Surface wave tomography :
1. dispersion or phase based approaches(part A)
Huajian Yao
USTC April 19, 2013
Surface wave propagates along the surface of the earth, mainly sensitive to the crust and upper mantle (Vs) structure
From
IR
IS
Surface waves
Love and Rayleigh waves
Generated by constructive interference between postcritically reflected body waves
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.
Surface wave dispersion: frequency-dependent propagation speed
(phase or group speed)
Group V: Energy propagation speed
Phase or group velocity dispersion curves(PREM model)
Phase or group velocity depth sensitivity kernels
is the 1-D depth sensitivity kernel
Usually 80-90% importance
Phase or group velocity depth sensitivity kernels
fundamental mode
Rayleigh wave Love wave
dc/dVSVdc/dVSH
dU/dVSV
(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
Rayleigh wave phase velocity depth sensitivity kernels: An image view
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.
(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)
(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
Eurasia surface wave group velocity tomography
Ritzwoller and Levshin, 1998
(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”
SW China Rayleigh wave phase velocity tomography from the two-station method
Yao et al., 2006,GJI
(3). Single-station phase velocity approach
Observed Seismogram:
Theoretical reference Seismogram from a spherical Earth model
Propagation phase
Perturbation Theory
Ekstrom et al, 1997
Spherical harmonics representation of the 3-D model
circle skipping problem at shorter
periods!
Example: Global phase velocity tomography (Ekstrom et al., 1997)
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
Iterative linearize inversion: example
The results may depend on the initial velocity model. Better to give appropriate prior constraints, e.g., Moho depth.
Nonlinear inversion: example using neighborhood algorithm (Yao et al. 2008)
http://rses.anu.edu.au/~malcolm/na/na.html (Sambridge, 1999a, b)
Neighborhood search
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