An introduction to global seismic tomography

Institute of Geophysics course on seismic tomography, fall 2009

Institute of Geophysics course on seismic tomography, fall 2009

web: http://www.seg2.ethz.ch/boschil/tomography/tomography.html

to contact us: lapo@erdw.ethz.ch, husen@sed.ethz.ch

or come visit, NO building, rooms H1.3, H62.

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

Filippo Cecchi John Milne

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

Discovery of the Earth’s inner core (1936)

P-wave paths S-waves

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)

The deepest hole in the world (12 km)

Kola drill (until 1992)

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: