Toward the next generation of earthquake source models by accounting for model prediction error
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Toward the next generation of earthquake source models by accounting for model prediction error. Zacharie Duputel Seismo Lab, GPS division, Caltech. Acknowledgements: Piyush Agram, Mark Simons, Sarah Minson, James Beck,

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Toward the next generation of earthquake source models by accounting for model prediction error

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Toward the next generation of earthquake source models by accounting for model prediction error

  • Zacharie Duputel

  • Seismo Lab, GPS division, Caltech

Acknowledgements: Piyush Agram, Mark Simons, Sarah Minson, James Beck,

Pablo Ampuero, Romain Jolivet, Bryan Riel, Michael Aivasis, Hailiang Zhang.


Project : Toward the next generation of source models including realistic statistics of uncertainties

SIV initiative

  • Modeling ingredients

    • Data:

      • Field observations

      • Seismology

      • Geodesy

      • ...

    • Theory:

      • Source geometry

      • Earth model

      • ...

  • Sources of uncertainty

    • Observational uncertainty:

      • Instrumental noise

      • Ambient seismic noise

    • Prediction uncertainty:

      • Fault geometry

      • Earth model

  • A posteriori distribution

Izmit earthquake (1999)

Slip, m

Depth, km

Slip, m

Depth, km

Single model

Slip, m

Depth, km

Ensemble of

models

2


A reliable stochastic model for the prediction uncertainty

The forward problem

  • posterior distribution:

Exact theory

Stochastic (non-deterministic) theory

p(d|m) = δ(d - g( ,m))

p(d|m) = N(d | g( ,m), Cp)

Calculation of Cp based on the physics of the problem: A perturbation approach

Covariance matrix describing uncertainty

in the Earth model parameters

Partial derivatives w.r.t. the elastic parameters (sensitivity kernel)

3


Prediction uncertainty due to the earth model

1000 stochastic realizations

Covariance

Cp


Toy model 1: Infinite strike-slip fault

μ1

- Data generated for a layered half-space (dobs)

- 5mm uncorrelated observational noise (→Cd)

- GFs for an homogeneous half-space (→Cp)

- CATMIP bayesian sampler (Minson et al., GJI 2013):

μ2

Synthetic Data + Noise

shallow fault + Layered half-space

Inversion:

Homogeneous half-space

Slip, m

Slip, m

?

μ1

0.9H

0.9H

H

H

μ2

Depth / H

Depth / H

μ2

μ2/μ1 =1.4

2H

2H


Toy model 1: Infinite strike-slip fault

Posterior Mean Model

Input (target) model


Why a smaller misfit does not necessarily indicate a better solution

No Cp (overfitting)

Cp Included (larger residuals)

Depth / H

Depth / H

Slip, m

Slip, m

Displacement, m

Displacement, m

Distance from fault / H

Distance from fault / H


Toy Model 2: Static Finite-fault modeling

Input (target) model

  • Finite strike-slip fault

  • Top of the fault at 0 km

  • South-dipping = 80°

  • Data for a layered half-space

Slip, m

Dist. along Dip, km

Dist. along Strike, km

Earth model

Data

Horizontal Disp., m

Vertical Disp., m

North, km

Depth, km

Shear modulus, GPa

East, km

8


Toy Model 2: Static Finite-fault modeling

Input (target) model

  • Finite strike-slip fault

  • 65 patches, 2 slip components

  • 5mm uncorrelated noise(→Cd)

  • GFs for an homogeneous half- space (→Cp)

Slip, m

Dist. along Dip, km

Dist. along Strike, km

Earth model

Data

Horizontal Disp., m

Vertical Disp., m

North, km

Depth, km

Model for

Data

Model for

GFs

Shear modulus, GPa

East, km

9


Toy Model 2: Static Finite-fault modeling

Input (target) model - 65 patches average

  • Finite strike-slip fault

  • 65 patches, 2 slip components

  • 5mm uncorrelated noise(→Cd)

  • GFs for an homogeneous half- space (→Cp)

Slip, m

Dist. along Dip, km

Dist. along Strike, km

Earth model

Posterior mean model, No Cp

Slip, m

Dist. along Dip, km

Dist. along Strike, km

Depth, km

Posterior mean model, including Cp

Uncertainty on the

shear modulus

Slip, m

Dist. along Dip, km

Dist. along Strike, km

Shear modulus, GPa

10


Conclusion and Perspectives

  • Improving source modeling by accounting for realistic uncertainties

    • 2 sources of uncertainty

      • Observational error

      • Modeling uncertainty

    • Importance of incorporating realistic covariance components

      • More realistic uncertainty estimations

      • Improvement of the solution itself

    • Accounting for lateral variations

    • Improving kinematic source models


Application to actual data: Mw 7.7 Balochistan earthquake

Jolivet et al., submitted to BSSA

AGU Late breaking session on Tuesday


Toy Model 2: Static Finite-fault modeling

Posterior mean model, including Cp

  • Finite strike-slip fault

  • 65 patches, 2 slip components

  • 5mm uncorrelated noise(→Cd)

  • GFs for an homogeneous half- space (→Cp)

Slip, m

Dist. along Dip, km

Dist. along Strike, km

Earth model

Covariance with respect to xr

CpEast(xr), m2

x 104

Depth, km

North, km

Uncertainty on the

shear modulus

xr

Shear modulus, GPa

East, km

13


Toy Model 2: Static Finite-fault modeling

Posterior mean model, including Cp

  • Finite strike-slip fault

  • 65 patches, 2 slip components

  • 5mm uncorrelated noise(→Cd)

  • GFs for an homogeneous half- space (→Cp)

Slip, m

Dist. along Dip, km

Dist. along Strike, km

Earth model

Covariance with respect to xr

CpEast(xr), m2

x 104

Depth, km

North, km

xr

Log(μi / μi+1)

East, km

14


Toy model 1: prior: U(-0.5,20)

Posterior Mean Model

Input (target) model


Toy model 1: prior: U(0,20)

Posterior Mean Model

Input (target) model


Toy model including a slip step


Toy model including a slip step


Evolution of m at each beta step


Evolution of Cp at each beta step


Covariance Cμ

1000 realizations


Covariance Cp

1000 realizations


On the importance of Prediction uncertainty

  • Observational error:

    • Measurements dobs : single realization of a stochastic variable d* which can be described by a probability density p(d*|d) = N(d*|d, Cd)

  • Prediction uncertainty: whereΩ = [ μT , φT ]T

    • Ωtrue is not known and we work with an approximation

    • The prediction uncertainty:

      • scales with the with the magnitude of m

      • can be described by p(d|m) = N(d | g( ,m), Cp)

  • A posteriori distribution:

    • In the Gaussian case, the solution of the problem is given by:

  • Measurements

    Displacement field

    Earth

    model

    Source

    geometry

    Prior information

    Prediction

    errors

    Measurement

    errors

    D: Prediction space


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