surface wave tomography--what are surface...
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![Page 1: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/1.jpg)
Surface wave tomography--what are surface waves
![Page 2: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/2.jpg)
Surface wave tomography--what are surface waves
![Page 3: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/3.jpg)
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
![Page 4: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/4.jpg)
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
![Page 5: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/5.jpg)
Surface wave tomography--what are surface waves
Following the ray-theory (infinite frequency) approximation:
introduce phase velocity:
first-order Taylor expansion:
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Surface wave tomography--what are surface waves
compare with body-wave results:
![Page 7: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/7.jpg)
Surface wave tomography--what are surface waves
compare with body-wave results:
![Page 8: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/8.jpg)
Surface wave tomography--measuring δψ
Ekström, Tromp and Larson (1997)
![Page 9: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/9.jpg)
Surface wave tomography--measuring δψ
Ekström, Tromp and Larson (1997)
![Page 10: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/10.jpg)
Surface wave tomography--phase velocity maps
start from:
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Surface wave tomography--phase velocity maps
start from:
parameterize:
![Page 12: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/12.jpg)
Surface wave tomography--phase velocity maps
start from:
parameterize:
substitute:
![Page 13: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/13.jpg)
Surface wave tomography--phase velocity maps
start from:
parameterize:
substitute:
if c is constant (e.g. PREM)…
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Surface wave tomography--phase velocity maps
introduce matrix A:
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Surface wave tomography--phase velocity maps
introduce matrix A:
substitute into:
![Page 16: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/16.jpg)
Surface wave tomography--phase velocity maps
introduce matrix A:
substitute into:
write in tensor notation:
![Page 17: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/17.jpg)
Surface wave tomography--phase velocity maps
Ekström, Tromp and Larson (1997)
![Page 18: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/18.jpg)
Surface wave tomography--phase velocity maps
Ekström, Tromp and Larson (1997)
![Page 19: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/19.jpg)
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):
![Page 20: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/20.jpg)
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:
![Page 21: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/21.jpg)
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):
![Page 22: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/22.jpg)
Surface wave tomography--3D shear velocity models
can be used to formulate a linear inverse problem as we did before:
![Page 23: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/23.jpg)
Surface wave tomography--3D shear velocity models
can be used to formulate a linear inverse problem as we did before:
parameterize:
![Page 24: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/24.jpg)
Surface wave tomography--3D shear velocity models
can be used to formulate a linear inverse problem as we did before:
parameterize:
substitute:
![Page 25: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/25.jpg)
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:
![Page 26: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/26.jpg)
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:
![Page 27: Surface wave tomography--what are surface waveshestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2009-09-30 · Surface wave tomography--what are surface waves energy trapped](https://reader033.vdocuments.net/reader033/viewer/2022043011/5fa732dc852a161d86161111/html5/thumbnails/27.jpg)
The unique anisotropy of the pacific upper mantle
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Heterogeneity of crustal properties
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Sensitivity kernels K Love Rayleigh
long period
short period
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Sensitivity kernels K
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Sensitivity kernels K
Relevance of crustal correction and lateral variations of K