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2008 Bi-Lateral Workshop, under the
Sino-US Earthquake Studies Protocol
Boulder, Colorado, USA, November 11-14, 2008
Geodynamic Questions Answerable using
Eastern Asia as a Field Laboratory
At what depths in the lithosphere
does strength lie, and how does
that distribution manifest itself
geodynamically?
Peter Molnar
Department of Geological Sciences
Cooperative Institute for Research in Environmental Science (CIRES)
University of Colorado at Boulder
Equation of equilibrium:
Governing equation for geodynamics
g = 0
Gradients in stress + (gravitational) body force = 0
Simple assumption: Thin Viscous Sheet
(Horizontal stresses) + (Potential Energy/area) = 0
(Potential Energy/area)  (crustal thickness)2
Gradients in Potential Energy/area are largest
adjacent to regions of high terrain:
Tibet and its surroundings.
Lithospheric strength
Gradients in stress + Gradients in PE/Area = 0
Stress = “Viscosity” x Strain rate
So:
“Viscosity” x Gradients of Strain rate
+
Strain rate x Gradients of “Viscosity”
+
Gradients in PE/Area
=0
Eastern Asia offers large gradients in PE/Area,
large strain rates, and large gradients in strain rate.
Mantle Strain Gauge:
Seismic anisotropy, with
Shear-wave splitting
Crustal Strain
Rates: GPS
Zhang Pei-zhen et al. [2004]
Wang, Flesch, Silver,
Chang, and Chan [2008]
Seismic anisotropy: How much strain is
needed?
Infinitesimal Strain or
Finite strain
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Holt [2000]
Davis, England, & Houseman [1997]
Blocks or Continuum in Geodynamics
(not earthquake hazards)
1. Blocks of crust? Of course!
2. Prediction: N~nk, Number of blocks is
fractally related to number of GPS points.
3. Blocks: no dynamic theory, but
4. Continuum: related by Stokes Equation.
Blocks or Continuum in GPS-dynamics
(not earthquake hazards)
1. Blocks of crust? Of course!
2. Prediction: N~nk, Number of blocks is
fractally related to number of GPS points.
3. Blocks: no dynamic theory, but
4. Continuum: related by Stokes Equation.
Blocks are to a Continuum description
what
Ptolemy’s epicycles are to Copernicus’s
sun-centered elliptical orbits.
Eastern Asia as field laboratory to study
lithospheric strength. What do we need?
1. Improved strain-rate field: we need a densely
sampled, accurate GPS velocity field.
GPS gives us velocities;
Strain = spatial derivatives of velocity,
We need gradients in strain!
Gradients in stress + Gradients in PE/Area = 0
Stress = “Viscosity” x Strain rate
So:
“Viscosity” x Gradients of Strain rate + Strain rate x Gradients of “Viscosity”
+ Gradients in PE/Area = 0
2. Improved understanding of seismic anisotropy:
how much strain is needed, or how well does
anisotropy serve as a strain-gauge?
Brace-Goetze
Strength
Profile
Brittle faulting in upper crust
(and uppermost mantle
where it is cold).
Ductile deformation in the lower
continental crust and
through most of the mantle
lithosphere.
Strength in the Mantle
an admonition
Do not be deceived by inordinately
high stresses implied by dislocation
(“power-law”) creep at the low
temperatures appropriate for mantle
lithosphere.
Creep strength of olivine
High strength: Evans & Goetze [1979]; parameters: Raterron et al. [2004]
Dislocation creep: Hirth & Kohlstedt [1996, 2003] (data: Karato et al. [1986])
Average creep strength across mantle lithosphere
Note rapid decrease with increasing temperature at Moho.
For sensible Moho Temperatures (T > 500°C), lithosphere is
not too strong to prevent deformation of it.
Stress and strength
Vertically averaged stresses associated with
buoyancy of crust and uppermost mantle:
<100 MPa, closer to 50 MPa or less.
Vertically averaged creep strengths of olivine at
geological strain rates:
<100 MPa, closer to 10-50 Mpa,
but where hot, perhaps only 1 MPa.
Shear stresses on major faults (in upper 10-20 km)
~10-20 MPa
(10 x smaller if averaged over lithosphere ~100 km thick)
Brace-Goetze
Strength
Profile
Brittle faulting in upper crust (and
uppermost mantle where it is
cold).
Ductile deformation in the lower
continental crust and through
most of the mantle
lithosphere.
Upper Crust and Uppermost Mantle:
Coupled or uncoupled?
Upper Crust and Uppermost Mantle:
Coupled or uncoupled?
Stupid question
Stress is continuous:
Therefore inextricably coupled.
Upper Crust and Uppermost Mantle:
Coupled or uncoupled?
Stupid question
Stress is continuous:
Therefore inextricably coupled.
Yet, strain rates can vary enormously.
(As connoisseurs of tofu, or a peanut
butter and jelly sandwich, know well.)
The question is: How is strain distributed with
depth through the lithosphere?
Channel Flow
in the crust:
Flux ~ P h3/
Obviously, channel
flow is more likely,
more rapid, and
more important,
where crust is hot
and thick:
Clark and Royden [2000]
Tibet
Rayleigh-Love wave difference
In red areas, Love waves require the higher speeds.
Shapiro et al. [2004]
Reorientation of anisotropic crystals
If anisotropic crystals, like mica, were
preferentially oriented so that
more were horizontal than
vertical, SH (Love waves)
would propagate faster than
SV (Rayleigh waves).
Mica is very anisotropic: shear
waves propagate 20% faster
parallel to crystals than
perpendicular to them.
Horizontal extension and crustal
thinning (vertical compression)
could induce such a preferred
orientation.
[Shapiro et al., 2004]
Radial anisotropy, where SH is faster than SV
(red areas).
Normal faulting dominates where dots are red.
Thrust faulting dominates where dots are blue.
Shapiro et al. [2004]
Required strain in the lower crust seems to be more than
the known geology implies.
Radial anisotropy in the crust
supports the idea that lateral flow
within the crust redistributes
mass (channel flow).
[Shapiro et al., 2004]
Perhaps, no place on earth is better
for studying channel flow and radial
anisotropy than
Tibet and its surroundings
Eastern Asia as field laboratory: Channel
flow in the crust. What do we need?
1. Higher resolution (in space and over the
period range from 10 to 50 s) of radial
anisotropy, with more accurate Rayleighand Love-wave phase and group speeds.
2. Azimuthal anisotropy too, for orientations.
3. Higher resolution of both strain-rate (from
GPS) and total strain (from geology).
4. Perhaps, a good theory that predicts
something we have not thought of.
What does the US do well?
(Question put to French Post-doc, Jean-Daniel Champagnac in 2006)
First answer:
“Good question. I have to think about
that.”
What does the US do well?
(Question put to French Post-doc, Jean-Daniel Champagnac in 2006)
First answer:
“Good question. I have to think about
that.”
The next day:
“I can tell you what the US does well.
“The US is really good at sharing data, at
making data available.
“Americans are very generous with data!”