Surface wave tomography： 1. dispersion or phase based approaches

(part 1)

Huajian Yao

hjyao@ustc.edu.cn

USTC

Surface wave propagates along the surface of the earth, mainly sensitive to the crust and upper mantle (Vs) structure

Fro

m I

RIS

Surface waves

Love and Rayleigh waves

Generated by constructive interference between postcritically reflected body waves

Higher Mode Surface Waves

infinite number of higher mode solutions

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)

Usually: C(Love,T) > C(Ray, T), U(Love, T) > U(Ray, T), C(T) > U(T)

If the group velocities are constant over a wide period range, then they can produce a high-amplitude body-wave looking pulse that is called an Airy phase.

Phase or group velocity depth sensitivity kernels

is the 1-D depth sensitivity kernel，j is for the layer index

Usually 80-90% importance

Phase or group velocity depth sensitivity kernels

fundamental mode

Rayleigh wave Love wave

dc/dVSV dc/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)

(3) c= ωD/(Φr-Φs+2nπ)

(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”

（Yao et al., 2005, PEPI）

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 2-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.

(Chen et al. 2013, Gondwana Res.)

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

Higher-mode (overtone) surface wave tomography

Rayleigh wave Love wave

dc/dVSV dc/dVSH

Fundamental mode higher modes

high-frequency multi-mode surface wave dispersion (multi-channel analysis of surface waves – MASW)

Surface-wave mode-branch stripping technique:

isolate various modes of surface waves and

measure phase velocity dispersion for each mode

(Van Heijst & Woodhouse, 1997)

Traces are arranged in groups of three seismograms, (data, full synthetic and mode-branch synthetic) at the right and two corresponding cross-correlations (data * branch synthetic and synthetic * branch synthetic, where * denotes crosscorrelation) at the left.

Van Heijst & Woodhouse, 1999

Surface waves inversion for exploration seismology

Surface wave tomography from dispersion data: an one-step approach

(Boschi & Ekstrom, 2002)

(p: slowness)

: the set of unknown earth parameters (e.g., Vs, Vp, density)

Represent the model using basis functions fk

We simplify the notation by establishing a one-to-one correspondence

between the couples of indexes i, k and a single index l. Let L be the total

number of combinations i, k. We subsequently call Ajl the double integral in

the above equation. Finally we shall have