N. Shapiro, M. Ritzwoller, University of Colorado at Boulder

Thermal structure of old continental lithosphere from the inversion of surface-wave dispersion

with thermodynamic a-priori constraints

Thermal structure of old continental lithosphere from the inversion of surface-wave dispersion

with thermodynamic a-priori constraints

N. Shapiro, M. Ritzwoller, University of Colorado at Boulder

J.-C. Mareschal, Université du Québec à Montréal

C. Jaupart, Institut de Physique du Globe de Paris

ObjectivesObjectives

1. to reconcile thermal and seismic models of the old continental lithosphere

2. to develop methods for joint inversion of the seismic and the thermal data

Thermal models of the old continental lithosphereThermal models of the old continental lithospherefrom Jaupart and Mareschal (1999) from Poupinet et al. (2003)

1. Constrained by thermal data: heat flow, xenoliths

2. Derived from simple thermal equations

3. Lithosphere is defined as an outer conductive layer

4. Estimates of thermal lithospheric thickness are highly variable

Seismic models of the old continental lithosphereSeismic models of the old continental lithosphere

1. Based on ad-hoc choice of reference 1D models and parameterization

2. Complex vertical profiles that do not agree with simple thermal models

3. Seismic lithospheric thickness is not uniquely defined

Additional physical constraints are required to eliminate non-physical

vertical oscillations in seismic profiles and to improve estimates of seismic velocities at each particular depth

Inversion of seismic surface-wavesInversion of seismic surface-waves

global set of broadband fundamental-mode Rayleigh and Love wave dispersion measurements (more than 200,000 paths worldwide)

Group velocities 18-200 s.Measured at Boulder.

Phase velocities 40-150 s.Provided by Harvard and

Utrecht groups

1. Data 2. Two-step inversion procedure

1. Surface-wave tomography: construction of 2D dispersion maps

2. Inversion of dispersion curves for the shear-velocity model

Dispersion mapsDispersion maps

100 s Rayleigh wave group velocity

Local dispersion curvesLocal dispersion curves

All dispersion maps: Rayleigh and Love wave group and phase velocities at all periods

Inversion of dispersion curvesInversion of dispersion curves

Monte-Carlo sampling of model space to find an ensemble of acceptable models

All dispersion maps: Rayleigh and Love wave group and phase velocities at all periods

Details of the inversion: seismic parameterizationDetails of the inversion: seismic parameterization

1. Ad-hoc combination of layers and B-splines

2. Seismic model is slightly over-parameterized

3. Non-physical vertical oscillations

Physically motivated parameterization is required

Details of the inversion: Monte-Carlo approachDetails of the inversion: Monte-Carlo approach

Linearized iterative inversionMonte-Carlo inversion: random

sampling of the model space

1. Finds only one best-fit model. Does not provide reliable uncertainty estimates

2. Linearization can be numerically sophisticated

Details of the inversion: Monte-Carlo approachDetails of the inversion: Monte-Carlo approach

Linearized iterative inversionMonte-Carlo inversion: random

sampling of the model space

1. Finds only one best-fit model. Do not provide reliable uncertainty estimations

2. Linearization can be numerically sophisticated

1. Finds an ensemble of acceptable models that can be used to estimate uncertainties

2. Does not require linearization. Easy transformation between seismic and temperature spaces

conversion between seismic velocity and temperatureconversion between seismic velocity and temperature

Method of Goes et al. (2000)

β =

μ

ρ

Elastic parameters for one mineral:

μ ( P , T , X ) = μ0

+ ( T − T0

)

∂ μ

∂ T

+ ( P − P0

)

∂ μ

∂ P

+ X

∂ μ

∂ X

K ( P , T , X ) = K0

+ ( T − T0

)

∂ K

∂ T

+ ( P − P0

)

∂ K

∂ P

+ X

∂ K

∂ X

ρ ( P , T , X ) = ρ0

( X ) 1 − α ( T − T0

) +

( P − P0

)

K

⎡

⎣

⎢

⎤

⎦

⎥

ρ0

( X ) = ρ0 X = 0

∂ ρ

∂ X

α ( T ) = α0

+ α1

T + α2

T

− 1

+ α3

T

− 2

ρ - density P - pressureμ - shea r modulus X – iron contentK – bulk modulus α - coefficient of thermal expansionT - temperature

Followi ng parameters ar e defined fro mlaboratory experiment:

ρ0 X = 0

, μ0

, K0

,

∂ ρ

∂ X

,

∂ μ

∂ X

,

∂ K

∂ X

,

∂ μ

∂ T

,

∂ K

∂ T

,

∂ μ

∂ P

,

∂ K

∂ P

, α0

, α1

, α2

, α3

Voig -t Reuss-Hill averaging for a combinati on o f minera :ls

ρ = λi

ρi∑

μ =

1

2

λi

μi∑ +

λi

μi

∑

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

− 1 ⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

K =

1

2

λi

Ki∑ +

λi

Ki

∑

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

− 1 ⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

λI i s the volumetr icproportion of minera l i non-linear relation

computed with the method of Geos et al. (2000) using laboratory-measured thermo-elastic properties of main mantle minerals and cratonic mantle composition

Monte-Carlo inversion of the seismic data based on the thermal description of model Monte-Carlo inversion of the seismic data based on the thermal description of model

Monte-Carlo inversion of the seismic data based on the thermal description of model Monte-Carlo inversion of the seismic data based on the thermal description of model

1. a-priori range of physically plausible thermal models

Monte-Carlo inversion of the seismic data based on the thermal description of model Monte-Carlo inversion of the seismic data based on the thermal description of model

1. a-priori range of physically plausible thermal models

2. constraints from thermal data (heat flow)

Monte-Carlo inversion of the seismic data based on the thermal description of model Monte-Carlo inversion of the seismic data based on the thermal description of model

1. a-priori range of physically plausible thermal models

2. constraints from thermal data (heat flow)

3. randomly generated thermal models

Monte-Carlo inversion of the seismic data based on the thermal description of model Monte-Carlo inversion of the seismic data based on the thermal description of model

1. a-priori range of physically plausible thermal models

2. constraints from thermal data (heat flow)

3. randomly generated thermal models

4. converting thermal models into seismic models

Monte-Carlo inversion of the seismic data based on the thermal description of model Monte-Carlo inversion of the seismic data based on the thermal description of model

1. a-priori range of physically plausible thermal models

2. constraints from thermal data (heat flow)

3. randomly generated thermal models

4. converting thermal models into seismic models

5. finding the ensemble of acceptable seismic models

Monte-Carlo inversion of the seismic data based on the thermal description of model Monte-Carlo inversion of the seismic data based on the thermal description of model

1. a-priori range of physically plausible thermal models

2. constraints from thermal data (heat flow)

3. randomly generated thermal models

4. converting thermal models into seismic models

5. finding the ensemble of acceptable seismic models

6. converting into ensemble of acceptable thermal models

Lithospheric structure of the Canadian shieldLithospheric structure of the Canadian shield

Thermal data: heat flow

• Computation of end-member crustal geotherms

• Extrapolation of temperature bounds over a large area

• Conversion into seismic velocity bounds

Inversion with the seismic parameterizationInversion with the seismic parameterizationseismically

acceptable models

Inversion with the seismic parameterizationInversion with the seismic parameterizationseismically

acceptable models

Inversion with the seismic parameterizationInversion with the seismic parameterizationseismically

acceptable models

Thermal parameterization of the old continental uppermost mantle

Thermal parameterization of the old continental uppermost mantle

3D temperature model of the uppermost mantle3D temperature model of the uppermost mantle

3D temperature model of the uppermost mantle3D temperature model of the uppermost mantle

Lithospheric thickness and mantle heat flowLithospheric thickness and mantle heat flow

Power-law relation between lithospheric thickness and mantle heat flow is

consistent with the model of Jaupart et al. (1998) who postulated that the steady

heat flux at the base of the lithosphere is supplied by small-scale convection.

ConclusionsConclusions

1. Seismic surface-waves and surface heat flow data can be reconciled over broad continental areas, i.e., both types of observations can be fit with a simple steady-state thermal model of the upper mantle.

2. Seismic inversions can be reformulated in terms of an underlying thermal model.

3. The estimated lithospheric structure is not well correlated with surface tectonic history.

4. The inferred relation between lithospheric thickness and mantle heat flow is consistent with geodynamical models of stabilization of the continental lithosphere (Jaupart et al., 1998).

3D seismic model3D seismic model