Lecture 13

Lecture 13 - •  Surface displacement or fault slip 1964...

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Unformatted text preview: •  Surface displacement or fault slip 1964 Alaska earthquake displaced some parts of the seafloor by ~ 50 ft vertically. 1906 San Francisco earthquake shifted the San Andreas fault up to 24 ft horizontally, and 8-10 ft, on average, along much of the rupture. •  Size of area displaced Alaska: 70,000 square miles. •  Duration of strong shaking From seconds (for small earthquakes) to several minutes (for large earthquakes). •  Magnitude (quantitative measure) Based either on the amplitude of ground motion recorded on a seismograph or on the amount of energy released. •  Intensity (qualitative measure) Based on extent of damage and human perception. I.  People do not feel any Earth movement. II.  A few people might notice movement if they are at rest and/or on the upper floors of tall buildings. III.  Many people indoors feel movement. Hanging objects swing back and forth. People outdoors might not realize that an earthquake is occurring. IV.  Most people indoors feel movement. Hanging objects swing. Dishes, windows, and doors rattle. The earthquake feels like a heavy truck hitting the walls. A few people outdoors may feel movement. Parked cars rock. V.  Almost everyone feels movement. Sleeping people are awakened. Doors swing open or close. Dishes are broken. Pictures on the wall move. Small objects move or are turned over. Trees might shake. Liquids might spill out of open containers. VI.  Everyone feels movement. People have trouble walking. Objects fall from shelves. Pictures fall off walls. Furniture moves. Plaster in walls might crack. Trees and bushes shake. Damage is slight in poorly built buildings. No structural damage. VII. People have difficulty standing. Drivers feel their cars shaking. Some furniture breaks. Loose bricks fall from buildings. Damage is slight to moderate in well-built buildings; considerable in poorly built buildings. VIII. Drivers have trouble steering. Houses that are not bolted down might shift on their foundations. Tall structures such as towers and chimneys might twist and fall. Well-built building suffer slight damage. Poorly built structures suffer severe damage. Tree branches break. Hillsides might crack if the ground is wet. Water levels in wells might change. IX. Well-built buildings suffer considerable damage. Houses that are not bolted down move off their foundations. Some underground pipes are broken. The ground cracks. Reservoirs suffer serious damage. X. Most buildings and their foundations are destroyed. Some bridges are destroyed. Dams are seriously damaged. Large landslides occur. Water is thrown on the banks of canals, rivers, lakes. The ground cracks in large areas. Railroad tracks are bent slightly. XI. Most buildings collapse. Some bridges are destroyed. Large cracks appear in the ground. Underground pipelines are destroyed. Railroad tracks are badly bent. XII. Almost everything is destroyed. Objects are thrown into the air. The ground moves in waves or ripples. Large amounts of rock may move. VII. People have difficulty standing. Drivers feel their cars shaking. Some furniture breaks. Loose bricks fall from buildings. Damage is slight to moderate in well-built buildings; considerable in poorly built buildings. •  Earthquake
magnitude
is
a
quan2ta2ve
measure
of
earthquake
size.
 •  Magnitudes
of
different
earthquakes
allow
us
to
compare
their
rela2ve
sizes.
 •  “Earthquake
size”,
strictly
speaking,
refers
to
the
amount
of
energy
released
by
 the
earthquake.

However,
some
es2mates
of
magnitude
give
only
the
amount
 of
energy
contained
in
the
seismic
waves
generated
during
fault
rupture.
 •  There
are
a
variety
of
ways
to
es2mate
magnitude
(all
directly
measured
from
 seismograms),
with
none
being
perfect.
For
that
reason,
and
the
fact
that
the
 earth
is
a
heterogeneous
body
and
waves
don’t
radiate
equally
in
all
direc2ons, es2mates
of
the
magnitude
of
a
par2cular
earthquake
by
different
seismic
 sta2ons
at
different
points
around
the
globe
will
invariably
differ.
 •  Magnitudes
determina2ons
range
from
totally
empirical
(no
direct
connec2on
 to
the
physics
of
earthquakes)
to
semi‐physical
(some
connec2on
to
the
 physics).
 •  Richter magnitude scale: A logarithmic scale based on the maximum amplitude of ground motion recorded on a standard seismograph at a distance of 100 km from the earthquake. No upper or lower limit. Moment magnitude scale: A logarithmic scale based on the amount of energy released by the earthquake. Energy is the best estimate of earthquake size. Proportional to (rupture area)x(slip). •  •  The
idea
is
similar
to
that
of
astronomers
who
grade
the
size
of
stars
using
a
 magnitude
scale
based
on
their
rela2ve
brightness
as
seen
through
a
telescope.
 •  Richter
decided
to
grade
the
size
of
an
earthquake
based
on
the
rela2ve
 amplitudes
of
their
ground
mo2ons
(seismic
waves)
as
recorded
on
a
 seismogram.
 •  Because
the
size
of
earthquakes
varies
enormously
(as
does
the
brightness
of
 stars),
the
size
of

the
ground
mo2ons
(shaking)
differs
by
factors
of
thousands
 from
earthquake
to
earthquake.
 •  Thus,
it
is
useful
to
compress
the
range
of
reported
magnitudes
to
a
much
fewer
 set
of
numbers
(quan2ta2ve
measures).
 •  Richter
adopted
the
logarithmic
approach
(followed
by
all
later
magnitude
 scales),
where
numbers
are
replaced
by
their
logarithm
(to
the
base
10).
 •  For
example: 
 
 
log101
=
0,

log1010
=
1,

log10100
=
2,

log101000
=
3,

etc.
 
log100.1
=
‐1,

log100.01
=
‐2,

log100.001
=
‐3,

etc. 

 •  By
Richter’s
defini2on,
if
a
par2cular
earthquake
happens
to
be
exactly
100
 kilometers
away
from
the
seismographic
sta2on
and
records
a
maximum
 amplitude
of
10
microns
on
the
seismograph,
it
will
have
a
magnitude
of
1
 (log1010
=
1).
 •  If
another
earthquake
at
the
same
distance
is
recorded
with
an
amplitude
of
 1
micron,
it
will
have
a
magnitude
of
0
(log101
=
0).
 •  Now
if
a
third
earthquake
at
the
same
distance
is
recorded
with
an
 amplitude
of
one
tenth
(1/10)
micron,
it
will
have
a
magnitude
of
‐1
 (log101/10
=
log1010‐1
=
‐1).

This
would
be
equivalent
to
about
one
gram
of
 explosive
or
a
single
hammer
blow!
 •  The
Richter
Magnitude
scale
(or
for
that
maVer,
any
magnitude
scale)
has
no
 upper
or
lower
limit,
although
the
largest
size
of
an
earthquake
is
limited
by
 the
strength
of
the
rocks
of
the
earth’s
crust.

It
turns
out
that,
based
on
the
 historic
record,
this
limit
appears
to
be
somewhere
between
magnitude
9
 and
10.
 •  The
original
Richter
Magnitude
approach
proved
to
be
ineffec2ve
for
distant
 earthquakes
–
modifica2ons
were
needed.
 wire support weight Ground Determination of Richter Magnitude For
more
distant
earthquakes,
in
order
to
make
reliable
comparisons
between
earthquakes
of
 different
sizes,
it
became
necessary
to
use
other
informa2on
from
the
seismograms,
rather
 than
simply
the
maximum
amplitude.
 However,
these
other
“scales”
retained
the
logarithmic
approach
according
to
the
following
 rela2onship:
 M
=
log10(A/T)
+
Correc2on
for
distance
+
Regional
scale
factor
 where
A
is
the
amplitude
(in
microns)
of
the
signal
(adjusted
for
the
par2cular
seismograph
 being
used)
and
T
is
the
dominant
period
(in
seconds)
of
the
signal
whose
amplitude
is
being
 measured.
In
the
case
of
Richter
Magnitude,
T
≈
1
sec
and:
 ML
=
log10A
+
2.76log10Δ
‐
2.48
 for
southern
California
(Δ
is
the
distance
from
earthquake
to
observing
sta2on
(kilometers),
 and
A
is
measured
in
millimeters).
 Body
wave
magnitude,
mb,
uses
the
first
few
seconds
on
a
seismogram
from
a
distant
 earthquake
(teleseism)
with
periods
ranging
from
1
to
3
seconds.
 mb
=
log10A/T
+
Q(h,Δ)
 where
Q
is
derived
for
different
regions
of
the
earth
and
depends
on
both
focal
depth,
h,
 and
distance,
Δ.
The
amplitude,
A,
is
measured
in
microns.
 Surface
wave
magnitude,
MS,
uses
the
largest
amplitude
of
the
surface
waves
(typically
 with
periods
of
20
seconds).
 MS
=
log10A20
+
1.66log10Δ
+
2.0
 where
A20
is
the
amplitude
of
20‐second
surface
waves
in
microns.
 However,all
of
these
magnitude
scales
underes2mate
the
size
of
the
largest
earthquakes.
 We
need
something
beVer.
 Seismic
Moment
and
Moment
Magnitude
 •  Since
total
energy
release
by
an
earthquake
is
a
be<er
measure
of
earthquake
 size
than
the
amplitude
of
a
par?cular
wave
on
a
seismogram,
seismologists
 turned
to
the
classical
theory
of
mechanical
systems
and
introduced
the
no?on
 of
“seismic
moment”.
 •  Seismic
moment
is

is
an
es?mate
of
the
work
done
during
stress
and
strain
 build‐up.
It
is
equivalent
to
a
force
ac?ng
over
a
distance.
 •  The
work
is
then
stored
in
the
form
of
poten?al
(strain)
energy
which
is
 released
by
a
rupturing
fault
during
elas?c
rebound.
 •  It
can
be
shown
that
seismic
moment,
M0,
is
given
by:
 M0
=

(strength
of
the
rock)
x
(rupture
area)
x
(fault
slip)
 •  M0
can
be
determined
from
either
field
observa?ons
of
fault
dimensions
and
 slip,
or
certain
characteris?cs
of
the
seismic
waves
recorded
on
seismograms.
 •  But
just
as
before,
seismic
moments
range
over
many
orders
of
magnitude
 from
the
smallest
to
the
largest
earthquakes.
 Seismic
Moment
and
Moment
Magnitude
(con?nued)
 So
just
as
before,
we
return
to
the
logarithmic
approach
in
order
to
generate
a
magnitude
 scale
based
on
seismic
moment.

We
call
this
the
moment
magnitude.
 Moreover,
it
is
desirable
to
correlate
(as
closely
as
possible)
the
moment
magnitude
with
 other
magnitude
scales
where
they
are
both
reliable
(at
the
lower
magnitudes).
 The
following
formula
takes
care
of
both
of
these
issues.
We
call
the
moment
magnitude
 MW:
 MW
=
2/3log10M0
‐
6.0
 where
M0
must
be
given
in
MKS
units.
 •  Largest earthquake ever recorded had a moment magnitude of 9.5 (Chile, 1960). (Rocks are not strong enough to store more energy). •  Earthquakes less than M = 2 are generally not felt by people. •  Magnitude scales are logarithmic: An increase of 1 unit = 10 times greater amplitude of ground motion up to about a M=6.5, at which point the ground motions no longer increase by a factor of 10, and the Richter method of magnitude determination breaks down. Moment magnitude becomes a more reliable estimate of earthquake size for larger events.   Why
does
the
Richter
magnitude
break
down
at
M
=
6.5?
 •  It
can
be
shown
that
the
rela2onship
between
magnitude
and
energy
(in
MKS
 units)
is
given
by:
 

 
 
E
=
10(4.8
+
1.5M)
 •  This
means
that
for
each
unit
increase
in
magnitude
(say
from
M4
to
M5)
the
 energy
increases
by
101.5
=
32
?mes.
 •  Up
to
M6.5,
a
factor
of
32
increase
in
energy
produces
a
ten‐fold
increase
in
 wave
amplitude,
and
the
Richter
Magnitude
works.

However,
as
the
 earthquakes
get
bigger,
the
amplitude
no
longer
increases
by
a
factor
of
10
for
 each
32‐fold
increase
in
energy,
and
so
the
Richter
magnitude
underes2mates
 the
size.
 •  The
reason
has
to
do
with
the
fact
that
the
energy
from
a
big
earthquake
no
 longer
emanates
from
approximately
a
single
point
as
in
the
case
of
smaller
 events.
Rather
its
rupture
may
be
tens
or
even
hundreds
of
kilometers
long
 with
the
energy
release
spread
out
over
a
large
region.
This
effec2vely
 "moderates"
the
wave
amplitudes
and
puts
more
energy
in
low‐frequencies.
 Earthquakes
and
explosives
–
A
comparison
 

Richter 
 Magnitude 




TNT
for 
 
Energy
Yield 













Seismic
Example
 
 
 
(approximate)
 ‐1.5 
 
6
ounces

 
 

Breaking
a
rock
on
a
lab
table
 
1.0 
 
30
pounds
 
 

Large
Blast
at
a
Construc?on
Site
 
1.5 
 
320
pounds
 
2.0 
 
1
ton



 
 
 

Large
Quarry
or
Mine
Blast
 
2.5 
 
4.6
tons
 
3.0 
 
29
tons
 
3.5 
 
73
tons



 
4.0 
 
1,000
tons



 
 
Small
Nuclear
Weapon
 
4.5 
 
5,100
tons




 
 
Average
Tornado
(total
energy)
 
5.0 
 
32,000
tons
 
5.5 
 
80,000
tons



 
 
Li<le
Skull
Mtn.,
NV
Quake,
1992
 
6.0 
 
1
million
tons


 
 
Double
Spring
Flat,
NV
Quake,
1994
 
6.5 
 
5
million
tons




 
Northridge,
CA
Quake,
1994
 
7.0 
 
32
million
tons



 
 
Largest
nuclear
weapon
 
7.5 
 
160
million
tons



 
 
Landers,
CA
Quake,
1992
 
8.0 
 
1
billion
tons



 
 
San
Francisco,
CA
Quake,
1906
 
8.5 
 
5
billion
tons



 
 
Anchorage,
AK
Quake,
1964
 
9.0 
 
32
billion
tons



 
 
Chilean
Quake,
1960
 10.0 
 
1
trillion
tons



 
 
San‐Andreas
type
fault
circling
Earth
 12.0 
 
160
trillion
tons



 
 
Fault
Earth
in
half
through
center,
or
 
 
Earth's
daily
receipt
of
solar
energy
 
 
 
 
 Magnitude
versus
Ground
Mo?on
and
Energy

 Magnitude
Change 


Ground
Mo?on
Change 
Energy
Change
 
 
 








(Displacement)
 
1.0 
 
0.5 
 
0.3 
 
0.1 
 
 
 
 
 
10.0
?mes 


3.2
?mes 


2.0
?mes 


1.3
?mes 
 
 
 
 
about
32
?mes
 
about
5.5
?mes
 
about
3
?mes
 
about
1.4
?mes Important
note:

The
ground
mo2on
changes
indicated
above
only
hold
for
 magnitudes
less
than
about
M6.5.
Above
M6.5
the
ground
mo2ons
do
not
 increase
as
rapidly.
 ...
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