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
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 pmPrinceton University's Near Real Time
Simulation of Global Seismic Events Portal (Mw > 5.5)
http://shakemovie.princeton.edu/
Sep 9, 2010 Mw=6.2 Offshore Chile Event
S362ANI model (Kustowski 2008)
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?
Window Selection: FLEXWIN
Maggi et al (2008)
Available through CIG
Inverse ProblemII. Derivative of Misfit
Tromp et al 05Tape et al 08
Event kernel
Tape et al (2008)
Construction of Kernels (2D)Based on twoSEM simulations
- same for multipleSource-receiverPairs
- afternoon practicalsession
One measurement
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
Advantages and Disadvantages
3D initial modelAccurate 3D Green's functionsAccurate sensitivity kernelsMore phases
Computationally intensive: 3xE simulations/iteration
More iterations needed: 6 CG iterations ~ 1 iteration with Hessian
Southern California Crust
(Tape et al. 09, 10)
Initial model:
CVM-H
Tape et al 09,10
Waveform Fits
ReflectionsModel 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?
Solutions I:New dataset: micro-seismic noise correlation
Weaver, 2005
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
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)
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)
Representation Theorem
Toy Problem
Re-generate Forward field by Kirchhoff
Integral
S Kernel
Interaction between
Forward wave field and
Adjoint wave field
Kernel for S-coda Waves
HP Computing Facilities
Data
Theory
The End
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)