LECTURE 4 - Seismology
Hrvoje Tkalčić
Late Professor Bruce A. Bolt
(1930-2005)
with a model of
Chang Heng’s seismoscope
*** N.B. The material presented in these lectures is from the principal textbooks, other
books on similar subject, the research and lectures of my colleagues from various
universities around the world, my own research, and finally, numerous web sites. Some
colleagues to whom I am grateful for the material I used are: B. Bolt, P. Wu, B. Kennett,
E. Garnero, E. Calais and D. Dreger. I am thankful to many others who make their
research and teaching material available online; sometimes even a single figure or an
idea about how to present a subject is a valuable resource. Please note that this
Earthquakes as natural disasters: can we predict them?
San Francisco, 1906
Tokyo-Yokohama, 1923
• Victims in Banda Aceh, Indonesia, after the SumatraAndaman earthquake and tsunami in 2004
Pakistan, 2005
Strong motion simulation in SF Bay Area
A simulation of the San Simeon
earthquake, CA, through a model
of 3D structure. This is achieved
using a numerical finite difference
method on a grid of points.
Berkeley
The main wave front is visibly
refracted or bent by contrasts in
the velocity across both the
Hayward and San Andreas faults.
Concentrations of high amplitude
standing waves persist throughout
the movie around San Jose and in
San Pablo Bay. These areas are
low-velocity sedimentary basins
and cause the amplitudes of
ground motion to be amplified as
well as extend the duration of the
motions.
Both of these factors increase the
level of hazard to structures.
Oakland
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San
Francisco
San Jose
A simulation movie
Courtesy of Prof. Douglas Dreger, UC Berkeley and Dr. Shawn Larsen, LLNL
Seismology as a tool
for probing the internal
structure of the Earth
Global shear velocity structure
Lithospheric structure under Australia
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Li and Romanowicz 1996
van der Hilst, Kennett and Shibutani 1998
C ompressional
velocity
structure in the
lowermost mantle
Some examples
of seismic
tomography
Tkalčić, Romanowicz and Houy 2002
The beginnings
An artist’s conception of the Chinese scholar Chang Heng
contemplating his seismoscope. Balls were held in the dragons’
mouth by lever devices connected to an internal pendulum. The
direction of the first main impulse of the ground shaking was reputed
to be detected by the particular ball that was released.
Early seismographs and advances in seismology
• John Milne - constructed the first reliable
seismograph in 1892
• F. Reid - elastic rebound model in 1906 after the
Great San Francisco Earthquake and fire
Earthquakes happen on preexisting faults
• A notion that the core is needed to explain seismic
travel time proposed by R, Oldham in 1906
Emil Wiechert (1861-1928)
The 1200 kg Wiechert seismograph for measuring
horizontal displacements
Probing the Earth with seismology:
European discoverers of seismic discontinuities
Andrija Mohorovičić (1857-1936)
Beno Gutenberg (1889-1960)
Inge Lehmann (1888-1993)
Crust-Mantle boundary 1910
Mantle-Core boundary 1914
Inner Core 1936
Recipe for longevity: study the inner core!
The Earth’s Interior
CRUST-MANTLE BOUNDARY
Mohorovičić discontinuity (Moho)
(1910)
CORE-MANTLE BOUNDARY
Discovered by B. Gutenberg
(1914)
INNER CORE
Discovered by I. Lehmann
(1936)
* For Comparison: Pluto discovered in 1931
Berkeley Seismographic Station
•The first seismographs in the western hemisphere
installed at the University of California Berkeley campus
in 1887 (largely due to the interest of astronomers).
•The occurrence of the San Francisco Great Earthquake
and Fire in 1906 began a new era in seismology.
Portion o seismograms recorded by the short-period verticalcomponent seismograph at the Jamestown station of the
University of California Berkeley network. The wave packet
A is the core phase P4KP, and B isP7KP. These exotic
seismic phases are multiple reflections from the lower side
of the core mantle boundary.
The east-west component of ground motion at the Berkeley
station recorded by the Bosch Omori seismograph on March
10, 1922, from an earthquake source near Parkfield,
California.
The recording is part of the basis of the "Parkfield Prediction
Experiment" (1988 ± 5 years). Reproduced on a wine label
printed for the Centennial Symposium, May 28–30, 1987.
Seismographs on the Moon
APOLLO 11
Astronaut Edwin E. Aldrin Jr., lunar module pilot, is
photographed during the Apollo 11 extravehicular activity on
the Moon. He has just deployed the Early Apollo Scientific
Experiments Package (EASEP). In the foreground is the
Passive Seismic Experiment Package (PSEP); beyond it is
the Laser Ranging RetroReflector (LR-3); in the left
background is the black and white lunar surface television
camera; in the far right background is the Lunar Module.
Astronaut Neil A. Armstrong, commander, took this
photograph with a 70mm lunar surface camera.
APOLLO 14
Astronaut Alan B. Shepard Jr., foreground, Apollo 14
commander, walks toward the Modularized Equipment
Transporter (MET), out of view at right, during the first Apollo
14 extravehicular activity (EVA-1). An EVA checklist is
attached to Shepard's left wrist. Astronaut Edgar D. Mitchell,
lunar module pilot, is in the background working at a
subpackage of the Apollo Lunar Surface Experiments
Package (ALSEP). The cylindrical keg-like object directly
under Mitchell's extended left hand is the Passive Seismic
Experiment (PSE).
Hooke’s Law of elasticity
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When a force is applied to a material, it deforms: stress induces strain
– Stress = force per unit area
– Strain = change in dimension
For some materials, displacement is reversible = elastic materials
– Experiments show that displacement is:
• Proportional to the force and dimension of the solid
• Inversely proportional to the cross-section
– One can write: ΔL  FL/A
– Or ΔL/L  F/A
– Strain is proportional to stress = Hooke’s law
– Hooke’s law: good approximation for many
Earth’s materials when ΔL is small
1660 Robert Hooke
Stress and strain
Stress-strain relation:
Elastic domain
• Stress-strain relation is linear
• Hooke’s law applies
Beyond elastic domain
• Initial shape not recovered when stress is removed
• Plastic deformation
• Eventually stress > strength of material => failure
Failure can occur within the elastic domain = brittle behavior
Strain as a function of time under stress
• Elastic = no permanent strain
• Plastic = permanent strain
What is the mathematical relation between stress and strain?
Normal strain
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x1
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The series expansion of u1:
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Shear strain
Stress and strain
x2
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For small deformations:
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The series expansion of u2:
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and since u2(A)=0:
x1
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Shear tensor
Dilatation
For products of
u, v, w ≈ 0
Stress
Stress and strain
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Internal traction (stress):
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The stress field is the distribution of internal "tractions" that
balance a given set of external tractions and body forces.
Stress tensor:

ij
=
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
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Normal to the surface upon
which the stress acts

xx
=
for strain
11, 
xy=

ij
Direction of the
stress component
12 etc. using the notation we used
A cubic element in static equilibrium
For a medium to be in stable
equilibrium, the moments must sum to
zero. Moments are given by the product
of a force times the perpendicular
distance from the force to a reference
point. Let’s consider a moment around
x3 axis first:
As x1, x2 -> 0, we have 12= 21
Similarly, for the moments around x1 and
x2 axes, 13= 31 and 23= 32.
Thus, stress tensor is also symmetric,
with 6 independent elements.
The most general form of Hooke’s law
 ij  Cijklkl
The constants of proportionality, Cijkl are elastic moduli. We saw that the both strain and stress
tensors are second-order tensors, which are symmetric and have 6 independent elements. Cijkl
is thus a third-order tensor and in its most general form consists of 81 elements. However, since
the strain and stress tensors only have 6 independent elements, the number of independent
elements in Cijkl can be reduced to 36.
The first stress element is related to the strain elements by:

 ij  C111111  C111212  C111313  C112121  C112222  C112323  C113131  C113232  C113333
For an isotropic medium (material properties independent on direction or orientation of
sample), the number of elastic moduli can conveniently be reduced to only 2. These elastic
moduli are called the Lamé constants  and .
 ij  ij  2ij
where ij is Krönecker delta function (ij=0 when ij and ij=1 when i=j).
This was formulated by Navier in 1821 and Cauchy in 1823.
Definitions of elastic moduli - from Lay and Wallace book