3D Seismic Imaging based on Spectral-element Simulations and Adjoint Methods Qinya Liu Department of Physics University of Toronto 1 st QUEST Workshop, Sep 2010 Collaborations with Carl 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: Practical Sessions on Friday 4-6 pm Princeton University's Near Real Time Simulation of Global Seismic Events Portal (Mw > 5.5)

Sep 9, 2010 Mw=6.2 Offshore Chile Event S362ANI model (Kustowski 2008)

Inverse Problem I. 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 Problem II. Derivative of Misfit Tromp et al 05 Tape et al 08 Event kernel

Tape et al (2008) Construction of Kernels (2D) Based on two SEM simulations - same for multiple Source-receiver Pairs - afternoon practical session One measurement

Inverse Problem II. 2 nd order derivative – Hessian matrix? We need kernels for individual measurements! Numerically expensive when 3D simulations are used. Similarly, for multiple events: LS Nonlinear conjugate gradient method

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 Kernel Calculation 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)