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Transcript of 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
Acknowledgements: Piyush Agram, Mark Simons, Sarah Minson, James Beck,
Pablo Ampuero, Romain Jolivet, Bryan Riel, Michael Aivasis, Hailiang Zhang.
Zacharie DuputelSeismo Lab, GPS division,
Caltech
2
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
Project : Toward the next generation of source models including realistic statistics of uncertainties
Izmit earthquake (1999)
Dep
th,
kmD
ep
th,
kmD
ep
th,
km
Slip
, m
Slip
, m
Slip
, m
Single model
Ensemble of models
SIV initiative
3
Partial derivatives w.r.t. the elastic parameters (sensitivity
kernel)
Covariance matrix describing uncertainty
in the Earth model parameters
Exact theory
Stochastic (non-deterministic) theory
A reliable stochastic model for the prediction uncertainty
The forward problem‣ posterior distribution:
p(d|m) = N(d | g( ,m), Cp)p(d|m) = δ(d - g( ,m))
Calculation of Cp based on the physics of the problem: A perturbation approach
?
Slip, m
H
Dep
th /
H
2H
μ1
μ2
μ2/μ1 =1.4
0.9H
- 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):
Toy model 1: Infinite strike-slip fault
Slip, m
H
Dep
th /
H
2H
μ2
0.9H
Synthetic Data + Noiseshallow fault + Layered half-
space
Inversion:Homogeneous half-space
μ1
μ2
Slip, m
Slip, m
Depth
/
H
Dis
pla
cem
en
t, m
Distance from fault / H
No Cp (overfitting)
Cp Included (larger residuals)
Depth
/
H
Why a smaller misfit does not necessarily indicate a better solution
Distance from fault / H
Dis
pla
cem
en
t, m
8
Toy Model 2: Static Finite-fault modeling
Dist. along Strike, km
Dis
t. a
long D
ip,
km
East, km
Nort
h,
km
Shear modulus, GPa
Depth
, km
Horizontal Disp., m
Vertical Disp., m
Slip, m
Input (target) model
Earth model
Data
Finite strike-slip fault‣ Top of the fault at 0 km‣ South-dipping = 80°‣ Data for a layered half-space
9
Toy Model 2: Static Finite-fault modeling
Dist. along Strike, km
Dis
t. a
long D
ip,
km
East, km
Nort
h,
km
Shear modulus, GPa
Depth
, km
Horizontal Disp., m
Vertical Disp., m
Slip, m
Input (target) model
Earth model
Data
Model for
Data
Model forGFs
Finite strike-slip fault‣ 65 patches, 2 slip components‣ 5mm uncorrelated noise
(→Cd)‣ GFs for an homogeneous half- space (→Cp)
10
Toy Model 2: Static Finite-fault modeling
Dist. along Strike, km
Dis
t. a
long D
ip,
km
Shear modulus, GPa
Depth
, km
Slip, mFinite strike-slip fault‣ 65 patches, 2 slip components‣ 5mm uncorrelated noise
(→Cd)‣ GFs for an homogeneous half- space (→Cp)
Input (target) model - 65 patches average
Earth model
Dist. along Strike, km
Dis
t. a
long D
ip,
km
Slip, m
Posterior mean model, No Cp
Dist. along Strike, km
Dis
t. a
long D
ip,
km
Slip, m
Posterior mean model, including Cp
Uncertainty on the shear
modulus
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
Jolivet et al., submitted to BSSAAGU Late breaking session on Tuesday
Application to actual data: Mw 7.7 Balochistan earthquake
13
Toy Model 2: Static Finite-fault modeling
Shear modulus, GPa
Depth
, km
Finite strike-slip fault‣ 65 patches, 2 slip components‣ 5mm uncorrelated noise
(→Cd)‣ GFs for an homogeneous half- space (→Cp)
Earth model
Uncertainty on the shear
modulus
Dist. along Strike, km
Dis
t. a
long D
ip,
km
Slip, m
Posterior mean model, including Cp
CpEast(xr), m2
x 104
East, km
Nort
h,
km
Covariance with respect to xr
xr
14
Toy Model 2: Static Finite-fault modeling
Log(μi / μi+1)
Depth
, km
Finite strike-slip fault‣ 65 patches, 2 slip components‣ 5mm uncorrelated noise
(→Cd)‣ GFs for an homogeneous half- space (→Cp)
Earth model
Dist. along Strike, km
Dis
t. a
long D
ip,
km
Slip, m
Posterior mean model, including Cp
CpEast(xr), m2
x 104
East, km
Nort
h,
km
xr
Covariance with respect to xr
Measurement
errors
Prediction
errors
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: where Ω = [ 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:
Earthmode
l
Sourcegeometr
y
Measurements
Displacement field
Prior information
On the importance of Prediction uncertainty
D: Prediction space