surface wave tomography--what are surface...

Surface wave tomography--what are surface waves

Surface wave tomography--what are surface waves

Surface wave tomography--what are surface waves

energy trapped near surface of the Earth

elastic waves

describe them using again the law of optics, except now it’s a 2D problem: at each frequency wavespeed depends only on latitude, longitude

dispersive

Surface wave tomography--what are surface waves

energy trapped near surface of the Earth

elastic waves

describe them using again the law of optics, except now it’s a 2D problem: at each frequency wavespeed depends only on latitude, longitude

dispersive

Surface wave tomography--what are surface waves

Following the ray-theory (infinite frequency) approximation:

introduce phase velocity:

first-order Taylor expansion:

Surface wave tomography--what are surface waves

compare with body-wave results:

Surface wave tomography--what are surface waves

compare with body-wave results:

Surface wave tomography--measuring δψ

Ekström, Tromp and Larson (1997)

Surface wave tomography--measuring δψ

Ekström, Tromp and Larson (1997)

Surface wave tomography--phase velocity maps

start from:

Surface wave tomography--phase velocity maps

start from:

parameterize:

Surface wave tomography--phase velocity maps

start from:

parameterize:

substitute:

Surface wave tomography--phase velocity maps

start from:

parameterize:

substitute:

if c is constant (e.g. PREM)…

Surface wave tomography--phase velocity maps

introduce matrix A:

Surface wave tomography--phase velocity maps

introduce matrix A:

substitute into:

Surface wave tomography--phase velocity maps

introduce matrix A:

substitute into:

write in tensor notation:

Surface wave tomography--phase velocity maps

Ekström, Tromp and Larson (1997)

Surface wave tomography--phase velocity maps

Ekström, Tromp and Larson (1997)

Surface wave tomography--3D shear velocity models

“Kernel” functions K can be found (see spherical Earth seismology lecture notes) relating δc

and δv (shear velocity anomaly):

Surface wave tomography--3D shear velocity models

“Kernel” functions K can be found (see spherical Earth seismology lecture notes) relating δc

and δv (shear velocity anomaly):

substitute into:

Surface wave tomography--3D shear velocity models

substitute into:

and find:

“Kernel” functions K can be found (see spherical Earth seismology lecture notes) relating δc

and δv (shear velocity anomaly):

Surface wave tomography--3D shear velocity models

can be used to formulate a linear inverse problem as we did before:

Surface wave tomography--3D shear velocity models

can be used to formulate a linear inverse problem as we did before:

parameterize:

Surface wave tomography--3D shear velocity models

can be used to formulate a linear inverse problem as we did before:

parameterize:

substitute:

Surface wave tomography--3D shear velocity models

can be used to formulate a linear inverse problem as we did before:

parameterize:

substitute:

change order of integration:

Surface wave tomography--3D shear velocity models

can be used to formulate a linear inverse problem as we did before:

parameterize:

substitute:

introduce A and translate into tensor notation:

The unique anisotropy of the pacific upper mantle

Heterogeneity of crustal properties

Sensitivity kernels K Love Rayleigh

long period

short period

Sensitivity kernels K

Sensitivity kernels K

Relevance of crustal correction and lateral variations of K