuation (1/Q)
Vs=(G/)1/2
attenuation: energy loss per cycle
Here are representative microstructures of two samples in this study. On the left is a transmission electron microscope image showing the most fine-grained sample with a very regular microstructure of nearly hexagonal grains. All samples have very low dislocation densities. On the right is a band contrast image derived from electron backscatter diffraction mapping of the samples. This sample has a mean grain size nearly one order of magnitude larger than the sample on the left. The reason for showing these images is the grain size sensitivity of the shear modulus and attenuation that we measured.

6. Temperature dependence of shear modulus: transition from elastic to viscoelastic behaviour
Period: 8s
Another point I would like to emphasize is the transition from elastic to viscoelastic behavior at a temperature around 900ºC.

7. Modulus Reduction/Attenuation Mechanism
Grain boundary sliding causes shear modulus reduction and energy loss (attenuation).
This process is temperature and timescale dependent.
The underlying mechanism for modulus reduction and energy loss is grain boundary sliding. In the case of melt-free aggregates we have identified diffusionally accommodated grain boundary slinding as the most likely candidate. For melt-bearing aggreagetes elastically accommodated grain boundary sliding is superimposed over diffusionally accomodated grain boundary sliding.
grain boundary sliding can be:
- diffusionally accommodated: continuous process, no peak
- elastically accommodated: unique equilibrium state, attenuation peak

8. Because grain boundaries are strongly implicated in the deformation processes we have examined them closely. Here are TEM images of grain boundaries. GB are ~1 nm wide regions that do not have olivine structure. The observable grain boundary structure does not change, whether the samples contain melt or not.

9. Application to the Upper Mantle: Extrapolation in Grain Size
This slides illustrates that we don’t have to extrapolate our experiments very far to apply them to mantle conditions. Particularly, in contrast to large strain experiments we don’t have to extrapolate in time-scale as our measurements are done at seismic frequencies.

10. thickness of thermal boundary layer is a function of time
Oceans:
thickness of thermal boundary layer is a function of time
In order to calculate shear velocities and attenuation in the mantle we have to calculate geotherms first. This is relatively straight forward for oceans where at least up to ages of 80 to 100 Myrs the geotherms can be calculated for a conductively cooling half-space as a function of age. Shown on the right is the geotherm for 100 Myr old oceanic crust. Indicated by the dashed line is the temperature and corresponding depth of the deepest observed earthquakes. While the geotherm approaches the adiabat asymptotically the depth of the thermal boundary layer can be well defined in a small temperature range.

11. Oceanic Upper Mantle: Calculated and Observed Velocity Structure
Shown here is the geotherm on the right and associated shear wave velocity structure on the left. The black line indicates the velocity model of Gaherty et al., including the depth range of the observed velocity anisotropy. It is very clear that the velocity minimum and low velocity zone, that is Gutenberg’s asthenosphere, is part of the thermal boundary layer. As envisioned by Gutenberg, the velocity minimum is determined by the trade-off between temperature gradient and pressure effect on the (an-)elastic moduli. For a significant increase in shear velocity below the low velocity zone an activation volume > 5E-6 m3/mol is required.
Gaherty et al., 1996

13. Confirmation of the velocity calculations by being able to match the age dependence of the deepening and lessening of the LVZ. So, to explain Gutenberg’s low velocity zone no melt or water is necessary!

14. Dots: seismological model (Fishwick et al., 2004)
Solid lines: Vs calculated from geotherms
Again good match to the seismological model. We can explain the large velocity variations with reasonable temperature differences between cratons and oceans. Continental cratons have sub-adiabatic Ts to the transition zone.
The main point is that we can explain the full range of velocity variations observed in the upper mantle, both vertically (I.e. the low velocity zone) and laterally (the difference between continental cratons and oceanic lithosphere).
Maximum temperature difference ~ 600º
at km depth

15. Comparison of geotherms derived from cratonic xenoliths and seismological models:
Xenolith-based geotherms record temperature associated with emplacement event?
Present day geotherms are indicated by seismological models.
Xenolith geotherms intersect the adiabat around 200km depth. If we put this into context of Australian geotherms and calculated velocities it means that a pronounced velocity minimum is unavoidable as shown by the magenta curve. The near constant velocities observed beneath cratons require a much thicker thermal boundary layer in order to avoid a low velocity zone. One solution to this problem could be that xenolith geotherms reflect the (perturbed?) thermal state at the time of eruption, whereas seismological models show the present-day thermal state.
Rudnick et al., 1998

16. A closer look at variations of Vs and Q
with temperature, grain size and period
(depth fixed at 50 km)
Both velocity and Q decrease with increasing temperature, but decreases are temperature, frequency and grain size dependent. I want to emphasize again that we calculate Vs and Q fully self consistently from the experimental data.

17. Temperature derivatives at a fixed depth
Velocity derivaties are a function of temperature and grain size as well as frequency. The range increases with increasing temperature from 1 m/s /deg. To over 2 m/s / deg.
Temperature derivative of Q exactly the opposite: large changes at low T but assymptotically little change at high T!
Velocity derivatives at a given grain size and frequency are similar for P and S.

18. Temperature derivatives as a function of pressure
Derivatives are also depth dependent due to activation volume and pressure dependence of elastic moduli. Calculated at a fixed temperature of 1350ºC. Calculation for surface waves takes increasing wavelength into account.

19. Subduction Zones: Tonga - Fiji
Conder and Wiens, 2006

20. T calculated from corner flow model with back-arc spreading center (Conder et al., 2002)

21. Calculated absolute velocities include a grain size increase at ~160 km depth. Below ~200 km good correspondence of calculated and observed velocity. Above, both wedge and slab are anomalous.
Conder and Wiens, 2006

22. For Vs: reduction in velocity from 4
For Vs: reduction in velocity from 4.2 to below 4 at this depth requires about 100ºC at 10s. If average S wave period is significantly longer than P wave periods one would expect a larger S anomaly for a given T difference.

23. Comparison of calculated and observed velocity ratios
Comparison of calculated and observed velocity ratios. Relatively high ratio in the tomographic model where the anommalies in the velocity and Q models are. But derived quantities like this are much more sensitive to slight differences in the data that went into the models. For example, the frequencies of P and S waves are not the same (1 s for P and 10 s for S). The resolution is like not the same, particularly considering the low Q in this case.

24. Here is a comparison of calculated and observed Q
Here is a comparison of calculated and observed Q. Calculated Qs here are just below 70, whereas the observed Q goes to very low values, to below 20. Generally the observed distribution of low Q, the band between 50 and 150 km depth is again similar to the velocity anomalies.
Conder and Wiens, 2006

25. Would need 400º + DT (anharmonic), earthquakes! -> Free fluids?
Anomaly in slab:
Would need 400º + DT (anharmonic), earthquakes!
-> Free fluids?
Anomaly in wedge:
Both velocities and Q are very low. Large lateral extent, but not a higher potential temperature change due to restricted depth range.
Relatively good agreement between P, S and Q models on the location of the most anomalous regions. Both P and S show a slow anomaly in the slab. The temperatures there are so low that the rocks are in the anharmonic regime. To produce this anomaly with temperature would require K. Since there are earthquakes in this region it seems unlikely that the slab is this warm. Speculative: could this be due to free fluid?
The wedge is similarly highly anomalous. The anomaly is at greater depth and has a greater lateral extent than expected for an anomaly solely due to melt. It is not confined to regions directly below the VF or the spreading center.
If it is temperature the temperature is confined to depth above ~150 km, I.e. it is not a variation in potential temperature in the conventional sense, but would require shallow, lateral flow of hot material.

26. These are very rough back-of-the envelope estimates of the temperatures required to reduce the velocities from the calculated 4.2 km/s to the observed 4 km/s. This indicates at least 100º, at higher frequencies the temperature difference would be larger.To reduce the calculated Q from 70 to the observed Q of 20 would require a temperature difference in excess of 250º. Although this would be somewhat smaller for higher frequencies, this small Q as well as the low velocities strongly suggest that temperature alone is not sufficient to explain them, and that melt and possibly water also contribute, at least to some of the anomaly.

27. Conclusions:
Application of laboratory data to the upper mantle can explain the first order velocity variations seen in regional and global velocity models.
In tectonic settings such as subduction zones, mid-ocean ridges and hot-spots lower velocities and Q are observed than can be explained by temperature alone, and strongly suggest the presence of melt/water.

28. Effect of depletion on shear velocity
By comparison:
T = 400º -> Vs ~ 7%,
d = 10x -> Vs ~ 3%
Last a quick look at the effect of composition on velocities. This is from a paper that just came out by Schutt and lesher, but essentially confirms earlier calculations of Jordan.
Schutt and Lesher, JGR 2006

29. Mode and mineral effects add.
For density:
Mode and mineral effects add.
For moduli and velocities:
Mode and mineral effects cancel each other.
(As olivine becomes more magnesian, garnet proportion decreases!)
Schutt and Lesher 06

31. Possible Causes of Velocity Variations
Outlook:
Temperature
Grain Size
Melt
Fluid (Water)
Dislocations
Composition
Fishwick et al., 2004

32. Temperature, Velocity and Viscosity
The trade-off between increasing temperature and pressure that determines the low velocity zone also applies to viscosities. In fact the Burger’s model to which we fit our shear modulus and attenuation data contains a viscous term, similar to commonly used diffusion creep flow-laws. (INSERT SLIDE SHOWING BURGER’S MODEL EQUATION AND H&K FLOW LAWS) Viscosities calculated with the flow-law and parameters from Hirth and Kohlstedt (2003), assuming a wet rheology, are shown on the right.Viscosities are calculated for temperatures above 900ºC. The purple curve shows the stress-independent viscosity calculated for diffusion creep. The green curves are calculated for 3 different stress levels in dislocation creep. Only dislocation creep produces crystalline alignment and hence anisotropy. This requires stresses above about 0.3MPa. Since no anisotropy is observed in the convecting part of the upper mantle diffusion creep presumably dominates at this depth where stress levels are plausibly lower.

33. Comparison Oceans - Continents
While geotherms joining the adiabat above 250 km result in a low velocity and low viscosity zone, this is no longer case if this occurs much deeper. Therefore cratons do not have an asthenosphere as defined by Gutenberg.

34. Continental velocities and geotherms
Australia: Fishwick et al., 2004
Kapvaal Craton: Freybourger et al., 2001
Baltic Shield: Bruneton et al., 2004
In contrast to oceans, calculated geotherms for continental lithosphere need to include heat production due to radioactive decay. Shown here is a tomographic shear wave model for Australia and surrounding oceans at 200 km depth. On the right are geotherms calculated for velocity depth profiles through this model, indicated by the dots. The solid lines are the velocities calculated for the geotherms. While oceanic upper mantle is characterized by a pronounced low velocity zone cratons have only a very mild or even completely absent velocity minimum. Again using Gutenberg’s concept of the Asthenosphere as a low velocity and low viscosity zone, this implies that no ashtenosphere is present beneath cratons.

35. Vs = (G/)1/2 Jackson et al., 2004
You have already seen the experimental data as a function of temperature, period and grain size. What I also would like to point out is that while for the velocity the spacing for increasing temperature increases, it does the opposite for attenuation.
Vs = (G/)1/2
Jackson et al., 2004

36. Just to recap some of what Ian presented, at the timescales of seismic waves and the range of upper mantle temperatures we encounter the full range of behavior from purely elastic at low temperatures to purely viscous at high temperatures and long periods. Therefore we need to also take the transitions into account.

37. San Carlos olivine derived
Sol-Gel olivine derived
The composition of the grain boundary does vary however with bulk composition. Here are TEM analyses of grain boundaries both of melt free and melt bearing olivine, either San Carlos derived or fully synthetic. Melt-free sol-gel olivine essentially contains no detectable Ca or Al. When melt is added both grain interiors and grain boundaries contain a certain amount of these elements. San Carlos olivine to which no melt is added contains Ca and Al, but at an intermediate level between the melt-free and the melt-added sol-gel olivine. When melt is added to the San Carlos olivine the composition becomes similar to the sol-gel olivine.

38. Grain Size Faul and Jackson, 2005
The increase in shear velocity for a fixed grain size of 1 mm and activation volume of 1.2 E-5 m3/mol is shown here. As you can see the velocity in the model of Gaherty et al. increases significantly more rapidly with depth. To match this increase the grain size has to increase from 1 mm in the upper 165 km (the depth extend of the observed anisotropy) to 5 cm at 350 km depth. The increase in grain size is linked to the transition from dislocation creep in the thermal boundary layer to diffusion creep below. This change in dominant deformation mechanism is required to explain the presence of seismic anisotropy in the thermal boundary layer and the absence below.
Faul and Jackson, 2005

39. Calculated absolute velocities include a grain size increase at ~160 km depth. Below ~200 km good correspondence of calculated and observed velocity. Above, both wedge and slab are anomalous.
Conder and Wiens, 2006