Role of Geodynamic Models in Interpreting Upper Mantle Images

Magali BillenUniversity of California,

DavisMARGINS Workshop, May 2006

Coupled Imaging & Dynamics Studies

• Wiens & Conder :– Synthetic Velocity & Attenuation

• Lassak, Fouch et al., EPSL 2006:– Corner flow models & regions of A vs. B type fabric

– Predicted shear wave splitting magnitudes.

Why do we need Geodynamic Models?

Parameters Seismology E&M MethodsGeodynamic

Models

Primary Travel times Electrical and magnetic field

TemperatureRheology

Secondary Vp, Vs, Q &Anisotropy

ConductivityResistivity

Density, flow law, elasticity, thermal expansion, thermal conductivity.

Tertiary Density, elastic moduli, LPO, slip systems

Temperature, melt fraction, water content

Composition, stress, melt, water content,

Already need to know/assume a lot to make geodynamic model…

Primary Geodynamics Parameters

Density Temperature

Composition

Phase Changes

Melt

Thermal Expansion

Thermal Conductivity

Pressure

Advected during convection: requires tracers.

Depth dependent.

Geodynamicist’s Goal:Translate your observations andexperiments into density and rheology.

Rheology

Rheology: Where Things Complicated

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10 mm ignorefixedn = 1 & 3.5

• Viscosity depends on pressure, temperature, stress (strain-rate), grain size, water, melt, & mineralogy …

• Ideally: water, melt content and grain-size should vary spatially, with composition, and evolve with time in a physically/chemically consistent way• Most models: fixed everywhere or fixed in regions.

Primary Geodynamics Parameters

Density RheologyTemperature

Composition

Phase Changes

Melt

Thermal Expansion

Thermal Conductivity

Pressure

Melt

CompositionPressure

Water

Phase Changes

Grain-Size

Stress/Strain-rate

Advected during convection: requires tracers.

Depth dependent.

Geodynamicist’s Goal:Translate your observations andexperiments into density and rheology.

Geodynamic Models:A Tool for Hypothesis Testing

• Why do we need Geodynamic Models?– Physically consistent way of synthesizing/testing a range of observations.

• Only as good as what you put in…– Initial conditions (geometry, temperature, composition)

– Boundary conditions (geometry, isolating region of interest)

– Rheology (crust, lithosphere, mantle)– Compositional variations (bulk, water content, melt)

• … and the questions you ask.– What are the underlying physical processes?

• Generic models (2D & 3D).• When are steady-state models appropriate?

– What is the structure/history in a specific region?• Region specific models.• Input constraints v. Observational constraints.

Types of Geodynamic Models

• Equations of Motions– Conservation of mass, Momentum & energy– Fully Dynamic

• Time-dependent.• Each time step, solve for: temperature, pressure, velocity (stress, strain-rate…), & viscosity.

• Boundary conditions important.– Mechanical model

• Dynamic, but no temperature evolution (no energy equation).

– Instantaneous Dynamic• No time dependence: instantaneous balance of forces.

• Solve for: pressure & velocity– Coupled Kinematic/Dynamic

• Some regions evolve in time (e.g. mantle wedge) - dynamic

• Other regions have prescribed flow (e.g. slab) - only temperature changes in time.

Rules of Road

1.BEWARE: There are always more knobs to turn than there are observational constraints.

2.Additional layers of complexity ≠ additional understanding.

3.Clever use of observations & well-conceived simulations are required.

Road Map• Examples & lessons learned from coupled imaging and geodynamic studies.

– Regional Models:• 1) Instantaneous Models: Tonga-Kermeadec Subduction Zone

• 2) Mechanical Model of the Lithosphere: S. Calif

– Process-Oriented Models:• 3) Kinematic Slab & Mantle Wedge Convection (Process)

• Dynamic Models of Subduction: – 4) Water in the Mantle Wedge– 5) Stress-Dependent Viscosity & Early Subduction

– 6) Rheology and Slab Dynamics

1. Instantaneous Dynamic Models

• Tonga-Kermadec SZ– Mismatch of back-arc region topography.

– Hypothesis: a low viscosity mantle wedge will basin topography.

– Observations: • Slow seismic velocity• High attenuation.• Laboratory constraints on water & viscosity

0 700 1400

18 20 22 24

0

-5

18 20 22 24

Topography

Log10(Viscosity)

1. Instantaneous Dynamic Models

• Works, but how low is mantle wedge viscosity & where is it low viscosity (geometry)?

– Geodynamic models are inconclusive• Only constrain minimum decrease in viscosity.• Only constrain shallow extent of low viscosity region.

1. Instantaneous Dynamic Models

• Constraining Mantle Wedge Viscosity– Tomography:

• regions of slow seismic velocity (too low for temperature alone).

• Low-Q regions indicate melt or water.

– Attenuation-Viscosity Relationship (Karato, 2001)• Assuming water affects attenuation and viscosity through a similar mechanism

/o = (Q/Qo)1/ = 0.23

• Predicts 25 - 100 x lower viscosity.

18 20 22 24

Log10(Viscosity)

D. Wiens

2. Mechanical Model of Lithosphere Downwelling

• S. California: Tomographic image and Geodynamic Model

– Observations: seismic tomography & surface deformation.

– 2D dynamic model consistent with observations.

Kohler, JGR 2002

2. Mechanical Model of Lithosphere Downwelling

• More data over larger region leads to different interpretation?

D. ForsythNielsen & Hopper, G3, 2004

Edge of Basin & Range extensioncould lead to small-scale convection(lithospheric instabilities).

3. Mantle wedge convection with kinematic slab

• Composition structure with variable rheology & buoyancy– Parameterized fluid and melt effects– Shear heating.– Develops “cold plumes”– What would this look like in seismic tomography images?

3. Water in Dynamic Models of Subduction

• Adding water to the wedge (fixed amount)– Triggers instability & convection– Creates thin overriding plate beneath “arc” region• Applicable to initial stages of subduction?

• What about melting?

Arcay et al, G3, 2006

5. Rheology in Time-Dependent Dynamic Models

• Observations:– Flow law for olivine predicts that dislocation creep accommodates deformation at high strain-rates in the upper mantle.

– LPO also requires dislocation creep.

• Effect on slab dynamics?

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5. Rheology in Time-Dependent Dynamic Models

• Initial stages of subduction

– Newtonian (Diffusion Creep) Model• Cooling of wedge corner• Viscous coupling and/or high suction forces: flat slabs

– Composite Diffusion & Dislocation Creep Model• High strain-rates in wedge corner• Counters cooling effect• Facilitates subduction initiation.

6. Time-dependent Dynamic Models

• Large-scale viscosity structure– Strong Temperature Dependence– Layered Structure– Composite Rheology (Diffusion + Dislocation Creep)

6. Time-Dependent Subduction Models

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6. Time-Dependent Subduction Models

Karason & van der Hilst, 2001

1) Comparison: need to make “synthetic” tomography from model.

2) Careful of interpretation of flow paths…

6. Time-Dependent Subduction Models

• Snap-shot of slab shape vs. tracer particle paths.

• Current slab shape is not necessarily indicative of flow path.

Conclusions• Geodynamical modeling is a well-suited tool for hypothesis testing, but…– there are limitations.– most models/programs focus on subset of behavior– issues of non-uniqueness.

• Need good input constraints– Geology, rock mechanics (lab, theory), mineralogy– Relationships between seismic observations and primary dynamics parameters.

• Need multiple ways of testing model uniqueness– Direct comparison to surface observations (be clever!)

– Comparing observational images to synthetic images from models.

– Tracing chemical compositions.

• Retain bottom-up approach… build up to complexity.

What is on the Horizon?

• Near future:– Compositional/geochemical tracing.– Parameterized effects of fluid & melts.

• A little later:– Coupled fluid & solid flow models

Katz & Speigelman, 2005

Questions for Discussion

• Is it possible to get error bounds on observations?– Show final models at end-members of acceptable range.

• How difficult is it to create synthetic tomography images or waveforms?– Not just maps of corresponding theoretical velocity/attenuation, trace real rays through model structure.

• Can we distinguish melt from water or temperature?– Probably not going to come from geodynamic models.

• Why is there such a big difference in apparent slab width in the upper vs. lower mantle?