2008 Bi-Lateral Workshop, under the Sino-US Earthquake Studies Protocol

Boulder, Colorado, USA, November 11-14, 2008

Peter Molnar Department of Geological Sciences

Cooperative Institute for Research in Environmental Science (CIRES)University of Colorado at Boulder

At what depths in the lithosphere does strength lie, and how does that distribution manifest itself

geodynamically?

Geodynamic Questions Answerable using Eastern Asia as a Field Laboratory

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 strengthGradients in stress + Gradients in PE/Area = 0

Stress = “Viscosity” x Strain rateSo:

“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.

Wang, Flesch, Silver, Chang, and Chan [2008]

Mantle Strain Gauge:Seismic anisotropy, with

Shear-wave splitting

Zhang Pei-zhen et al. [2004]

Crustal Strain Rates: GPS

Seismic anisotropy: How much strain is needed?

Infinitesimal Strain or Finite strain

Holt [2000] Davis, England, & Houseman [1997]

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

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, but4. 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, but4. 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 = 0Stress = “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 Mantlean 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 strengthVertically 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 questionStress is continuous:

Therefore inextricably coupled.

Upper Crust and Uppermost Mantle:Coupled or uncoupled?

Stupid questionStress 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:

TibetClark and Royden [2000]

Rayleigh-Love wave differenceIn red areas, Love waves require the higher speeds.

Shapiro et al. [2004]

Reorientation of anisotropic crystals

[Shapiro et al., 2004]

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.

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 Rayleigh- and 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!”