towards optimal network for source inversion n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Towards Optimal Network for Source Inversion PowerPoint Presentation
Download Presentation
Towards Optimal Network for Source Inversion

Loading in 2 Seconds...

play fullscreen
1 / 26

Towards Optimal Network for Source Inversion - PowerPoint PPT Presentation


  • 135 Views
  • Uploaded on

Towards Optimal Network for Source Inversion. Lingsen Meng, Jean-Paul Ampuero Seismo Lab,Caltech. Source Inversion Validation (SIV):. Finite fault inversion Different approaches and datasets Used to study source dynamics, ground motion ,coulomb stress

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Towards Optimal Network for Source Inversion' - annot


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
towards optimal network for source inversion

Towards Optimal Network for Source Inversion

Lingsen Meng, Jean-Paul Ampuero

Seismo Lab,Caltech

source inversion validation siv
Source Inversion Validation (SIV):
  • Finite fault inversion
  • Different approaches and datasets
  • Used to study source dynamics, ground motion ,coulomb stress
  • Huge discrepancies

SPICE blind test

  • Compare and validate current developed models
  • estimate the actual uncertainty of the model parameters
  • A blind-test for source inversion approaches
  • Lead by Martin Mai, Danjiel Schorlemmer, Morgan Page
motivation
Motivation

Best network for next SIV benchmark?

Inconsistency due to station distribution

Quantification of effectiveness of array geometry (resolution, uncertainty)

Tradeoff between information and cost

Experiment design example:

fault location, magnitude 7, N sensors available: where

do we install the sensors to achieve the most reliable source imaging?

outline
Outline

Review resolution and uncertainty of linear inverse theory

Optimal array geometry from prediction theory

Statistical approach for Nonlinear survey design

Optimal network for earthquake location

Best network for next SIV benchmark?

Summary

linear source inversion
Linear source inversion

NT*Nm

NT

Slip on the fault

Nt

Green’s function

seismograms

Nt*Ns

×

=

NT*Nm

Nt*Ns

(+constraints)

linear resolution and uncertainty
Linear resolution and Uncertainty

resolution

  • R = higher resolution when the diagnal term of resolution matrix appoach to 1
  • Data errors propagate in to model with amplification of 1/eigenvalue

uncertainty

Eigenvalues(diag matrix)

Eigenvectors(diag matrix)

Generalized inverse

(truncating small eigenvalues)

quality measures of eigenspectrum
quality measures of eigenspectrum

crosswell tomography(curtis et al,1999)

regular

optimal

slide8

Optimal array geometry from prediction theory(Iida,1990)

  • Known strike, dip ,rake, rise time, rupture time. invert for slip on each subfault
  • Quality metric Similar to

related to the std of slip of subfaults

  • Not an exhaustive search on array geometries: tested few geometries with simple parameterization(Ns, radius , azimuthal coverage)
uncertainty and ns radius

Number of station

Array radius

Uncertainty and Ns,radius

error

Two concentric rings, R/r = 2, Ns/2 stations on each ring

Free parameters: Ns and R

  • Inverse root Dependent on number of stations
  • Array radius good between 0.75-2 fault length
slide10

Fan array

Free parameters: Azimuth coverage (Phi), fixed station density or fixed number

Uncertainty and Azimuthal coverage

error

Azimuthal coverage

  • Inverse root Dependent on azimuthal coverage which contribute a lot to the inversion
test for optimization of geometry
Test for optimization of geometry

Optimal geometry

Testing geometry

strike slip

Dip slip

summary and limitations
Summary and Limitations
  • Green’s function of homogeneous half space
  • Non-linear effect

positivity constraint

rupture time , rise time

  • exhaustive optimization

needed

  • Linear prediction from propagation of errors
  • Quantification of uncertainties from array parameters
  • non-exhaustive optimization of network geometry
non linear experiment design theory curtis 2004
Non-linear experimentdesign theory(Curtis,2004)

Measure of information: negative entropy

Maximizing

(Model dependence on data and design)

=

Minimizing

(data dependence on design)

Only forward modeling required to optimize the design , still expensive

optimal network for earthquake location
Optimal network for Earthquake location
  • D-optimum ( )criteria for optimal network(Kijko,1977)
  • Optimal network for aftershocks ( Hardt and Scherbaum,1994)

Joint optimization for location, focal mechanism, tomography

  • Maximize for multiple sources (Steinberg et al,1995)

W: error correlation matrix for the sites

stations surround the epicenter

  • Online network optimization software(lomax & Curtis, 2004)
  • Double-difference and bootstrap(Bai et al,2006)

need stations close to the epicenter

not too large azimuthal gap

best network for benchmark
Possible solutions

rule of thumbs

good azimuth coverage

denser closer to the fault

too many stations not realistic

realistic network (SIV 1 , the Tottori earthquake)

a network minimize the contribution to errors from station geometry (focused design on the true slip distribution)

Best network for benchmark
solution focused experiment design
Solution?:Focused experiment design

Focused metric

crosswell tomography(curtis et al,1999)

Projection of uncertainty on subspace

Design focused on the subfaults actually slipped !

Keeping the errors from stations min on specific source

isochron theory
Isochron theory

Spudich et al, 1984

Schmedes & Archuleta, 2008

Contour of sum of travel time and rupture time = constant

Relate the amplitude of seismogram to slips on each subfault

network quality based on isochron theory
Network quality based on Isochron theory

Station distribution(N=6)

Stacked map for all stations

each station

Inverse of area between neighboring isochrons =

Sensitivity of each segment of seismograms to the slip on each subfaults

Geometrical spreading, attenuation , signal to coda ratio , radiation pattern

discussion
Discussion
  • What criterion should guide the selection of a station distribution for next SIV benchmark :
    • Realistic ?
    • Minimizes model uncertainties for any source?
    • Minimizes model uncertainties for a specific source?
  • Effective optimization scheme to search optimal network ,especially non-linear problem (isochron metric)
  • Network optimization for tomography (seistivity Kernels)
slide23

Station distribution(N=6)

Single station

inverse of Isocron band area

Stacked map

slide25

Fan array

Free parameters: Azimuth coverage (Phi), fixed station density or fixed number

Uncertainty and Azimuthal coverage

error

Azimuthal coverage

Component of seismogram

  • Inverse root Dependent on azimuthal coverage
  • Horizontal component of seismogram contribute to strike-slip fault; vertical to dip-slip
non linear experiment design theory curtis 20041

Not on S for

Non-linear experimentdesign theory(Curtis,2004)

Measure of information: negative entropy

Partition a vector into two parts

maximize

Not on S

minimize

Only forward modeling required, still expensive