Body wave traveltime tomography: an overview Huajian Yao USTC March 29, 2013

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

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

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

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

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

3-D variations of Earth’s Structure from Seismic Tomography Seismic waves in the Earth 3-D wave speeds Traveltime/waveform 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.

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. Seismic tomography: solving the inverse problem Liu & Gu (2012)

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

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

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

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

L: Laplacian operator Smooth model Solution: m = (G T G+λ 2 L T L) -1 G T d

Combined norm and Laplacian regularization

Solution: m = (G T G+λ 2 L T L) -1 G T d 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:

Ray-based traveltime tomography 4. Appraise the model (accuracy, resolution) (1)Synthetic model, checkerboard tests (2)Resolution matrix R = (G T G+λ 2 L T L) -1 G T G (m est = Rm true )

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

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

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

Automatic grids based on ray path density

Checkerboard resolution tests

Checkerboard and synthetic resolution tests

Horizontal slices

Vertical profiles

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

Station and events distribution

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

Ray density plot

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

Checkerboard tests

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

Model parameterization & reference model

Ray path distribution and checkerboard resolution tests

Vp, Vs, and Poisson’s Ratio

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

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

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

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. From ray-based traveltime tomography to finite frequency traveltime tomography

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

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).

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

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

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

See a lot more plumes (?)

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

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)

Example of adjoint tomography (Tape et al. 2010)