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 IRIS 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 waveLove wave dc/dV SV dc/dV SH dU/dV SV

(A) 0.15 Hz, (B) 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/t g (2) c = (D 2 – D 1 )/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 C TS (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) (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