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An introduction to global seismic tomography
Institute of Geophysics course on seismic tomography, fall 2009
web: http://www.seg2.ethz.ch/boschil/tomography/tomography.html
to contact us: [email protected], [email protected]
or come visit, NO building, rooms H1.3, H62.
Institute of Geophysics course on seismic tomography, fall 2009
what is a tomographic model?
Institute of Geophysics course on seismic tomography, fall 2009
Early (pre-seismology) studies of Earth’s structure
Edmund Halley’s hollow Earth model (1692)
Late 19th century: development of the seismometer
John Milne
Filippo Cecchi
Late 19th century: development of the seismometer
The first signal recognized as coming
from a distant earthquake (Japan to
Potsdam, Germany) was identified
by E. von Rebeur-Paschwitz in 1889.
(From Nature, Vol. 40, 1889.)
Richard Oldham
Discovery of the Earth’s (outer) core (1906)
Richard Oldham
Discovery of the Earth’s (outer) core (1906)
Andrija Mohorovicic
Discovery of the MOHO discontinuity (1909 or 1910?)
Andrija Mohorovicic
Discovery of the MOHO discontinuity (1909 or 1910?)
Beno Gutenberg
Accurate measure of the core-mantle boundary--or
“Gutenberg discontinuity”--radius (1912)
Harold Jeffreys
The core is fluid (1926)
Inge Lehmann
Discovery of the Earth’s inner core (1936)
Inge Lehmann
P-wave paths
S-waves
Discovery of the Earth’s inner core (1936)
Project MOHOLE (1960s)
oil drillship called CUSS I (Continental Union Superior Shell)
Project NO-HOLE
oil drillship called CUSS I (Continental Union Superior Shell)
Kola drill (until 1992)
The deepest hole in the world (12 km)
Kola drill (until 1992)
The deepest hole in the world (12 km)
digging does not work, information has
to be “extracted” from seismograms
1960s-present: development of world-wide instrument networks
“Travel time” of certain seismic phases vs. epicentral distance
Preliminary Reference Earth Model (1981)
Don Anderson
Adam Dziewonski
Preliminary Reference Earth Model (1981)
back to seismograms
back to seismograms
Bulletin of the Seismological Society of America; July 1963; v. 53; no. 4; p. 741-764
© 1963 Seismological Society of America
Velocities of mantle Love and Rayleigh waves over multiple paths
M. NAFI TOKSÖZ and ARI BEN-MENAHEM
“… Phase velocities of Love waves over paths that lie far from each other are
different, and this difference is consistent and much greater than the
experimental error. From this it is concluded that there are lateral variations in
the structure of the earth's mantle…”
in practice, the problem consists of describing mathematically the
response of the Earth to an earthquake (or other seismic excitation).
in practice, the problem consists of describing mathematically the
response of the Earth to an earthquake (or other seismic excitation).
eq. of motion:
in practice, the problem consists of describing mathematically the
response of the Earth to an earthquake (or other seismic excitation).
eq. of motion:
small deformation tensor:
stress tensor:
What tomographers need is the relationship between
displacement u and Earth’s “structure”, ρ(r) λ(r) µ(r)
What tomographers need is the relationship between
displacement u and Earth’s “structure”, ρ(r) λ(r) µ(r)
After writing this relationship in an explicit form:
What tomographers need is the relationship between
displacement u and Earth’s “structure”, ρ(r) λ(r) µ(r)
After writing this relationship in an explicit form:
we can linearize it in a perturbative approach: