Lab 3_ Earthquakes F22 (Emma Born)
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Astronomy
Date
Dec 6, 2023
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18
Uploaded by DrFreedom7290
110 points total
Name: Emma Born
Lab Section:
EPS 50: Fall 2022
LAB 3: EARTHQUAKES
Due one week from today
at the start of your lab section
Introduction
Earthquakes are natural phenomena. The ground shaking is caused by a sudden release
of strain energy stored in rocks. In an earthquake, the stored elastic strain energy is
released through slip across a fault, and a portion is radiated as seismic waves. Seismic
waves tell us about the nature of the earthquake process itself, but they also provide a
direct sampling of the deep interior of the Earth. Much of what we know about the
structure of the Earth is a result of studying seismic waves.
1. Earthquake Location
Figure 1.
Fault systems in the Bay Area.
Figure 2.
The travel-time curve.
Once an earthquake occurs, the most important task of seismologists is to find the
earthquake location. The location of the earthquake is the foundation of earthquake
studies, and any further analysis (e.g., magnitude estimation, focal mechanism, damage
levels, etc.) relies on the precision of the earthquake location.
Knowing the locations of earthquakes is also essential when probing the interior of Earth.
Seismologists can interpret the Earth structure by using waveform and travel-time data
when they know the earthquake sources (locations). Various methods are used to locate
earthquakes, but the basic idea is simple triangulation. To apply this we need the absolute
arrival times
that the P-wave and S-wave reached each seismic station. Seismologists
use GPS (±5 μs) in tandem with the Internet to collect waveforms and correlate them into
absolute time from thousands of seismic stations around the world.
P waves
are the primary compressional (push-pull) waves and also the fastest seismic
waves.
S waves
are secondary waves characterized by traveling shear disturbances
(sideways motion). Accurate measurements of arrival time are compared to predicted
arrival times from an accepted model of the Earth (i.e., Figure 2). To achieve a more
accurate earthquake location and origin time, seismologists try to minimize the difference
between the observed and predicted wave arrival times.
Figure 2
illustrates the different wave speeds by comparing travel-time vs. distance
(travel
time curve)
for a representative model of the crust beneath the San Francisco Bay area.
Notice that P waves
always
take less time than S waves to arrive at the same point, and
the time separation between the P- and S-waves increases with increasing distance. This
separation is a very important general property used to locate earthquakes. Using a
measurement of S minus P wave time (
T
s-p
), the distance between the source and the
particular
recording
station
may
be
determined.
Several
estimates
of
this
specific
source-to-station distance and subsequent triangulation provide a good approximation of
the earthquake location.
For the event we will study in this lab, you are given two seismograms for each of five
stations shown in Figure 3. One seismogram recorded the ground motion in the E-W (BHE)
direction and the other, in the N-S (BHN) direction. The P wave is the first to arrive and
therefore the easiest to identify on the seismogram. The S wave arrival is more difficult to
determine, because it may be perturbed by the preceding P wave. However, the
S wave
can be distinguished by a relatively sharp increase in amplitude
. The x-axis is the
time (seconds) starting from 05:00:0.0 UTC (hrs:min:sec), and the y-axis is the amplitude
(mm). Be mindful of your measurements, as the scale of the y-axis (amplitude) varies
between each station’s seismograms (Figures 5-9).
2
Question 1 (5 pts)
Locate and circle five stations on the map in Figure 3. Use colored pencils to
trace over the fault systems, using a different color for each fault system. Label
the main systems using the fault names in Figure 1.
Answer 1
Figure 3.
Location of the five seismic stations amongst roughly NW-SE striking faults.
3
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Question 2 (2 pts)
Based on what you have learned about wave propagation, which of the five
stations
is the closest to the event and why? Refer to Figure 4 from the
seismogram packet.
Answer 2:
Based on figure 4, the MHC station is hit first, because it is the first station to
show any activity/readings
Question 3 (25 pts total)
A) Using Figures 5-9 (other handout), record the P- and S-wave arrival times
for each station in the table below using either the N-S (BHN) or E-W
(BHE) records. Indicate which one you use on the table. (10 pts)
B)
Calculate the T
s-p
times in seconds for the five stations. (5 pts)
C) Relate your T
s-p
times to the travel time curve to estimate the distance of
the earthquake source from each of the stations. (5 pts)
D) Use the travel time curve to determine when T
s-p
reaches the value you
recorded in the table. Then use the corresponding P-wave travel time to
determine the origin time of the earthquake. (5 pts)
4
Answer 3
TABLE 1
Seismic
station
N-S or E-W
seismograph
P-wave arrival
time
(hr:min:sec)
S-wave
arrival time
(hr:min:sec)
T
s-p
(sec)
Distance
(km)
Origin Time
(hr:min:sec)
MHC
N-S
5.00.38
5.00.43
5
40km
5.00.32
BKS
5.00.49
5.00.58
6
75km
5.00.38
PKD
5.00.53
5.01.03
10
80km
5.00.41
FARB
5.00.52
5.01.06
14
100km
5.00.37
CMB
5.00.56
5.01.07
11
95km
5.00.42
Question 4 (3 pts)
Using your data from all five stations in Table 1, calculate the average origin
time of this seismic event and the standard deviation.
Answer 4
Subtract each time (derived from the travel time curve) from the p-wave arrival time to
get the origin time for each station. Take the average and std of these times
The average origin time is (32+38+41+37+42)/5 = 38
Standard deviation = 3.52
5
2. Earthquake Triangulation
If we had only one seismic station, the earthquake source could technically be located
anywhere along the circumference of a circle centered on the receiver station whose radius
is equal to the travel time distance from Figure 2. With two seismic stations, we are able to
obtain two source-to-receiver-distances, i.e. two circles with different locations and radii.
The location of the earthquake will be one of the two points where these two circles
intersect. If we have three seismic stations and homogeneous topography (no lateral and
vertical change in the Earth), the
location of the earthquake will ideally be the point
where the three circles intersect
. Unfortunately, regional geological structure is usually
heterogeneous. As a result, three circles will not intersect at one point but rather over an
overlapping area, and the earthquake may be at any point in this area. The size of this
overlapping area represents the uncertainty of the earthquake location.
Question 5 (5 pts)
Use a compass and your estimated distances (from the table) as the circle radii
to draw a circle around each of the stations on Figure 3.
Question 6 (2 pts)
Shade the region of intersection of the curves you have drawn and comment on
the sources of error in estimating the earthquake location.
Answer 6
The intersection of the curves implies that the earthquake is located on the San
Andreas Fault line at roughly -122 latitude and 37.15 longitude, south of San
Jose
6
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Question 7 (2 pts)
Which
fault
did
this
earthquake
probably
occur
on?
Briefly
explain
your
reasoning.
Answer 7
Judging by the lines made in step 5, it seems that the Earthquake occurred on the San Andreas
Fault Line. the lines from the MHC, BKS, and FARB stations all overlap on the San Andreas
Fault Line
3. Earthquake Magnitude
Charles Richter introduced the concept of earthquake magnitude in 1935 by creating the
Richter magnitude scale. The
Richter magnitude
assigned to an earthquake depends on
the amount of seismic energy it releases.
The Richter scale is an arbitrary scale that gives
relative
earthquake magnitudes rather than
absolute magnitudes. Richter designed this scale such that a 1 mm ground motion
amplitude recorded by a Wood-Anderson instrument located 100 km away from the
earthquake source represents a magnitude 3 event. A 10 mm ground motion recorded by
the same instrument in the same distance from the earthquake source represents a
magnitude 4 event. In other words, a
one-unit increase in the
Richter
or
local
magnitude
means
a
10-fold
increase
in
amplitude
recorded
by
the
Wood-Anderson instrument
. The ground motion amplitude for a local magnitude 5 (M5)
event is 10x larger than a local magnitude 4 event (M4), but a local
M5 earthquake
releases ~32x more energy than an M4!
7
8
9
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The formula of the local magnitude scale is
M
L
= log(A) - C(r),
where M
L
is the Richter (local) magnitude, log(A) is the logarithm (base 10) of the observed
Wood-Anderson
amplitude
(mm),
and
C(r)
is
a
distance-dependent correction term.
Charles Richter compiled the table of C(r) values in Figure 10 and used this information to
develop the nomogram shown in the figure above.
Figure 10.
Richter magnitude correction factors.
10
Use Figure 10 to help answer the following questions:
Question 8 (4 pts)
Calculate how many times greater the amplitude of a local magnitude 4.7 is
compared to a magnitude 4.2, both recorded at a distance of 100 km. Show
your work.
Answer 8
4.7 = log(A_1) - (-3)
4.2 = log(A_2) - (-3)
A_1 = 50.12
A_2 = 15.85
How many times greater is the amplitude of 4.7 earthquake than a 4.2 earthquake:
A_1/A_2 = 3.16 times greater
Question 9 (2 pts)
How
many
times
more
energy
does
a
magnitude
8.0
earthquake
release
compared to a magnitude 5.0 earthquake? Show your work.
Answer 9
8-5 = 3
32^3 = 96
32,768x more energy
Question 10 (2 pts)
What
is
the
Richter
magnitude
of
an
earthquake
that
produces
a
1
mm
amplitude at a station 500 km away? Use the nomogram on pg. 8 to make this
estimate.
11
Answer 10
Using the Richter scale, the magnitude of an earthquake that produces 1mm amplitude at a
station 500 km away is 4.75
Question 11 (30 pts total)
Using Figures 4-10, measure the peak amplitudes (maximum height of waves) of
both
the
N-S
and
E-W
components
for
each station. Then determine the
individual M
L
using either the equation or the nomogram.
Answer 11
TABLE 2
Seismic
station
N-S
amplitude
(mm)
E-W
amplitude
(mm)
log(A
N-S
)
log(A
E-W
)
C(r)
M
L
(N-S)
M
L
(E-W)
MHC
280
320
2.45
2.50
-2.4
4.89
4.96
BKS
140
155
2.15
2.19
-2.8
4.95
4.99
PKD
60
50
1.78
1.7
-2.9
4.68
4.60
FARB
65
72
1.81
1.86
-3
4.84
4.86
CMB
26
26
1.41
1.41
-3
4.65
4.41
Question 12 (4 pts)
A)
Calculate the average magnitude (M
L
) of the earthquake and the standard deviation.
B) Briefly
discuss
some
probable
causes
of
the
“scatter”
in
your
estimated
magnitudes.
12
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Answer 12
A)
The average magnitude of the earthquake is 4.78
The standard deviation of the earthquake is 0.18
B)
The biggest sources of error in calculating the magnitude is reading the seismographs. Particularly
extracting the arrival time of S and P-waves as well as reading the amplitude off the graph
4. Focal Mechanisms
Seismologists
study not only slip and slip
direction
of
earthquakes
but
also
the
orientation
and
type
of
fault
movement
triggered
by
earthquakes.
The
focal
mechanism
describes
the
sense
of
deformation around the earthquake source
region.
The
stress-field
orientation
at
the
time
of
rupture governs the direction of slip on the
fault
plane,
and
the
“beach
ball”
(
focal
sphere
) depicts this stress orientation. The
direction
of
first
motion
of
the
seismicity
divides the focal sphere into quadrants of
compression
and
dilation
. The planes that
separate these quadrants are nodal planes,
one being the
fault plane
and the other the
auxiliary plane
, which are always 90° apart.
Seismologists estimate the focal mechanism
based
on
information
gathered
from
seismograms and represent it with a “beach
ball” symbol on the map. Fault planes (middle
column
of
Figure
11)
will
intersect
the
hemisphere as a curve. The two curved lines
on the 2D projection (map view) of the focal
spheres are the
stereographic projections
of
13
the fault and auxiliary planes onto the surface. In this scheme, the
shaded quadrants
represent compression
, and the
white quadrants represent dilation.
Figure 11.
Focal mechanisms.
The first three examples in Figure 11 describe fault motion that is either purely horizontal
(strike
slip)
or vertical (normal or reverse). The last two examples describe
oblique
mechanisms
which
illustrate
that
the
slip
motion
has
both
horizontal
and
vertical
components.
Question 13 (6 pts)
Draw arrows along each fault plane to show the relative motion of each fault
block.
Name the type of fault (reverse, normal, strike-slip) that each block
diagram represents.
Answer 13
Fault type:______________
Fault type:______________
Fault type:______________
Question 14 (12 pts)
Draw
the
cross-section
and
map
views
of
the
focal
sphere
(beach
ball
diagrams) for each fault type below. Refer to Figure 11 on the previous page for
diagram examples.
14
Answer 14
Fault Type
Cross Section View
Map View
Strike-slip
N
N
Normal
N
N
15
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Reverse
N
N
Question 15 (6 pts)
Examine the focal mechanisms, shown in map view, associated with each
earthquake event area in the diagrams below. Indicate in the white boxes if
each mechanism corresponds to a strike-slip fault (SSF), normal fault (NF),
reverse fault (RF), or oblique fault (OF) rupture.
16
5. Earthquake Preparedness
*BONUS* (5 pts)
Living
in
California,
it
is
especially important to take the
proper steps to be as prepared
as
possible
for
earthquake
hazard events. After visiting the
link below, list 5 items (besides
food
and
water)
that would be
most useful for you to include in
17
your earthquake evacuation “go-bag”.
https://www.earthquakecountry.org/library/Margin_Step_3_Infographics_Flyer.pdf
*BONUS*
Five items in my earthquake evacuation ‘go-bag’
-
Dust mask + goggles
-
First aid supplies + emergency blanket
-
Copies of ID/ important documents
-
Batteries, battery pack, charging cables
-
Tools!
18
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