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Elastic Rebound Theory

This theoryy was discovered byy making
g
measurements at a number of points across a
fault.

Prior to an earthquake it was noted that the
rocks adjacent to the fault were bending
bending. These
bends disappeared after an earthquake
suggesting that the energy stored in bending the
rocks was suddenly released during the
earthquake.
Elastic Rebound Theory
Elastic Rebound
Sequence of elastic rebound: Stresses
Sequence of elastic rebound: Bending
Sequence of elastic rebound: Rupture
Sequence of elastic rebound: Rebound
Sudden Slip by Elastic
Rebound

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Stresses (force/area) are applied to a fault
fault.
Strain (deformation) accumulates in the
vicinity of friction
friction-locked
locked faults
faults.
Strain accumulation reaches a threshold
and
d ffaultlt slips
li suddenly
dd l
Rupture (slip) continues over some portion
of the fault. Slip is the distance of
displacement along a fault.
Fault
A ffracture
t
(crack)
(
k) in
i the
th earth,
th where
h
th
the ttwo sides
id move
past each other and the relative motion is parallel to the
fracture.
90˚ dip = vertical fault plane
0˚ strike = north parallel fault plane
Surface Trace of a
fault
Different Fault Types
n)
shear)
Normal DipDip-slip fault
hanging wall moves down
A Normal dip slip
fault
Reverse DipDip-slip fault
Hanging wall moves up
Thi iis also
This
l called
ll d a Thrust
Th
t
Fault.
A reverse dip-slip
fault
Strike--slip fault
Strike
Displacement in horizontal directio
A strike-slip fault
Strike--Slip
Strike
p Fault – Left Lateral
Strike--Slip
Strike
p Fault – Right
g Lateral
Oblique--slip fault
Oblique
Displacement in both
vertical and horizontal
directions
An oblique-slip fault
Blind/Hidden faults
Sequence of Events





1) Tectonic loading of faults
2) Earthquakes
3) Seismic
S i i waves
4) Shaking (ground motion)
5) Structural failure
Seismic Waves
(Earthquake’s energy is transmitted through the
earth as seismic waves)

Two types of seismic waves

Body waveswaves- transmit energy through earth’s
interior
Pi
Primary
(P) wavewave- rocks
k vibrate
ib t parallel
ll l to
t direction
di
ti
of wave
 Compression and expansion (slinky example)
 Secondary (S) wave
wave-- rocks move perpendicular to
wave direction
 Rock shearing (rope
(rope--like or ‘wave’ in a stadium)


Surface waves
waves-- transmit energy along earth’s
surface
Rock moves from side to side like snake
 Rolling
R lli pattern like
lik ocean wave

Primary waves
P-waves,
compressional or
longitudinal.
Typical
crustal velocity: 6 km/s (
~13,500 mph)
Travel
T
l
th
through
h solids,
lid liliquids,
id or
gases
Material
movement is in the same
direction as wave movement
Behavior:
Cause dilation and
contraction (compression) of the earth
material through which they pass.
Arrival:
They arrive first on a
seismogram
seismogram.
Even for P waves
(which can travel all
the way through) we
see some changes in
the path at certain
points within Earth.
This is due to the
discontinuities present
at different boundaries
in earth structure
Secondary waves






S waves (secondary)
Typical crustal velocity: 3 km/s
( ~6,750 mph)
Behavior: Cause shearing and
stretching
t t hi off the
th earth
th material
t i l
through which they pass.
Generally cause the most
g; very
y
severe shaking;
damaging to structures.
Travel through solids only
shear waves - move material
perpendicular to wave
movement
Arrival: Second on a
seismogram
seismogram.
S-wave velocity drops
to zero at the coremantle boundary or
Gutenberg
Discontinuity
Shadow Zone - no earthquake waves
Variation of P and S wave velocities within the
earth
M disc
M-disc
G disc
G-disc
M-Disc : The Mohorovicic
discontinuity
G-disc: The Gutenberg
di
discontinuity
ti it
Surface Waves
Travel
a e
just be
below
o or
o along
a o g the
t e
ground’s surface
Slower
than body waves;
rolling and side
side--to
to--side
movement
Especially
b ildi
buildings
damaging to
Two most common types of surface
waves
Rayleigh Waves



Typical
yp
velocity:
y ~ 0.9
that of the S wave
Behavior: Causes
vertical together with
back-and-forth horizontal
motion. Motion is similar
to that of being in a boat
in the ocean when a
swell moves past.
Arrival: They usually
arrive last on a
seismogram.
Love Waves



Typical
yp
velocity:
y Depends
p
on earth structure, but
less than velocity of S
waves.
Behavior: Causes
shearing motion
(horizontal) similar to S
waves.
Arrival: They usually
arrive after the S wave
and before the Rayleigh
wave.
Primary Waves
Secondary Waves
Movement of Earth
Locating an Earthquake’s Epicenter
Seismic wave behavior
 P waves arrive first, then S waves, then L and R
 After an earthquake
earthquake, the difference in arrival times at a
seismograph station can be used to calculate the distance
from the seismograph to the epicenter (D).
If average speeds for all these waves is known, use the
S P (S minus P) time formula: a method to compute the
S-P
distance (D) between a recording station and an event.
Distance
Velocity
P wave has a velocity VP ; S wave has a velocity VS .
VS is less than VP .
Both originate
g
at the same place--the
p
hypocenter.
yp
They travel the same distance
but the S wave takes more time than the P wave.
D
Time for the S wave to travel a distance D: TS 
;
VS
D
Time for the P wave to travel a distance D: TP 
.
VP
The time difference
Time 
TS  TP 
 1
V VS 
D D
1 

 D    D P

VS VP
VS VP 
 VP VS 
Now solve for the Distance D:
 V V 
D =  P S TS  TP 
VP VS 
Seismic TravelTravel-time Curve: If the speeds of the seismic
waves are not known, use Travel
Travel--Time curve for that region
to g
get the distance
1. Measure time
between P and S
wave on
seismogram
i
2. Use traveltime graph to get
distance to
epicenter
Global Travel Time Curve
3-circle method:
3-circle steps:
1) Read S-P time from
3 seismograms.
north
D1
D2
2) Compute distance for
each
h event/recording
t/
di
station pair (D1, D2, D3)
using S-P time formula.
3) Draw each circle of
radius Di on map.
4) Overlapping point is
the event location.
D3
Assumption: Source is
relatively shallow;
epicenter is relatively
close
l
tto h
hypocenter.
t