Body wave traveltime tomography: an overview

1. Body wave traveltimetomography: an overview Huajian Yao USTC March 29, 2013

2. Seismic waves • Seismic wave is currently the only effective tool that can penetrate the entire earth  Structural information of the Earth From IRIS

3. 1939: Jeffreys & Bullen First travel-time tables：Jeffreys-Bullen Seismological Tables → 1D Earth model Jeffreys-Bullen 1-D Earth Model

4. More 1-D Earth’s Model PREM: 1981 (Dziewonski & Anderson) iasp91: 1991 (Kennett) ak135: 1995 (Kennett, Engdahl, Buland)

5. However, the Earth structure is not just simply 1-D ! Plate tectonics and mantle convection Topography

6. Travel time picks Travel time table from ak135 model Shearer, 2009

7. 3-D variations of Earth’s Structure from Seismic Tomography Seismic waves in the Earth Traveltime/waveform 3-D wave speeds Inverse problem Researchers at MIT and Harvard, led by Keiti Aki and Adam Dziewonski in late 1970’s and 1980’s, pioneered the technique of seismic tomography.

8. Seismic tomography: solving the inverse problem Liu & Gu (2012) 1. Writing the problem based on a set of discrete model coefficients. 2. Computing the predicted data based on the choice of model parameters for an a priori structure, the majority being known 1D model structures. 3. Defining an objective function and adjusting the model parameters to meet the pre-defined goodness-of-fit criteria. 4. Estimating the accuracy and resolution of the inversion outcome, repeating the above steps when necessary.

9. 1. The forward problem: • Ray-based traveltime tomography (Infinite frequency approximation) or δ δ Travel time pick: first break

10. 2. Linearization and parameterization • Ray-based traveltime tomography (1) Blocks (2) Grids (similar as blocks) 2-D blocks 3-D grids

11. (3) Basis function (e.g., spherical harmonics) Degree-18 spherical harmonic expansion of crustal thickness angular order l=18 azimuthal order m=6 Liu & Gu (2012)

12. 3. Solve for the inverse problem • Ray-based traveltime tomography (1) Standard Least Squares Solution GTG may be singular or ill-conditioned  singular value decomposition (SVD) (2) Damped Least Squares Solution minimize

13. minimize Smooth model Solution: m = (GTG+λ2LTL)-1GTd L: Laplacian operator

14. Combined norm and Laplacian regularization

15. Solution: m = (GTG+λ2LTL)-1GTd For small problems (number of m < 1000 or so),the above equation can be directly solved. (3) Iterative methods (LSQR, conjugate gradient, etc) for large and sparse systems of equations for 3-D tomography, #m ~ 1,000,000 LSQR link: http://www.stanford.edu/group/SOL/software/lsqr.html

16. 4. Appraise the model (accuracy, resolution) • Ray-based traveltime tomography • Synthetic model, checkerboard tests • Resolution matrix R = (GTG+λ2LTL)-1GTG • (mest = Rmtrue)

17. Examples on ray-based traveltime tomography • (1). Global P traveltime tomography (Li et al., 2008)

18. Station coverage misfit function Model roughness Model norm Crust correction Data misfit

19. Crust correction: using 3-D Crust 2.0 as the reference crust model Crust 2.0 Input model 1-D crust reference model 3-D crust reference model

20. Automatic grids based on ray path density

21. Checkerboard resolution tests

22. Checkerboard and synthetic resolution tests

23. Horizontal slices

24. Vertical profiles

25. Examples on ray-based traveltime tomography • (2) Regional teleseismic traveltime tomography (Waite et al., 2006, JGR, Yellowstone)

26. Station and events distribution

27. Station delay times Positive station delay times (red) : slow anomaly beneath the stations Negative station delay times (blue) : fast anomaly beneath the stations

28. Ray density plot

29. 3D Vp structure from tomographic inversion (vertical & horizontal smoothing, crustal correction)

30. Checkerboard tests

31. Examples on ray-based traveltime tomography • (3) Regional traveltime tomography using local events (Wang et al., 2009, EPSL, Sichuan, Longmenshan)

32. Model parameterization & reference model

33. Ray path distribution and checkerboard resolution tests

34. Vp, Vs, and Poisson’s Ratio

35. Examples on ray-based traveltime tomography • (4) Double difference tomography (Zhang & Thurber, 2003, BSSA) Origin time Body wave travel time (event i  station k) : propagation time Misfit between the observed and predicted travel time (after linearization): perturbations to Source location propagation time Origin time

36. Double difference traveltime: can be obtained from waveform cross-correlation. Very useful in obtaining structure near the earthquakes

37. Double difference tomography examples: a section across the San Andreas Fault Conventional tomo. DD tomo. DD tomography result for subducting slab beneath northern Honshu, Japan, where a double Benioff zone is present Thurber & Ritsema, 2007

38. From ray-based traveltime tomography to finite frequency traveltime tomography • The ray-based tomography using the infinite frequency limit is very successful to determine the 3-D structure of the Earth. Travel time measurements are only sensitive to structure along the ray path (infinitely thin ray). • However, seismic waves have certain frequency bandwidths, which are sensitive to structure within the first fresnel zone (tube) along the ray path based on single scattering theory.  Finite frequency traveltime tomography.

39. Finite frequency traveltime tomography fat ray or finite-frequency sensitivity kernel Fresnel zone of body waves (single scattering theory)

40. Calculation of finite frequency kernels 1. mode coupling (e.g., Li and Romanowicz, 1995; Li and Tanimoto, 1993; Marquering et al., 1998) 2. body-wave ray theory (e.g., Dahlen et al., 2000; Hung et al., 2000) (based on born approximation) 3. surface-wave ray theory (e.g., Zhou, 2009; Zhou et al., 2004, 2005) 4. normal-mode summation (e.g., Capdeville, 2005; Zhao and Chevrot, 2011a; Zhao and Jordan, 1998; Zhao et al., 2006) 4. full 2D/3D numerical simulations via the adjoint method (Tromp et al., 2005; Liu and Tromp, 2006, 2008; Nissen-Meyer et al., 2007).

41. finite frequency kernels for travel time perturbations Princeton group “Banana-doughnut” kernel: zero sensitivity along the ray path! Hung et al. 2000

42. More kernels The use of proper finite frequency sensitivity kernels makes it possible to image heterogeneities of sizes similar to the first Fresnel zone. PP PcP Hung et al. 2000

43. Finite frequency traveltime tomography: example (Montelli et al., 2004, Science)

44. See a lot more plumes (?)

45. Big debates on ray-based and finite-frequency tomography B-D Kernel: zero sensitivity along the ray path B-D Kernels are based on 1-D model Parameterization …… Dahlen and Nolet, 2005; de Hoop and van der Hilst, 2004; Montelli et al., 2006; van der Hilst and de Hoop, 2005, 2006 https://www.geoazur.fr/GLOBALSEIS/nolet/BDdiscussion.html

46. Although debates on ray-based and finite-frequency tomography, more and more studies are now considering the finite frequency effect of body wave propagation.More accurate 3-D kernels are computed for 3-D models based on numerical simulation methods (e.g., SEM and adjoint method). P traveltime kernel (Liu & Tromp. 2006)

47. Example of adjoint tomography (Tape et al. 2010)