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