surface wave tomography--what are surface...
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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