1. Roland Burgmann and Georg Dresen
Rheology of the Lower Crust and Upper Mantle: Evidence from Rock Mechanics, Geodesy, and Field Observations
Roland Burgmann and Georg Dresen

2. Key Purposes
Concerned with describing material properties through constitutive equations that relate stress and strain.
Rheology is fundamental to understanding the evolution and dynamics of Earth and other planets
Ex: localized, episodic deformation (earthquake cycle) in brittle upper crust is coupled to viscous flow in lower crust and upper mantle. Thus, rheology of viscously deforming rocks at depths are fundamental when trying to understand time-dependent deformation and hazard along fault zones.
Strength models
Earth's compositional layering and increasing pressure and temperature can result in strong rheological layering.
Constitutive laws
Time dependent equations relating stress to strain or strain rates.
Dominant Deformation Mechanisms
Illustrates primary mechanism and appropriate flow law as a function of stress, temperature, content/composition, grain size.
Geodetic/Field observations
Postseismic deformation, nontectonic loading events, shear zones.

3. Jelly Sandwich: Lithospheric Strength
Earth's compositional layering and increasing pressure and temperature can result in strong rheological layering. Earth's upper crust thought to be in a state of frictional equilibrium with active faults limiting strength, consistent with Mohr-Coulomb theory and lab derived friction coefficients.
Pressure-dependent increase of frictional strength of rocks with depth is bound by thermally activated creep processes reducing viscous strength with increasing pressure and depth.
Across the brittle-ductile transition, deformation mode and dominant deformation mechanisms in continental rocks gradually change over a broad range of temperatures (300 to 500 C.
Mafic rocks have higher viscosities at given temperatures. Resulting profiles are weak middle and lower crust sandwiched between strong upper crust and strong mantle lithosphere (jelly sandwich).
Figure 1
Differential stresses with depth.
Frictional strength increases with pressure and depth in upper crust
Frictional coefficient (Byerlee's law:shear stress required to slide rock surfaces over one another decrease with normal stress, becomes nearly independent of rock type) and Hydrostatic fluid pressure are assumed in a strike-slip tectonic regime
Low friction due to high pore fluid pressure assumed in bananas
Jelly sandwich has strong mantle of dry olivine. Pudding has weak mantle (resulting from a high geotherm, adding water would further reduce strength). Dry and brittle crust defines strength of lithosphere. Banana split considers weakness of major
Long-term stress lies in lithospheric mantle
In contrast, some have suggested strength of continental lithosphere resides entirely in the crust and that upper mantle is significantly weaker, owning to high temperature and weakening by water (pudding).
Proponents infer correlation between thickness of seismogenic layer and elastic thickness of the continental lithosphere, but Te estimates vary and do not preclude a strong mantle layer.
Bananas
Argues strength of lithosphere is greatly reduced along plate boundaries, owed to weakening processes involving thermal, fluid, and strain-rate effects.
Relative weakness of major fault zones may exist at all depths.
It continues to be a question of much debate as to whether the overall style of continental deformation is governed by the properties and activity of
discrete, weakened shear zones or by the bulk rheological properties of the viscously deforming lower lithosphere.
Degree of localization at depth below fault zones is also uncertain about the first-order nature of earthquake-cycle deformation. End-member models are distributed viscous flow or frictional aseismic faulting.

4. Represents viscoelastic rheologies by an assemblage of springs + dashpots.
Represents linear elastic (Hooke Solid), linear viscous (Newtonian fluid) elements.
Elements + equations they represent form idealized constitutive relationships that are basis of most geodynamic deformation models.
Burger body exhibits early Kelvin solid, long term Maxwell fluid response by:
High-level constitutive relations empirically derived from lab.
Plastic flow of rocks at high T accommodated by diffusion of ions and vacancies in crystal lattice, and along grain boundaries, boundary sliding/creep, dislocation creep
Each result in different stress-strain relationships
May also involve solution-precipitation with ions transported through a liquid melt or water.
Steady state deformation at constant stress when rate of recovery and recrystallization compensate deformation from crystal defects.

5. Deformation mechanisms operating in a rock that determine constitutive behavior depend on:
Phase content
Chemical composition
Thermodynamic variables
A = material constant
n = power law stress exponent
Q = activation energy
p = pressure
V = activation volume
T = absolute temperature
R = molar gas constant
d = grain size
m = grain size exponent
fH20 = water fugacity
r = fugacity exponent

6. Silicate rocks deformed under hydrous conditions are significantly weaker than at anhydrous conditions. (as high as four orders of magnitude)
Observed commonly when only trace amounts of H2O are present (~ wt%) are present in nominally anhydrous silicates as structurally bound point defects or dispersed fluid inclusions in grains/boundaries.
Anhydrous conditions are likely exception in tectonically active regions. Partial melt may also be involved.
Melt reduces confining pressure, acts as fast diffusion pathway.
Few experimental polyphase rock studies. Most focus on mechanical interaction between two phases with different end-member viscosities.
Strength of synthetic polyphase rocks is bound by strength of respective end members.

7. Postseismic Deformation
Recognition of elastic rebound and earthquake cycle.
Postseismic accelerated deformation plays an important role.
models of 90 year post-1906 earthquake deformation data are best explained by models incorporating weak vertical shear zones in crust beneath major faults, as well as relaxation of deep lower crust or mantel layer with certain viscosities.
Challenge in using postseismic deformation: multitude of relaxation processes following earthquakes. Arguements
Can parameterize viscous shear and localized aseismic slip at depth to produce post-seismic surface deformation pattern
Some interpretations from large earthquakes include:
Viscoelastic relaxation in lower crust only
primary deep aseismic afterslip
combination of poroelastic rebound and crustal afterslip
poroelastic rebound and viscoelastic relaxation in lower crust
Freed and Burgmann found distribution of vertical and horizontal surface motinos requres that the initial relaxation of the leastic earthquake stress primarily occurred in upper mantle.
Freed 2007 found deformation transients in continuous GPS time series >200km from Mojave earthquakes as strong evidence for dominant contribution of broadly distributed mantle relaxation below 40km depth.
Freed 2006 suggests rapidly decaying, far-field GPS time series reflecting a stress-dependent mantle viscoelastic rheology (Figure 4)
Other postseismic studies show deep rheology differs depending on local lithospheric structures and tectonics.

8. Nontectonic Loading Events
Earthquakes represent well-constrained stress changes, but occur along active fault zones and probe what might be anomalous lithospheric structure and rheology at depth (ice cream in banana split).
Nontectonic loading events by lakes and glaciers offer advantage of examining rheology away from faults. Afterslip vs distributed viscous relaxation should be absent.
Historic changes in lake levels result in significant elastic stress fields that produce viscous flow at depth.
Surface deformation from ice-age glacial unloading cycles are at far end of spectrum in terms of magnitude and spatial extent of loading source and duration and depth of viscous relaxation processes.
Active uplift in these regions has been known for some time and provided first direct evidence of viscous mantle deformation.

9. Characteristic feature of large-scale shear zones is that they constitute anastomosing networks of densly intertwined mylonite layers with varying width, length, displacement, separating lozenges of less deformed material.
Irrespective of scale, internal structure of high-strain zones indicates formation and growth of kinematically linked shear zone networks.
Typically display slip transfer between cooperative shears and partitioning of strain between network structures from regional to grain scale.
Pronounced grain size reduction in mylonite layers promotes strain localization and may substantially reduce viscosity of shear zones in lower crust compared to host rock, up to a factor of 100.
High-strain shear zones also frequently observed in exposed mantle peridotite massifs and subcontinental mantle from some mantle-derived xenoliths, as well as dredged MOR peridotites
Suggests shear zones relatively common in uppermost mantle where temperatures are lower and strength commonly assumed to be highest.
Pressure and temperature estimates from shear zones suggest these form in situ or during crustal emplacement of peridotite massifs at depth
Shear strain found accommodated at all scales in anastomosing networks of kinematically linked substructures (mylonites/ultramylonites bands). Grain size reduction.
Suggested grain size reduction promotes transition from dislocation creep to grain-size-sensitive flow, resulting in large degree of softening in upper mantle, enhanced by fluid/melt presence.
Xenolith brought up from 40 km depth beneath San Andreas exhibit olivine lattice-preferred orientations, quantitatively compared to seismic anisotropy observations in the region. Supports model of broadly distributed (~130km) mantle shear zone below San Andreas.
Inference of broadly distributed mantle shear fabrics deep below active plate boundary zones from seismic anisotropic studies suggests that at increasing depths and temperatures, mantle deformation ocurs by more coherent bulk flow. Does not preclude localized shear zones embedded in distributed shear fabric.
Grain-Size Data and Paleostress Estimates from Natural Shear Zones
Grain size is a critical parameter reflecting evolution of strength and deformation mechanisms in lithospheric shear zones.
reflects strain-dependent breakdown process in tip region of shear zones
Readily measured from exposed rock samples
Inverse relationship between grain size and flow stress.
Possibility at decreasing grain size, diffusion creep becomes more important deformation mechanism.

10. Paleostress estimates from mylonite shear zones transecting lower crust (a) and upper mantle(b)
Each box represents stress-temperature estimates for a particular shear zone.
Stress estimates mostly based on inverse relationship between recrystallized grain size and flow stress.
Graphs are lab data at hydrous conditions.

11. Summary
Robust constitutive equations exist for major constituents of lower crust and upper mantle that appear consistent with field and geophysical observations.
Viscosity estimates based on lab data for rocks deformed at hydrous conditions likely span full range of flow strengths of rocks with more complex mineralogical compositions.
Lithospheric strength and rheology differ as a function of makeup, tectonic evolution, and environment of a region. Rheology strongly varies with depth across continental lithosphere of varying age, temperature, composition.
Rheology varies with age, temperature, composition
Food models of rheology should be considered end member cases
Backarc and former backarc regions:
Upper mantle is viscously weaker than low crust due to high temperatures and possibly water
Mantle below old cratonic shields is order of magnitude stronger than that found in tectonically active regions
Viscosity can vary on orders of magnitude based on location
Strength of crust below seismogenic fault zones weakened through earthquake-cycle effects and other strain weakening processes
Strain weakening up to several orders of magnitude and localization are ubiquitous at all scales
Deformation mechanisms and rheology depend on:
Thermodynamic conditions
Material parameters
Mechanical state
Can vary over short distances (inside vs outside shear zone) and timescales (earthquake cycle)

12. Future Issues
Despite direct evidence for localized shear in lower crust and upper mantle, it's not conclusive if low-crust deformation below active faults is always highly localized, broadly distributed, or transitioning from one to the other with depth.
Transients in mechanical response due to abrupt or slow changes in loading, structural state, high strain, and others remain to be explored in detail.
Must further quantify flow parameters for partially molten and polyphase rocks
Changes in rheology and weakening caused by metamorphic reactions are neither well understood nor quantified
Geodetic explorations of deep rheology form postseismic deformation need to consider deformation early and late in earthquake cycle and couple physically realistic model parameterizations of distributed plastic flow and localized shear.
More postloading studies needed of all types to explore distribution of rheology across continents and plate boundary zones.
Field studies should aim to quantitatively evaluate distribution of strain in space and time as fault zones evolve.
Detailed documentation of structural parameters (grain size, variation with shear strain, phase content, temperature) is needed within and away from shear zones