Transcript Body wave tomography: an overview

Body wave traveltime
tomography: an overview
Huajian Yao
USTC
March 29, 2013
From IRIS
Seismic waves
 Seismic wave is currently the only effective tool that
can penetrate the entire earth  Structural
information of the Earth
1939:
Jeffreys &
Bullen
First travel-time
tables：JeffreysBullen
Seismological
Tables
→ 1D Earth
model
Jeffreys-Bullen
1-D 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
Travel time table from ak135 model
Travel time picks
Shearer, 2009
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.
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.
 Ray-based traveltime tomography
1. The forward problem:
(Infinite frequency approximation)
or
δ
δ
Travel time pick: first break
 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)
angular order l=18
azimuthal order m=6
Degree-18 spherical harmonic
expansion of crustal thickness
Liu & Gu (2012)
 Ray-based traveltime tomography
3. Solve for the inverse problem
(1) Standard Least
Squares Solution
GTG may be singular or ill-conditioned
 singular value decomposition (SVD)
(2) Damped Least
Squares Solution
minimize
minimize
Solution: m = (GTG+λ2LTL)-1GTd
L: Laplacian operator
Smooth model
Combined norm and Laplacian regularization
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
 Ray-based traveltime tomography
4. Appraise the model (accuracy, resolution)
(1) Synthetic model, checkerboard tests
(2) Resolution matrix R = (GTG+λ2LTL)-1GTG
(mest = Rmtrue)
Examples on ray-based traveltime
tomography
 (1). Global P traveltime tomography (Li et al., 2008)
Station coverage
misfit function
Data misfit
Model
roughness
Model
norm
Crust
correction
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)
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
Origin time
propagation time
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
 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.
 Finite frequency traveltime tomography
fat ray or finite-frequency sensitivity kernel
Fresnel zone of body waves (single scattering theory)
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; NissenMeyer et al., 2007).
finite frequency kernels for travel time perturbations
Princeton
group
“Bananadoughnut”
kernel: zero
sensitivity
along the ray
path!
Hung et al. 2000
More kernels
PP
PcP
The use of proper finite
frequency sensitivity
kernels makes it
possible to image
heterogeneities of sizes
similar to the first
Fresnel zone.
Hung et al. 2000
 Finite frequency traveltime tomography:
example (Montelli et al., 2004, Science)
See a lot more plumes (?)
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
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)