Toward the next generation of earthquake source models by accounting for model prediction error
This presentation is the property of its rightful owner.
Sponsored Links
1 / 23

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


  • 49 Views
  • Uploaded on
  • Presentation posted in: General

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,

Download Presentation

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

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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

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.


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

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


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

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


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

Prediction uncertainty due to the earth model

1000 stochastic realizations

Covariance

Cp


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

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


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

Toy model 1: Infinite strike-slip fault

Posterior Mean Model

Input (target) model


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

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


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

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


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

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


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

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


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

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


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

Application to actual data: Mw 7.7 Balochistan earthquake

Jolivet et al., submitted to BSSA

AGU Late breaking session on Tuesday


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

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


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

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


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

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

Posterior Mean Model

Input (target) model


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

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

Posterior Mean Model

Input (target) model


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

Toy model including a slip step


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

Toy model including a slip step


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

Evolution of m at each beta step


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

Evolution of Cp at each beta step


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

Covariance Cμ

1000 realizations


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

Covariance Cp

1000 realizations


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

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


  • Login