1. Seismic waveform inversion at the regional scale: application to southeastAsia
Barbara Romanowicz1, Aimin Cao2, M.Panning3, F. Marone4 ,Yann Capdeville5, Laurent Stehly1 and Paul Cupillard1
1Univ. of California, Berkeley
2Rice Univ.
3Princeton U.
4P. Scherrer Institute,Switz.erland
5 Institut de Physique du Globe, Paris, France

2. I- Background: In the context of global S velocity, long period tomography

3. Standard tomographic ingredients:
Parametric data
Body wave travel times
well separated phases
Ray theory or, more recently finite frequency (“Banana-doughnut”) kernels
Surface waves
Group/phase velocities
Path average approximation (PAVA)

5. Waveform Tomography observed synthetic
Need framwork for computation of 3D synthetics
(2) Framework needs to be appropriate for body waves

6. Waveform Inversion Methodology:
Non-linear Asymptotic Coupling Theory (NACT); 3 component waveforms
extension to anisotropic inversion
iterative inversion for elastic and anelastic structure SS
Sdiff
PAVA
NACT

7. Elastic structure- SAW24B16 (SH) Anelastic structure QRLW8
Mégnin and
Romanowicz, 2000
Gung and Romanowicz, 2004

8. II. Beyond PAVA and NACT (in the context of normal mode summation)

9. Born approximation:
Single scattering
Integration over the
Whole sphere S R M
PAVA approximation (1D in the
Vertical plane)
NACT (2D in the vertical plane)
Both include multiple forward
scattering

10. “N-BORN“ Application to South East Asia
Add PAVA term (multiple forward scattering) into BORN.
Application to South East Asia
Comparison of NACT and N-Born inversion

11. Spherical spline parametrization Starting NACT radially aniso-
tropic model
Level 4
Splines
l~800km
Level 6
Splines
l~200km
Red: NACT region
Blue: NBORN region

12. We include both fundamental mode and overtone waveforms
By including overtones, we improve depth resolution into the transition zone
after Ritsema et al, 2004

13. Isotropic S velocity
NACT
NBORN
80km
150km
250 km

15. NACT A B A B
Friederich, 2003
NBORN A B

16. NACT
NBORN Vs
Radial anisotropy: x

17. III. Beyond N-Born: Towards numerical methods

18. Waveform Tomography observed synthetic
Normal mode perturbation theory (generally to 1st order)
(2) Numerical methods (e.g. SEM)

19. “Hybrid” Approach u(m) ∂u(m)/ ∂m
Use coupled spectral element method of Capdeville et al. (2002) to accurately forward model wave propagation through a 3D medium.
Use NACT, with the hope that the derivatives are the correct sign. Much faster than cSEM!
NACT
NACT accounts for coupling between modes that do not share the same radial order. In terms of traveling waves, this practice is equivalent to considering not only average structure, but also variations in material properties within the plane defined by the great circle path joining source and receiver. Even when we’re passing straight through, we don’t capture full effects without focusing.
First order perturbation theory requires that the perturbations be small…
We do better than other groups because we have the non-linear e(iwt) term which does not grow with time, allowing us to do a better job at late times (born theory is short-time approximation in some way).
We also do not update kernels, which means that we assume the perturbations do not affect eigenfunctions non-linearly (we know this is false, Federica and Mark’s crustal corrections). For eigenfrequencies, Adam showed that linearization is fine.
G1= Normal modes in 1D
G2 = Spectral element method
Li and Romanowicz,
1995
Capdeville et al., 2002

20. Preliminary “Level 4” radially anisotropic upper mantle model
Obtained using SEM, starting from 1D model – courtesy of Ved Lekic

21. IV-exploratory: summed event inversion
SEM is accurate but very time consuming: the wavefield computation for a single event can take a couple of hours (depending on the computer and the maximum frequency, and distance) not very practical for tomography
Can we speed up the computation by computing SEM synthetics for many events simultaneously (e.g. Capdeville et al., 2005, GJI)?

22. Summed seismogram inversion
Start with N-Born model
Restrict study to smaller region
Collect a dataset of waveforms in the distance range 4 to 40 degrees (~100 events)
period range sec
Data: summed waveforms for all events at one or a subset of stations
Synthetics: RegSEM for summed events in the N-Born model

24. XAN Summed seismograms at station XAN
Time (seconds)
Black: observed trace (filtered between 60 and 250 s)
Red: RegSEM synthetic in the 3D N-Born starting model

25. NBorn starting model
Inversion usingRegSEM –
Individual seismograms

26. “Summed seismogram” inversion
“Individual seismogram” inversion

27. Current developments:
larger dataset,
Extended tests
-progressively reach shorter periods and higher resolution

28. Thank You!

30. Seismic tomography dd = A dm mi+1 = mi + dm dd = u(t)obs- u(t)pred
- Linearized inverse problem:
dd = A dm
Step 1: forward
mi+1 = mi + dm
dd = u(t)obs- u(t)pred
A: Fréchet
Derivatives
Wave propagation
theory

31. Seismic tomography dd = A dm mi+1 = mi + dm dd = u(t)obs- u(t)pred
- Linearized inverse problem:
Step 2: inverse
dd = A dm
Step 1: forward
mi+1 = mi + dm
dd = u(t)obs- u(t)pred
A: Fréchet
Derivatives
Wave propagation
theory

32. Surface wave tomography
P-wavespeed
S-wavespeed
Surface wave tomography
(Lebedev et al., 2006)
PRI-P05 (Montelli et al.)
MIT-P06 (Li et al.)
Courtesy of Rob van der Hilst

34. NBORN model predictions: NBORN/NACT
Residual variance
Damping Factor

35. Marone and Romanowicz,
2007

36. Radial anisotropy
Gung et al., Nature, 2003

37. AB CD
Hawaii
Pacific Superplume

38. Ritzwoller and
Shapiro, 2002
Kustowski et al.
2007
NACT
NBORN

39. Level 6
Spherical
splines
(preliminary)
Version
cargese

40. Panning et al., 2008

41. Panning et al., 2007

42. N-Born inversion 152 events One iteration only
Starting model: 3D “NACT” model
Forward model: N-BORN
Partial derivatives: BORN (Capdeville,2006)
Elastic and radially aniosotropic structure

43. Upper mantle:Q - lower mantle: Vsh
Degree 2 only