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 pm

Princeton 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 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

Southern California Crust

(Tape et al. 09, 10)

Initial model:

CVM-H

Tape et al 09,10

Waveform Fits

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?

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)