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![Page 1: Surface wave tomography : 1. dispersion or phase based approaches (part A) Huajian Yao USTC April 19, 2013.](https://reader035.fdocuments.us/reader035/viewer/2022062518/56649e625503460f94b5f043/html5/thumbnails/1.jpg)
Surface wave tomography :
1. dispersion or phase based approaches(part A)
Huajian Yao
USTC April 19, 2013
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Surface wave propagates along the surface of the earth, mainly sensitive to the crust and upper mantle (Vs) structure
From
IR
IS
Surface waves
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Love and Rayleigh waves
Generated by constructive interference between postcritically reflected body waves
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Surface waves: evanescent waves
Decreasing wave amplitudes as depth increases
Wave displacement patterns in a layer over half space
Wavelength
increases
Generally, wavespeed increases as the depth increases. Therefore, longer period (wavelength) surface waves tend to propagate faster.
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Surface wave dispersion: frequency-dependent propagation speed
(phase or group speed)
Group V: Energy propagation speed
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Phase or group velocity dispersion curves(PREM model)
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Phase or group velocity depth sensitivity kernels
is the 1-D depth sensitivity kernel
Usually 80-90% importance
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Phase or group velocity depth sensitivity kernels
fundamental mode
Rayleigh wave Love wave
dc/dVSVdc/dVSH
dU/dVSV
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(A) 0.15 Hz, (B) 0.225 Hz, (C) 0.3 Hz.
Rayleigh wave phase velocity depth sensitivity kernels at shorter periods: also quite sensitive to Vp and
density at shallow depth
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Rayleigh wave phase velocity depth sensitivity kernels: An image view
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1. Construct period-dependent 2-D phase/group velocity maps from many dispersion measurements
2. Point-wise (iterative) inversion of dispersion data at each grid point for 1-D Vs model; combine all the 1-D Vs models to build up the final 3-D Vs model
Surface wave tomography from dispersion data: a two-step approach
Now the global search approaches are widely used for this step due to very non-linear situation of this
problem.
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(1). Single-station group velocity approach
(event station)
(2). Two-station phase velocity approach
(event station1 station 2)
(3). Single-station phase velocity approach
(1) U = D/tg (2) c = (D2 – D1)/Δt
Popular approaches for surface wave tomography (Step 1)
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(1). Single-station group velocity approach
frequency-time analysis (matched filter technique) to measure group velocity dispersion curves
Widely used in regional surface wave tomography
Ritzwoller and Levshin, 1998
Possible errors:(1) off great-circle effect, (2) mislocations of earthquake epicenters, (3) source origin time errors and (4) the finite dimension and duration of source process.
(2 – 4): source term errors
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Eurasia surface wave group velocity tomography
Ritzwoller and Levshin, 1998
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(2). Two-station phase velocity approach (very useful for regional array surface wave tomography)
Teleseismic surface waves
CTS (20 – 120 s)
Yao et al., 2006,GJI
Narrow bandpass filtered waveform cross-correlation travel time differences between stations almost along the same great circle path(circle skipping problem!)
Advantage: can almost remove “source term errors”
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SW China Rayleigh wave phase velocity tomography from the two-station method
Yao et al., 2006,GJI
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(3). Single-station phase velocity approach
Observed Seismogram:
Theoretical reference Seismogram from a spherical Earth model
Propagation phase
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Perturbation Theory
Ekstrom et al, 1997
Spherical harmonics representation of the 3-D model
circle skipping problem at shorter
periods!
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Example: Global phase velocity tomography (Ekstrom et al., 1997)
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Iterative linearize inversion
Inversion of Vs from point-wise dispersion curves (Step 2)
2. non-linear inversion or global searching methods
Simulated annealing, Genetic algorithm
Monte Carlo method, Neighborhood algorithm
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Iterative linearize inversion: example
The results may depend on the initial velocity model. Better to give appropriate prior constraints, e.g., Moho depth.
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Nonlinear inversion: example using neighborhood algorithm (Yao et al. 2008)
http://rses.anu.edu.au/~malcolm/na/na.html (Sambridge, 1999a, b)
Neighborhood search
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Bayesian Analysis of the model ensemble
Posterior mean:
1-D marginal PPDF
2-D marginal PPDF
1-D PPDF: resolution & standard error of model parameter;
2-D PPDF: correlation between two model parameters