Download P-wave compression propagating wave

Did you feel it? That side to side, up and down, ground-shaking motion felt by many Californians
every year, not to mention folks all around the world. The shaking motion is referred to as an
earthquake, quake, or tremor. In any case, you are feeling a sudden release of energy or
vibrations propagating through the earth as a result of shifting masses of the earth’s crust. The
created vibrations are in the form of seismic waves, similar to dropping a stone in a pond of calm
water and watching the ripples emanate from a central point. Areas of the earth producing
earthquakes are typically associated with stress (forces) building between shifting plates,
specifically at plate boundaries. Once the buildup of stresses has exceeded the elastic limits of the
particular rocks involved, potential energy converts to kinetic energy, and movement of the
earth’s crust takes place, or the crust “snaps” and releases seismic waves. Three types of seismic
waves are released: the primary wave, secondary wave (body waves), and surface waves.
The Primary Wave or P-Wave
The primary wave, referred to as the P-wave, is the fastest moving wave and travels through both
solid and liquid media. As this wave propagates through the earth’s media, it compresses the
material, similar to the action of a playing accordion. Therefore, this wave is also known as a
compressional wave. The diagram below depicts the P-wave motion:
P-wave compression
propagating wave
The primary wave or P-wave is propagating
through the earth’s surface. Note the circled
areas being compressed. After compression,
the media is expanded (dilation). The P-wave
motion traverses through both liquids and
solids.
The Secondary Wave or S-Wave
The secondary wave, referred to as the S-wave, travels approximately 2/3 the speed of the P-wave.
As the S-wave propagates through the earth’s media, it subjects the crust to sheering motions,
where particles move up and down at right angles. This can be analogous to using a pair of shears
or scissors when cutting. Shearing motions will move through solids but NOT liquids. For example,
have you ever tried to use scissors and cut water? The diagram below depicts the S-wave motion:
S-wave Shearing
propagating wave
The S-wave is propagating through the
earth’s surface. Note the arrows showing
how material is sheared and/or moving up
and down at right angles. The S-wave
motion travels through solids only, not
liquids.
The Surface Waves (L-Waves and Rayleigh Waves)
Surface waves are the slowest waves propagating through earth and represent the most destructive
type of waves since they primarily move across the surface. In other words, these waves are
primarily felt by humans. Due to the motions of surface waves, they can be divided into two types
of waves: the Love wave (L-wave) and Rayleigh wave (R-wave). Motions of the L-wave are
characterized by the ground moving in a side-to-side direction, and the L-wave is the fastest of the
two surface waves. Motions of the R-wave are characterized by rolling the surface up and down.
This is analogous to sitting in a boat on the ocean going up and down from the body of water
moving beneath you. Because the R-wave creates a rolling motion in the direction of wave
propagation, most shaking on the earth’s surface is primarily caused by the R-wave. The diagram
below shows the motion of both the L and R waves.
This is the motion of both the L-wave and
R-wave. Note the side-to-side motion
shown with the L-wave and the rolling
motion depicted in the R-wave. Both
waves are characterized by slow-moving
waves and propagate across the surface.
Measuring the Energy Released by Earthquakes
Mercalli Scale of Intensity
The Mercalli scale of measuring earthquake intensity was invented by Giuseppe Mercalli in 1902.
This particular scale relies on damage observations stated by people who witnessed and
experienced the earthquake. Ultimately, by observing various types of damage, people estimate
the earthquake’s intensity. The Mercalli scale is based on the Roman numeral system from I to XII.
Roman numeral I indicates the least intensity while Roman numeral XII is used to show the highest
intensity. How reliable or scientific is the Mercalli scale? Some observers of the earthquake may
exaggerate the intensity, or in some cases, two witnesses may not agree with what happened to the
same area with respect to the intensity. Additionally, different building codes applied to various
communities all over the world may give the illusion of less or more damage with the same energy
release. In other words, different parts of the world would experience various damage reports
caused by the earthquake and not accurately record the real strength of the quake. Below is the
Mercalli Intensity chart with damage reports and associated Roman numerals. In 1934, Charles
Richter recognized the “people factor” when measuring the intensity of earthquakes and invented
the Richter scale, in which one can calculate the magnitude of an earthquake eliminating the
inconsistent observations of individuals.
Here is the Mercalli Intensity
scale showing Roman numerals
assigned to various types of
damage. Damage is reported
by people and assigned a
Roman numeral. Reports of
damage are very subjective, and
the Mercalli scale does not prove
scientifically reliable for
measuring the actual amount of
energy release during an
earthquake.
The Richter Scale
From 1934 to the early 1970’s, the magnitude of earthquakes was measured using the Richter
scale. Richter magnitudes are calculated based on the largest wave amplitude recorded on a
seismogram. Amplitude lines are recorded on the seismogram by incoming P, S, and surface
seismic waves. The diagram below shows a seismogram with amplitudes from both P and Swaves. Note the largest amplitude recorded on the S-wave.
Largest
amplitude
P-wave
arrival
S-wave
arrival
The seismogram represents incoming
P and S-waves. Note the recorded
amplitudes on both P and S-waves.
The largest amplitude is noted on the
S-wave arrival.
Richter magnitudes (M1, M2, M3,….) are based on a logarithmic scale using base 10. For
example, for each Richter magnitude increase, the amplitude of the ground motion recorded by a
seismograph increases by a factor of ten. Therefore, a magnitude 4 (M4) would result in ten times
the level of ground shaking as an M3 earthquake and consequently release 32 times more energy.
How much ground shaking and energy release would one expect between an M3 and M5?
ANS: One would calculate that 2 Richter magnitudes have occurred (5M – 3M = 2 Richter
magnitudes). Therefore, since each Richter is equal to an increase in amplitude by a factor
of ten, then 10 x 10 = 100. The amplitude increased by 100 times, or there is 100 times more
ground shaking. The energy released between M3 and M5 can be calculated by multiplying
32 x 32 (each Richter releases 32 times the energy), so energy release is approximately 1000
more times.
How much ground shaking and energy release would one expect between an M6 and M3?
Use the above answer, and make your own calculations.
The amount of energy released from different earthquake magnitudes can be analogous to the
energy released by explosives. For example, an M1 release of energy is equivalent to the energy
release from blowing up 6 ounces of TNT. However, an M8 would release as much energy as
detonating 6 million tons of TNT. Note the logarithmic or exponential increase in energy between
each Richter magnitude.
Given the logarithmic nature of the Richter scale, it has no upper limit. Therefore, earthquakes can
theoretically be measured up to M10 and beyond – can’t imagine the energy release from quakes
greater than M10.
The Richter scale assumes the focus of the earthquake at a single point and is best suited for
energy release in small areas. Additionally, the intensity of the earthquake is based on amplitude
measurements. To accurately measure the actual energy release from earthquakes, scientists
have now made other magnitude scales, namely the Moment magnitude scale developed in the
1970’s and currently used by the USGS. The Moment magnitude scale is calibrated to incorporate
Richter magnitudes and considers waves propagating through different rock properties.
Determining Earthquake Magnitude
Interpreting the Seismogram / Determining the Earthquake Magnitude
Determining the magnitude of an earthquake requires accurate interpretation of the seismogram.
From the seismogram, a seismologist measures the wave amplitude height and S-P time interval.
A typical seismogram will show a “squiggly” straight line, which is considered background noise
during non-earthquake activity. When earthquake activity begins, the P-wave arrives and is
interpreted as the first “jog” in wave activity (bigger than the background noise). The P-wave
recordings will continue until the second “jog” on the recorder (larger than the recorded P-waves).
The second large “jog” is interpreted as the first S-wave arrival. The S-P time interval represents
the time difference between the first appearance of the P-wave (first “jog”) and the first appearance
of the S-wave (second “jog”). In other words, the S-P interval is equal to the P-wave arrival time
subtracted from the S-wave arrival time. The diagram below depicts a typical seismogram showing
the amplitude height and S-P interval.
The seismogram shows arrivals of P and
S-waves, wave amplitude, and the S-P
interval. To calculate the S-P interval,
subtract the P-arrival time from the
S-arrival time. The S-P interval for this
seismogram is:
38 seconds
P-arrival time = 0 seconds
S-arrival time = 38 seconds
S-arrival time – P-arrival time:
38 sec – 0 sec = 38 sec
S-P interval is 38 seconds
Typically, S-P intervals can be calculated directly from time intervals indicated on the seismogram
as shown in the above diagram. However, in some cases, time intervals for P and S-wave arrivals
are given, and one must calculate the S-P interval. For example, arrival times may be given using
the military time clock. Below are examples of P and S wave arrival times using the military clock.
P- wave arrival time
S-wave arrival time
S-P interval
21 hr, 32 min, 40 sec
21 hr, 33 min, 10 sec
30 seconds
15 hr, 23 min, 19 sec
15 hr, 24 min, 5 sec
46 seconds
3 hr, 16 min, 32 sec
3 hr, 17 min, 13 sec
____________
19 hr, 43 min, 12 sec
19 hr, 43 min, 52 sec
____________
Once the S-P interval and amplitude are correctly interpreted from the seismogram, the magnitude
and distance to the epicenter is determined for that particular seismograph. The values
representing the S-P interval and amplitude wave height are plotted on the magnitude chart on the
following page. Graphically plot the S-P interval. Graphically plot the amplitude. Construct a line,
using a straight edge, from the plotted S-P interval to the plotted amplitude. The line will pass
through the magnitude scale revealing the earthquake magnitude for the indicated S-P interval and
amplitude height. Additionally, once the S-P interval is plotted along the S-P interval line, the
epicenter distance is determined by observing the value adjacent to the plotted S-P interval.
The chart below shows how the magnitude of an earthquake is determined:
Using the chart, the magnitude of
an earthquake is determined as
well as the distance to the
epicenter.
In this case the S-P interval is 24
seconds, and amplitude is 23
mm. The line connecting both the
S-P interval and amplitude
passes through the magnitude
scale resulting in an M5
earthquake. Using the S-P
interval time, the distance to the
epicenter is determined to be
approximately slightly greater
than 200 km.
The Triangulation Method for Locating the Epicenter
The use of triangulation provides a method for locating the epicenter of an earthquake.
Triangulation involves the use of three or more seismic stations recording the same seismic waves
during an earthquake at different distances from the epicenter. Distances to the epicenter can be
determined by the S-P time interval from each seismic station. Using the seismic station as the
center point, circles can be drawn with the epicenter distances represented by the radius of each
circle. After constructing at least 3 circles, the intersection of all three circles determines the point
or location of the epicenter. The diagram below shows the triangulation method and location of an
epicenter.
SS-B
SS-A
Distance
radius
Triangulation is used to determine the
location of epicenters. Note that 3
seismic stations (SS-A,B,C) are used
along with circle radii representing the
distance from each seismic station to
the epicenter. Epicenter distances are
determined from S-P intervals.
The intersection of all three circles
represent the epicenter location.
SS-C
epicenter
LAB EXERCISES
PART A: Earthquake Definitions
Provide the definition for each vocabulary term listed below:
earthquake
seismic waves
potential energy
kinetic energy
primary wave
secondary wave
surface waves
Mercalli Scale
amplitude
Richter Scale
S-P time interval
triangulation
PART B: P, S, and Surface Waves and the Earth’s Interior
1. Draw a colored diagram that represents the propagated motion of the P-wave, and list three
distinct characteristics.
2. Draw a colored diagram that represents the propagated motion of the S-wave, and list three
distinct characteristics.
3. Draw a colored diagram that represents the propagated motions of both the Love wave (Lwave) and Raleigh wave (R-wave). Identify at least 2 characteristics each for both waves.
4. Given the diagram below (the layered earth) and your descriptive wave characteristics in
questions 1, 2, and 3, how do scientists understand the layered nature of our earth? Label
the interior parts of the earth, and show how the P and S-waves move through the interior
acting as predictors regarding the earth’s internal layers.
The Earth’s Interior
PART C: Measuring the Magnitude of Earthquakes
Reading a seismogram
1. Find the S-P time intervals.
S-P time interval __________________________________
S-P time interval ___________________________________
2. Given the P-wave arrival of 21h 45m 34s, S-wave arrival of 21h 46m 09s, what is the S-P
time interval?
3. Given the P-wave arrival of 19h 16m 17s, S-wave arrival of 19h 16m 52s, what is the S-P
time interval?
4. Given the P-wave arrival of 22h 32m 42s, S-wave arrival of 22h 33m 13s, what is the S-P
time interval?
5. An earthquake is recorded at three different seismic stations (A, B and C).
(Station A) P-wave arrival 20h 12m 56s, S-wave arrival 20h 13m 22s
(Station B) P-wave arrival 20h 12m 40s, S-wave arrival 20h 12m 49s
(Station C) P-wave arrival 20h 13m 12s, S-wave arrival 20h 13m 44s
Indicate the proximity of each seismic station A, B, and C to the epicenter.
Which stations would report the greatest and least Mercalli intensity values?
PART C: Measuring the Magnitude of Earthquakes
Using the magnitude chart below, answer questions 1, 2, and 3.
1. Given the P-wave arrival of 10h 26m 41s and S-wave arrival of 10h 27m 13s and with an
amplitude of 8mm, fill in the blanks below:
S-P time interval _____________
Magnitude
_____________
Epicenter distance _____________
2. Given the P-wave arrival of 14h 19m 22s and S-wave arrival of 14h 19m 40s and amplitudes
of 0.3mm and 4mm, fill in the blanks below:
S-P time interval _____________
Magnitude
_____________
Epicenter distance ___________
3. Given the S-P interval of 10 seconds and wave amplitude of 0.4mm, fill in the following
blanks:
a. What is the Richter magnitude ?
__________
b. If the amplitude were 40mm, what is the Richter magnitude?
_________
c. Given answer b, the amplitude increased by a factor of
__________
d. Given answer c, the Richter magnitude increased by a factor of
__________
e. If the amplitude were 4mm, the Richter magnitude =
__________
f. If the amplitude were 400mm, the Richter magnitude =
__________
g. If the amplitude were 0.04mm, the Richter magnitude =
__________
4. Given the seismogram below, label the P-wave and S-wave arrivals and fill in the blanks
below. The wave amplitude is .5 mm.
S-P interval ________
EQ magnitude _________ Epicenter distance ______
PART D: Locating Epicenters Using the Triangulation Method
1. Seismic activity is recorded at 3 separate seismic stations from the same earthquake.
Given the world map (handout), as a seismologist, determine the location of the
epicenter using the triangulation method. Accuracy when determining S-P intervals,
epicenter distances, plotting longitude/latitude locations, and compass settings is
extremely crucial to proper triangulation.
1. Obtain the handout that includes the world map, seismograms, and the time
difference vs. distance to epicenter chart.
2. Fill in the table below using data provided from question 1.
Seismic
station
P-wave
arrival time
S-wave
arrival time
S-P time
Interval (min)
Distance to
epicenter (km)
Honolulu
Sitka
Charlotte
3. Plot the longitude and latitude locations for each city (Honolulu, Sitka, and Charlotte)
on the world map.
4. Using your epicenter distances, construct circles from each city location. Use the
provided compasses, and match the distance scale on the world map with proper
compass opening.
5. Once your circles have been constructed and your S-P intervals accurately
determined (epicenter distances and compass techniques are extremely accurate),
the circles should show an intersection point.
6. From question 5, the epicenter of this earthquake is ______________, which is
located at ________________ longitude and __________________ latitude.
7. Measure the highest amplitude using the seismogram generated from Sitka, Alaska.
Determine the magnitude of the earthquake.
The earthquake magnitude is ____________.
2. Seismic activity is recorded at 3 separate seismic stations from the same earthquake.
Given the California map (handout), as a seismologist, determine the location of the
epicenter using the triangulation method.
1. Obtain the handout that includes the California map, seismograms, and the time
difference vs. distance to epicenter chart. Below are latitude/longitude
readings for the California seismograph stations.
Bakersfield:
San Francisco
San Diego
35.4O N. Latitude, -119.0O W. Longitude
37.8O N. Latitude, -122.4O W. Longitude
32.7O N. Latitude, -117.2O W. Longitude
2. Follow the directions outlined in the previous question, and determine the location of
the California epicenter.
Seismic
station
P-wave
arrival
S-wave
arrival
S-P time
interval
Distance to
epicenter (mi)
Bakersfield
San Francisco
San Diego
3. Using a map of California, determine the epicenter of this earthquake. The epicenter is
located at _____________________.
4. Given the location of the epicenter, what plate boundary does the epicenter represent?
Critical Thinking Questions:
1. An M7 magnitude earthquake takes place and three seismic stations at different
locations record the incoming waves. What is the magnitude of the earthquake at
each station? Explain your answer.
2. Given your answer in question 1, describe how the S-P time intervals would differ at
each seismic station. Draw a picture that would represent the S-P time interval from
the closest, middle and farthest seismic station.
3. Given your answer in question 2, how does the Mercalli scale relate to the proximity
of each seismic station from the epicenter and reported damage?