Sound Waves and Seismic Waves
• Seismologists record and analyze waves to determine
where an earthquake occurred and how large it was
• Waves are fundamental to music and seismology
• Similarities:
– More high frequency waves if short path is traveled
• Trombone is retracted, short fault-rupture length (small earthquake)
– More low frequency waves if long path is traveled
• Trombone is extended, long fault-rupture length (large earthquake)
ISNS 4359 Earthquakes and Volcanoes
(aka shake and bake)
Lecture 6: Locating EQ’s, EQ Magnitude
and Intensity
Fall 2005
Seismic Velocity
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Seismic velocity is a material property (like density).
There are two kinds of waves – Body and Surface waves.
There are two kinds of body wave velocity – P and S wave velocities.
P waves always travel faster than S waves.
Seismic velocities depend on quantities like chemical composition,
pressure, temperature, etc.
Faster Velocities
Slower Velocities
• Lower temperatures
• Higher temperatures
• Higher pressures
• Lower pressures
• Solid phases
• Liquid phases
Locating the Source of an Earthquake
• P waves travel about 1.7 times faster than S waves
• Farther from hypocenter, greater time lag of S wave
behind P wave (S-P)
• (S-P) time indicates how far away earthquake was
from station – but in what direction?
Locating the Source of an Earthquake
• Need distance of earthquake from three stations to
pinpoint location of earthquake:
– Computer calculation
– Visualize circles drawn around each station for appropriate
distance from station, and intersection of circles at
earthquake’s location
– Method is most reliable when earthquake is near surface
Fig. 4.23
Solution to epicenter and hyopcenter
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Mathematically, the problem is solved by setting up a system of linear
equations, one for each station.
The equations express the difference between the observed arrival times and
those calculated from the previous (or initial) hypocenter, in terms of small
steps in the 3 hypocentral coordinates and the origin time.
We must also have a mathematical model of the crustal velocities (in
kilometers per second) under the seismic network to calculate the travel times
of waves from an earthquake at a given depth to a station at a given distance.
The system of linear equations is solved by the method of least squares which
minimizes the sum of the squares of the differences between the observed and
calculated arrival times.
The process begins with an initial guessed hypocenter, performs several
hypocentral adjustments each found by a least squares solution to the
equations, and iterates to a hypocenter that best fits the observed set of wave
arrival times at the stations of the seismic network.
Magnitude of Earthquakes
• Richter scale
– Devised in 1935 to describe magnitude of
shallow, moderately-sized earthquakes
located near Caltech seismometers in
southern California
– Bigger earthquake Æ greater shaking Æ
greater amplitude of lines on seismogram
– Defined magnitude as ‘logarithm of
maximum seismic wave amplitude recorded
on standard seismogram at 100 km from
earthquake’, with corrections made for
distance
– For every 10 fold increase in recorded
amplitude, Richter magnitude increases one
number
Magnitude of Earthquakes
• Richter scale
– With every one increase in Richter magnitude, the energy
release increases by about 45 times, but energy is also
spread out over much larger area and over longer time
– Bigger earthquake means more people will experience
shaking and for longer time (increases damage to
buildings)
– Many more small earthquakes each year than large ones,
but more than 90% of energy release is from few large
earthquakes
– Richter scale magnitude is easy and quick to calculate, so
popular with media
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Magnitude of Earthquakes
Magnitude of Earthquakes
Magnitude of Earthquakes
21,688 earthquakes recorded by NEIC in 1998
http://www.iris.iris.edu/volume2000no1/RevFigure2.big.gif
Magnitude of Earthquakes
21,688 earthquakes recorded by NEIC in 1998
http://www.iris.iris.edu/volume2000no1/RevFigure2.big.gif
Other Measures of Earthquake Size
• Richter scale is useful for magnitude of shallow,
small-moderate nearby earthquakes
• Does not work well for distant or large earthquakes
– Short-period waves do not increase amplitude for bigger
earthquakes
– Richter scale:
• 1906 San Francisco earthquake was magnitude 8.3
• 1964 Alaska earthquake was magnitude 8.3
– Other magnitude scale:
• 1906 San Francisco earthquake was magnitude 7.8
• 1964 Alaska earthquake was magnitude 9.2 (100 times more
energy)
Other Measures of Earthquake Size
Two other magnitude scales:
• Body wave scale (mb):
– Uses amplitudes of P waves with 1 to 10-second periods
• Surface wave scale (ms):
– Uses Rayleigh waves with 18 to 22-second periods
• All magnitude scales are not equivalent
– Larger earthquakes radiate more energy at longer periods
not measured by Richter scale or body wave scale
– Richter scale and body wave scale significantly
underestimate magnitudes of earthquakes far away or
large
Moment Magnitude Scale
• Seismic moment (Mo)
– Measures amount of strain energy released by movement
along whole rupture surface; more accurate for big
earthquakes
– Calculated using rocks’ shear strength times rupture area
of fault times displacement (slip) on the fault
• Moment magnitude scale uses seismic moment:
– Mw = 2/3 log10 (Mo) – 6
– Scale developed by Hiroo Kanamori
Foreshocks, Main Shock and Aftershocks
• Large earthquakes are not just single events but part
of series of earthquakes over years
– Largest event in series is mainshock
– Smaller events preceding mainshock are foreshocks
– Smaller events following mainshock are aftershocks
• Large event may be considered mainshock, then
followed by even larger earthquake, so then reclassified as foreshock
Magnitude, Fault-Rupture Length and
Seismic-Wave Frequencies
• Fault-rupture length greatly influences magnitude:
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100 m long fault rupture Æ magnitude 4 earthquake
1 km long fault rupture Æ magnitude 5 earthquake
10 km long fault rupture Æ magnitude 6 earthquake
100 km long fault rupture Æ magnitude 7 earthquake
Magnitude, Fault-Rupture Length and
Seismic-Wave Frequencies
• Fault-rupture length and duration influence seismic
wave frequency:
– Short rupture, duration Æ high frequency seismic waves
– Long rupture, duration Æ low frequency seismic waves
• Seismic wave frequency influences damage:
– High frequency waves cause much damage at epicenter
but die out quickly with distance from epicenter
– Low frequency waves travel great distance from
epicenter so do most damage farther away
Ground Motion During Earthquakes
• Buildings are designed to handle vertical forces
(weight of building and contents) so that vertical
shaking in earthquakes is typically safe
• Horizontal shaking during earthquakes can do
massive damage to buildings
• Acceleration
– Measure in terms of acceleration due to gravity (g = 9.8
m/s2)
– Weak buildings suffer damage from horizontal
accelerations of more than 0.1 g
– In some locations, horizontal acceleration can be as much
as 1.8 g (Tarzana Hills in 1994 Northridge, California
earthquake)
Periods of Buildings and
Responses of Foundations
Just as waves have natural frequencies and periods, so
do buildings
• Periods of swaying are about 0.1 second per story
– 1-story house shakes at about 0.1 second per cycle
– 30-story building sways at about 3 seconds per cycle
• Building materials affect building periods
– Flexible materials (wood, steel) Æ longer period of
shaking
– Stiff materials (brick, concrete) Æ shorter period of
shaking
Periods of Buildings and
Responses of Foundations
Velocity of seismic wave depends on material it is
moving through
• Faster through hard rocks
• Slower through soft rocks
• When waves pass from harder to softer rocks, they
slow down
• Must therefore increase their amplitude in order to
carry same amount of energy Æ greater shaking
• Shaking tends to be stronger at sites with softer
ground foundations (basins, valleys, reclaimed
wetlands, etc.)
Periods of Buildings and
Responses of Foundations
• If the period of the wave matches the period of the
building, shaking is amplified and resonance results
– Common cause of catastrophic failure of buildings
Earthquake Intensity –
What We Feel During an Earthquake
• Mercalli intensity scale was developed to quantify
what people feel during an earthquake
• Used for earthquakes before instrumentation or
current earthquakes in areas without instrumentation
• Assesses effects on people and buildings
• Maps of Mercalli intensities can be generated
quickly after an earthquake using people’s input to
the webpage http://pasadena.wr.usgs.gov/shake
Earthquake Intensity –
What We Feel During an Earthquake
What To Do Before and
During an Earthquake
• Before an earthquake:
– Inside and outside your home, visualize what might fall
during strong shaking, and anchor those objects by
nailing, bracing, tying, etc.
– Inside and outside your home, locate safe spots with
protection – under heavy table, strong desk, bed, etc.
• During an earthquake:
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Duck, cover and hold
Stay calm
If inside, stay inside
If outside, stay outside
Mercalli Scale Variables
Mercalli intensity depends on:
• Earthquake magnitude
– Bigger earthquake, more likely death and damage
• Distance from hypocenter
– Usually (but not always), closer earthquake Æ more damage
• Type of rock or sediment making up ground surface
– Hard rock foundations vibrate from nearby earthquake body
waves
– Soft sediments amplified by distant earthquake surface waves
– Steep slopes can generate landslides when shaken
Mercalli Scale Variables
Mercalli Scale Variables
Mercalli intensity depends on:
• Building style
– Body waves near the epicenter will be amplified by rigid
or short buildings
– Low-frequency surface waves are amplified by tall
buildings, especially if on soft foundations
• Duration of shaking
– Longer shaking lasts, more buildings can be damaged
Design of Buildings in
Earthquake-Prone Areas
• Eliminate resonance:
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Change height of building
Move weight to lower floors
Change shape of building
Change building materials
Change attachment of building to foundation
Hard foundation (high-frequency vibrations) Æ build tall,
flexible building
– Soft foundation (low-frequency vibrations) Æ build
short, stiff building
Design of Buildings in
Earthquake-Prone Areas
• Floors, Roofs and Trusses
– Give horizontal resistance by transferring force to vertical
resistance elements
• Shear Walls
– Designed to receive horizontal forces from floors, roofs and
trusses and transmit to ground
– Lack of shear walls typically cause structures like parking
garages to fail in earthquakes
Design of Buildings in
Earthquake-Prone Areas
• Bracing
– Bracing with ductile materials offers resistance
• Moment-resisting frames
– Devices on ground or within structure to absorb part of
earthquake energy
– Use wheels, ball bearings, shock absorbers, ‘rubber
doughnuts’, etc. to isolate building from worst shaking
A Case History of Mercalli Variables: The San
Fernando Valley, California, Earthquake of 1971
• Earthquake magnitude
– M 6.6, with 35 aftershocks of magnitude 4.0
or higher
• Distance from epicenter
– Bull’s-eye damage pattern
• Foundation materials
– Not a major factor
• Building style
– ‘Soft’ first-story buildings were major
problem
– Hollow-core bricks at V.A. Hospital caused
collapse
– Collapse of freeway bridges
Fig. 4.32
A Case History of Mercalli Variables: The San
Fernando Valley, California, Earthquake of 1971
• Duration of shaking
– Lasted 12 seconds (at that magnitude, can last from 10 to 30
seconds), relatively short time
– Lower Van Norman Reservoir
• 11,000 acre-feet of water behind earthen dam, above homes of 80,000
• When shaking stopped, only four feet (of original 30) of dam was still
standing above water level
• Another few seconds of shaking might have caused catastrophic flood
Fig. 4.29
Fig. 4.30
Fig. 4.33a
Fig. 4.33b
Fig. 4.34
Problem Set 1, Journals, Term Paper
• Problem set 1 and term paper format will be
available on WebCT by tomorrow morning.
• Problem set 1 will now be due on Sept 20, rather than
Sept 15.
• Submit a topic for approval for term paper by Sept
22, if you have not already done so
• Journals - to reiterate - track 1 event (EQ or V) per
week for four weeks and submit a journal on what
you find. Length and format is up to you, but all
work (other than figures) should be original and all
sources cited