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3D Seismic Imaging based on
Spectral-element Simulations
and Adjoint MethodsQinya Liu
Department of Physics
University of Toronto
1st QUEST Workshop, Sep 2010
Collaborations withCarl Tape, Alessia Maggi, Jeroen Tromp, Dimitri Komatitsch and many others
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Numerical Simulation of Seismic Wave Propagation based on SEM
SPECFEM3D (GLOBE, SESAME) packages are available through CIG website:
http://www.geodynamics.org/cig/software/
Practical Sessions on Friday 4-6 pm
Princeton University's Near Real Time Simulation of Global Seismic Events Portal (Mw > 5.5)
http://shakemovie.princeton.edu/
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Sep 9, 2010 Mw=6.2 Offshore Chile Event
S362ANI model (Kustowski 2008)
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Inverse ProblemI. Define Misfit Function
Travel time Misfit
Other types of Measurements:
waveform misfit (Tarantola 84,05) cross-correlation travel time (Luo & Schuster 91) frequency-dependent phase and amplitude (e.g. Zhou et al 04,
Fichtner 09 et al, Chen et al 04)
How to identify phases?
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Window Selection: FLEXWIN
Maggi et al (2008)
Available through CIG
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Inverse ProblemII. Derivative of Misfit
Tromp et al 05Tape et al 08
Event kernel
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Tape et al (2008)
Construction of Kernels (2D)Based on twoSEM simulations
- same for multipleSource-receiverPairs
- afternoon practicalsession
One measurement
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Inverse Problem II. 2nd order derivative – Hessian matrix?
We need kernels for individual measurements! Numerically expensive when 3D simulations are used.Similarly, for multiple events:
LS
Nonlinear conjugate gradientmethod
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Advantages and Disadvantages
3D initial model
Accurate 3D Green's functions
Accurate sensitivity kernels
More phases
Computationally intensive: 3xE simulations/iteration
More iterations needed: 6 CG iterations ~ 1 iteration with Hessian
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Southern California Crust
(Tape et al. 09, 10)
Initial model:
CVM-H
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Tape et al 09,10
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Waveform Fits
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Reflections
Model error estimation (sample the posterior model distribution)
Faster convergence? (source subspace methods)
Parameterization
Restrictions: Sources and receivers in the same domain
(local events) Tele-seismic data for local structure? Array data?
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Solutions I:New dataset: micro-seismic noise correlation
Weaver, 2005
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Ambient Noise for SoCal
Black: cc data (10-20 s)
Red: 3D Green's function
Blue: synthetic 3D cc based on Tromp et al 10
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Tele-seismic Data
High-resolution regional scattered-wave imaging using coda waves of main seismic phases
Receiver Functions Scattered-wave imaging, GRT
e.g. Zhu & Kanamori (2000) e.g. Bostock et al (2001)
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Sensitivity kernels for tele-seismic phases
Global SEM simulations run regularly at accuracy up to 20 seconds, but become extremely demanding at shorter periods.
Representation Theorem (Aki & Richards, 2002)
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Representation Theorem
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Toy Problem
Re-generate Forward field by Kirchhoff
Integral
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S Kernel
Interaction between
Forward wave field and
Adjoint wave field
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Kernel for S-coda Waves
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HP Computing Facilities
Data
Theory
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The End
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Forward simulation
Adjoint Simulation
KernelCalculation
Numerical simulation of wave propagation in 3D media both at local and regional scales.
Komatitsch & Tromp (02a,b)Komatitsch et al (04)
(Liu & Tromp 06,08)