Techniques for Mapping Theoretical Shadow Zones for Direct P
and S Waves Propagated as Rays from an Earthquake Epicenter
Richard L. Kroll
Department of Geology and Meteorology, Kean University, Union, N.J. 07083,
[email protected]
John F. Dobosiewicz
Department of Geology and Meteorology, Kean University, Union, N.J. 07083
[email protected]
ABSTRACT
This paper presents results about the effectiveness of different student-centered instructional methods on undergraduate student perceptions of a spatial phenomenon,
earthquake P and S wave shadow zones, in introductory
geology classes. Textbooks commonly illustrate earthquake P and S wave shadow zones using ray tracing
techniques with an epicenter at the North Pole and the
shadow zone south of the equator. Shadow zones differ
for earthquake locations elsewhere. Shadow zones for
earthquakes at locations around the world can be hand
plotted using a globe and a map of the Earth. The plotter
gains experience in using latitude and longitude for plotting, understanding global geography, translating spherical geographic data to a two-dimensional map, and
gains a better understanding of seismic waves and the
Earth's interior. The concept also explains how satellite
orbits appear on flat maps and the concept of great circle
paths. The shadow zone can also be mapped digitally using a Geographic Information System (GIS), such as
ArcView GIS with the similar results. Overall, 81.5% of
the student participants considered both instructional
methods an enhancement to their understanding of the
earth's interior, globes, maps and shadow zones. The results suggest that student alternate conceptions of the
representation of geospatial data in 2D and 3D can be influenced by both traditional paper exercises and activities that teach with GIS technology.
INTRODUCTION
time maps and uses values of 103° to 140°
(http://earthquake.usgs.gov/recenteqsww/Quakes/
quakes_all.html).
Problems exist, however, with the traditional
portrayal of the shadow zone. While the shadow zone
concept originally was validated by recordings from
primitive low sensitivity seismographs, modern
techniques and analysis indicate the reality is more
complicated. The concept of the shadow zone arises from
treating seismic waves as rays. However, P and S wave
waveforms are spherical and they refract, reflect and
diffract as they propagate. P and S waves do indeed
appear in the classically portrayed shadow zone in
several ways. Some diffract along the core-mantle
boundary (Wyession and Baker, 2002). Other waves
enter the shadow zone by refraction through the inner
core. Wysession and Baker (2002) demonstrate that wave
tracing using a normal mode summation algorithm
produces a more realistic representation of seismic
waves than ray tracing techniques, and this simulation
illustrates how waves appear in the shadow zone. The
location of the ray shadow zone also varies depending
upon seismic velocity models used. For example, Stein
and Wysession (2003, p. 167) indicate a zone from 98° to
145°.
Although it is a simplification, the shadow zone still
has value as an instructional tool. Recognition of the
shadow zone first suggested the presence and size of the
core (Oldham, 1906) and the shadow zone concept
illustrates the effect of varying seismic velocity with
depth. Typical shadow zone representations using ray
tracing techniques use a cross-section of the Earth with
an epicenter at the North Pole and the shadow zone as a
belt south of the equator between 103° and 143° south
latitude. This is fine for an earthquake that occurs at the
North Pole and this shadow zone around the Earth is
easily visualized on a globe or map. But few (if any?)
earthquakes occur at the North Pole, so the diagrams do
not apply to, as students like to say, "the real world."
Students also get the impression that an orderly, precise
shadow zone exists in this location south of the equator.
Earthquakes may and do occur almost anywhere so the
resulting shadow zones can be located in many places
across the globe (Figures 1 and 2). Hence, students gain a
better understanding of the relationship between the
Earth's interior and paths of seismic waves by mapping
the shadow zone for an earthquake epicenter anywhere
on Earth and thus determining if direct P and S waves
should be expected to be recorded at a specific
seismograph location. Determining a shadow zone for a
specific earthquake is an interesting and motivating
laboratory activity that augments understanding of the
nature of seismic waves, the structure of Earth's interior,
and the concept of a shadow zone.
Most introductory geology courses cover seismology
and earthquakes and many institutions have local
seismographs for research or demonstration purposes
that are used to explain the generation of seismograms.
For example, a home-made Lehman seismograph is
running at the authors' institution (see Kroll, 1987, and
Gerencher and Jackson, 1991, for instructions and further
references). The concept of the compression and shear
wave seismic shadow zone is often discussed. The
shadow zone results from the properties of P and S
waves as they encounter the earth's low velocity liquid
core. Shear waves cannot be transmitted through a liquid
and so are converted to P waves or reflected at the
surface of the liquid outer core. Compression waves
refract at the mantle-core boundary and are bent from
their original path (Murphy and Nance 1999, p. 185).
The shadow zone phenomenon is illustrated in
virtually all introductory geology/earth science texts
that deal with seismology, earthquakes, and the internal
structure of the Earth. It has been traditional content for
decades with most texts using an angular distance of
103° to 143° as the boundaries of the zone (see for
example: Monroe and Wicander, 2001, p. 202; Hamblin METHODS
and Christiansen, 2001, p. 528; Skinner, Porter, and
We have developed two activities for visualizing and
Botkin, 1999, p. 97). The USGS seismology/earthquake
web-site denotes the shadow zone on its P-wave travel mapping shadow zones. The exercise is introduced after
596
Journal of Geoscience Education, v. 54, n. 5, November, 2006, p. 596-602
Figure 1. P and S wave shadow zone for an earthquake
near Kean University, Union Township, New Jersey
created from measurements from a globe transferred
to a world Mercator map projection by plotting Figure 2. P and S wave shadow zone for an earthquake
latitude and longitude.
occurring in Newark, NJ (the city nearest to Kean
University, Union Township, New Jersey in the ESRI
world cities shapefile) created using ArcMap 9.0 GIS.
The latlong shapefile (latitude and longitude) consists
of 5° grids.
Figure 3. Students in an undergraduate introductory
geology class demonstrating the technique using a
globe and angular distance measured with a strip or
string to create a hand plotted shadow zone.
a lecture discussing the nature of seismic waves and how
the shadow zone was used to postulate an Earth core.
The shadow zone concept arises from considering the
waves as geometric rays rather than spherical
wavefronts. The first method is plotting a P-S wave
shadow zone for an epicenter located anywhere on the
Earth by hand, using a three dimensional globe and a
two dimensional map based on a Mercator Projection.
The second method is visualizing and generating the
same shadow zone digitally using a Geographic
Information System (GIS) such as Arcview GIS. This
software has been used effectively in the K-12 and
undergraduate education communities for Earth Science
activities (Ramirez 1996; Hall-Wallace and McAuliffe
2002; Stewart, Schneiderman, and Andrews 2001).
The first method involves translating coordinate
points from a three dimensional globe to a two
dimensional map. First, an epicenter is identified and
located on the globe. Then a band is sketched around the
globe at angular distances of ≈103° and ≈143° from the
epicenter and these points are translated to a two
dimensional map. Translation of points from the globe to
the map gives a different visual representation of a
Kroll and Dobosiewicz - Mapping Theoretical Shadow Zones
shadow zone. This difference is analogous to the way
orbits of the space shuttle or other satellites appear on a
flat map.
The activities in this paper effectively support data
about seismic waves that our relatively low-sensitivity
homemade Lehman seismograph records. Students
become more engaged and interested in geology and
geologic hazards when they use hands-on activities to
learn about earthquakes and see our seismograph and
understand its operation. Many students hear of
earthquakes in the news and commonly ask, "Did we
pick it up? Was it in our shadow zone?" Equipped with a
shadow zone map one can determine whether or not the
direct P and S waves from a distant earthquake would be
expected to be detected by our local seismograph. We
have experienced this directly for earthquakes in Japan.
Our seismograph recorded the October 1994 Hokkaido
Province earthquake but did not record the direct P and S
waves of the January, 1995, Kobe earthquake in the
Shikoko Province. The angular distance from Hokkaido
Island to Union, NJ is less than 103°, whereas the angular
distance of Kobe is on the fringe of the theoretical
shadow zone. Students questioned why we have had
measurements from some earthquakes in a country
(Japan) and not others. Japan seemingly covers a
relatively small area of the Earth's surface but our
(Union, N.J.) shadow zone bisects the provinces of Japan.
The GIS-based activity allows for querying geographic
attribute data easily, and supports the observations from
our local seismograph.
HAND PLOTTING THE P-S WAVE SHADOW
ZONE
Materials
Earth globe sufficiently detailed to show latitude and
longitude in 10° or 15° intervals.
8 1/2 x 11 in. or larger map of the Earth, with latitude and
longitude lines.
597
1 inch wide strip of paper long enough to go at least 150
degrees around the globe, or somewhat longer piece of
string (extra length needed for gripping ends).
Procedure
1.
2.
3.
4.
5.
Place one end of the paper or string at the North Pole
and stretch it towards and past the equator directly
towards the South Pole. Locate an angular distance
of 103° from the North Pole (13° S. latitude) and mark
the paper or string.
Locate the starting end (north pole end) of the paper
or string at your location (or another specific
location) on the globe. Stretch the paper or string
around the globe and note the latitude and longitude
of the 103° mark (Figure 3). Translate this point to the
map. If convenient, a significant geographic point
may be used in lieu of latitude and longitude, as long
as it can be found on the map.
Move the paper or string around the globe and locate
about another 15 to 20 such points and mark each on
the map. Draw the line on the map connecting the
points. This line on the map marks the initiation of
the shadow zone at 103° away from your location or
epicenter.
Repeat the process for the 143° points.
The resulting map is the shadow zone an earthquake
occurring in Union Township, New Jersey, the
location of Kean University (Figure 1).
Given the location of an earthquake anywhere on the
Earth, students can use this map to determine whether or
not they are in its shadow zone and whether direct
earthquake P and S waves might have been detected.
Figure 4. Arcview GIS screenshot for selecting a city
A DIGITALLY GENERATED P-S WAVE
SHADOW ZONE MAP
The materials needed are the world data shapefiles
(latlong.shp (line file); country.shp (polygon file) and cities.shp (point file) provided with ESRI Arcview Software. The detailed student activity, explicitly for
ArcMap (Arcview v. 9.x*) is available for download at
http://hurri.kean.edu/~dobosiewicz. For other versions of Arcview please contact the authors.
Efforts were made to develop a scripted activity for
students and faculty with no GIS experience that could
be completed with minimal assistance from a GIS
professional. . Participants map the shadow zone for an
earthquake in Newark, New Jersey, a city in the ESRI
world data file that is close to Kean University in New
Jersey. Data management is an important aspect of
working with GIS projects in a class that has no GIS
experience. A GISDATA folder should be created on the
local C: drive and data files should be placed into this
folder in order to follow the steps in the procedure
explicitly. The shadow zone in Figure 2 is comparable to
the hand plotted shadow zone in Figure 1. It is easier to
use the ESRI world files that contain major cities than to
create a new point theme for specific coordinates.
Advanced GIS users can create a point file based on
latitude and longitude, maybe even derived from a GPS
unit, to use as the epicenter if they choose.
The following steps highlight some of the key GIS
skills and commands utilized in the activity for students
to perform spatial data exploration and querying and to
investigate map projections and coordinate systems.
598
by an attribute (Newark, NJ) using a Boolean
expression.
1.
2.
3.
Select by Attributes: A Boolean expression is used to
identify a city where an earthquake occurs (Figure 4)
Change the Data View: To use a predefined
continental projected coordinate system that allows
for accurately selecting by location (distance) and
then to display the shadow zone on a predefined
world geographic reference system. This is the most
important GIS command in translating the shadow
zone to a rectangular world map.
Select by Location: to identify the lines of latitude
and longitude within the shadow zone. In Figure 5,
the outer end of the shadow zone is selected at 143°.
The inner end must then be removed from the
currently selected features using 103°.
The spatial and statistical querying benefits of the
GIS allow the student to identify countries and cities
within the shadow zone in the attribute table. Students
are prompted to identify cities in the shadow zone for an
earthquake occurring in Newark, NJ. The attribute table
in Figure 6 is sorted to show that the Shikoku Province is
selected and therefore the city of Kobe would be in the
shadow zone while the Hokkaido Province is not
selected and therefore not in the shadow zone. This
detailed geographic information supports the
earthquake wave data detected by the Lehman
Seismograph data at the university (Figure 7).
Students are instructed that cities not found in the
shadow zone would receive direct earthquake P and S
waves. Students are asked to identify three cities NOT in
the shadow zone using the identify tool and include at
Journal of Geoscience Education, v. 54, n. 5, November, 2006, p. 596-602
Figure 6. Arcview GIS screenshot for identifying
provinces and cities in Japan that are either within or
out of the shadow zone for an earthquake occurring in
Newark, New Jersey, using the sorting function in the
GIS attribute table. Shaded rows or records indicate
that the data has been selected and therefore is
within the shadow zone. An arrow point to “Shikoko”
under the column or field ADMIN NAME is in a shaded
rows or record and therefore the city of Kobe in the
Shikoko Province in Japan is within the shadow zone.
Another arrow points to “Hokkaido, in the same field
but the record is not shaded. The Hokkaido Province
is not within the shadow zone.
Figure 5. Arcview 9.0 GIS screenshot for selecting by
a location to identify the outer end of the shadow
zone, 143 from the selected city and theoretical
epicenter, Newark New Jersey.
least one city closer than ≈103°, one city farther than
≈143°, and the last for a city 180° from the epicenter.
Students are asked to describe the types of earthquake P
and S waves you would expect to detect on a
seismograph in these 3 cities and relate the answers to
your knowledge of the Earth's Interior. One group
response indicated that water in the earth's oceans
influence the propagation of P and S waves.
PRE-ACTIVITY ASSESSMENT
1.
2.
Pick the letter that corresponds to your group
answer for the hypothetical shadow zone (Figure 8)
Discuss in one paragraph why your group chose that
shadow zone, or why you did not chose the other
possible shadow zones
POST-ACTIVITY ASSESSMENT
1.
2.
Compare your answer from the Pre-Activity to the
shadow zone you just created. If you were correct,
discuss what information was most useful in getting
you to hypothesize correctly. If you were not correct,
discuss what information was misleading or guided
Figure 7. Lehman seismograph recording from Kean
you to the flawed hypothesis.
You are now charged with developing a system for University for an earthquake in the Hokkaido
analyzing direct seismic waves that can be detected Province, Japan in October 1994.
for one earthquake-prone location in the world (such
as the location of the December 26, 2004 Indian
Ocean earthquake that generated a catastrophic
tsunami). You have funding for 3 seismographs, to
Kroll and Dobosiewicz - Mapping Theoretical Shadow Zones
599
with possible intended learning outcomes of the
activities. Students were asked to rate their learning
experience in the following 5 areas using "much better",
"slightly better", "no difference", or "more confused".
1.
2.
3.
4.
5.
Figure 8. Pre-activity assessment to determine
student alternate conceptions about the potential P
and S wave shadow zones for an earthquake occurring
in New Jersey. Letter B is the correct response.
3.
also allow for locating the epicenter. Where would
you place each seismograph and why?
Sketch a cross-section diagram of a round Earth
using a drawing compass. Look up the Earth's
radius, and use a scale of one inch equal to 1000 miles
for the radius. Mark the locations of the following
latitudes, north and south, on the perimeter of your
diagram: 0 (equator), 30 , 60 , and 90 (poles). Mark
the location of New Jersey as 40 N. latitude on the
perimeter. Look up the radius of the inner core and
thickness of the outer core and using a drawing
compass add the cores to your diagram. Locate
points that are103° and 143° away from the New
Jersey point in both directions on the perimeter.
Assuming that the P and S waves are traveling as
direct rays, sketch how the P and S waves would
travel from New Jersey to reach the shadow zone
perimeter latitudes on your diagram. What further
information might you need to know in order to
make a more accurate diagram?
STUDENT SURVEY AND DISCUSSION
The shadow zone activities were conducted in three
separate undergraduate introductory geology classes in
Fall 2005. This course fulfills both major and general
education requirements at the university and is typically
filled with a diverse group of students across academic
disciplines and grade levels and taught by full-time
faculty and adjuncts. We determined that the diversity of
the student population and the variety in instructors
participating in this study would not lend readily to a
formal quantitative form of assessment such a similar set
of summative test questions. Therefore, a survey was
given to students to evaluate the activities as learning
tools and the potential impact on their overall
understanding of earthquake waves, shadow zones,
earth's interior, and geography. The survey questions
were reviewed by the authors and the adjunct faculty
participant to determine the consistency of the questions
600
Rate your understanding about the Earth's Interior
Rate your understanding about differences between
globes and maps
Rate your understanding of how P and S waves
propagate through the Earth's Interior
Rate your understanding of why P-S wave shadow
zones form
Rate your understanding of where P-S wave shadow
zones form
Two classes taught by a full-time faculty members,
twenty eight students combined, participated in the
hand plotting shadow zone activity. One class taught by
an adjunct professor, thirteen students, participated in
the GIS shadow zone activity which was facilitated by a
guest full-time faculty member. Overall, students (n=40)
considered both activities an enhancement to their
understanding of the earth's interior, globes, maps and
shadow zones (Table 1). When the results for both
activities are combined, 81.5% rated their understanding
in all areas as much better or slighter better ( 72%- GIS,
85%- Plot). Students were also asked to respond to the
following question:
6.Do you feel the time spent (about 1 ½ hours) was a good
learning experience as compared to either a video,
lecture, or use of other visual aids? Choose only one
below:
A. This activity was a good learning experience and the
time well spent
B. I would have preferred a video
C. I would have preferred a lecture
D. I would have preferred other visual aids (overheads,
slides, powerpoint presentation)
A majority chose "A", (67% GIS, 54% Plot), indicating that
they felt that the activity was a good learning experience
and the time was well spent. The next highest response
was "D" (25% GIS, 21% Plot) indicating that other visual
aids would be beneficial to student learning. Videos (8%
GIS, 11% Plot) and Lectures (0% GIS, 14% Plot) received
the lowest responses, indicating that students perceive
these methods as the least beneficial for enhancing their
learning.
Since the survey was designed qualitatively, the
ratings were ranked from 1 through 4 to perform
parametric tests. Responses of "more confused" were
assigned a 1, "no difference" a 2, "slightly better" a 3, and
"much better" a 4. Descriptive statistics were generated
for all answers in questions 1-5 (Table 1) for participants
in both the GIS activity (n=60: 12 surveys with 5
questions each) and the hand plotting activity (n=140: 28
surveys with 5 questions). The median and mode of both
student groups was 3. The arithmetic means were 2.8 and
3.2 for the GIS and hand drawn activities, respectively.
The t-test statistic of -3.6 indicates that the responses to
the surveys for the GIS activity versus the hand drawn
activity varied significantly at the 95% confidence level.
A difference in the means of the activity is not intended
in this activity, however, is not entirely unexpected. The
GIS activity was conducted by a guest instructor in a
single class period. The students in the class had no prior
Journal of Geoscience Education, v. 54, n. 5, November, 2006, p. 596-602
Survey
Activity ®
1 - Earth’s Interior
2 - Globes & Maps
3 - PS Waves
4 - Why Shadow Zones Form
5 - Where Shadow Zones Form
Average for Questions 1-5
6 - Good Learning Experience?
Much Better
GIS
Plot
8
46
17
29
0
36
17
39
17
50
12
40
A. Yes
54
67
Slightly Better
GIS
Plot
75
46
43
58
92
57
33
50
42
32
60
45
B. Video
8
11
No Difference
GIS
Plot
17
4
25
29
8
0
50
4
42
11
28
10
C. Lecture
0
14
More Confusted
GIS
Plot
0
4
0
0
0
7
0
7
0
5
0
5
D. Other
25
21
Table 1. Results from the 6 questions for a survey rating student understanding about: 1. about the earth’s
interior, 2. differences between globes and maps, 3. how P and S waves propagate through the earth’s interior,
4. why P-S wave shadow zones form, 5. where P-S wave shadow zones form, and 6. for evaluating the activity
in the context of the class structure and the delivery of content. Data is represented as a percent of students
evaluating their perceived learning with five choices ranging from much better to more confused. GIS n=12;
Plot n=28.
GIS experience and were consequently learning a
powerful GIS tool and content simultaneously. Follow
up on the activity was coordinated by the regular class
instructor and unsolicited student responses indicated
that a follow up with the GIS instructor would be
beneficial. The hand plotted activity was conducted in
two classes by the regular instructor in that class. Regular
interaction with the instructor facilitated follow up to the
activity. In addition, the instructor has been doing the
activity in class for a number of years and undergraduate
students have prior experience with standard
measurement techniques.
The responses were re-ranked with "much better"
and "slightly better" assigned the same value of 3 to
determine if there would be no significant difference
between activities in "better" understanding of shadow
zones and related concepts. The median and mode
remained at 3 while the arithmetic means were 2.7 and
2.8 for the GIS activity and hand drawn activity
respectively. The t-test statistic for the re-ranked analysis
is -1.3 indicating that there is not a significant difference
between the responses to the survey and that overall
student understanding increased after both the GIS
activity and the hand drawn activity.
Students (n=12) were asked to hypothesize about
what a shadow zone would look like on a map as a
pre-activity assessment (Figure 8). The majority of the
students selected a circular shape, labeled "A" on Figure
6 with the epicenter located in the center. One student
selected "B", the correct answer and one student selected
"C". Students were asked to compare their hypotheses
with the shadow zone created using the GIS. The
majority of responses chose "A" and indicated that they
selected it because it is a circular shape with the epicenter
located in the center. The student who selected "C"
indicated that the shadow zone is theoretically a circle
which would then plot as a linear zone on a map. The
student who selected "B", the correct response, indicated
that the shadow zone could not be a perfect circle or
straight line because P and S waves travel at different
speeds. Therefore, by the process of elimination of the
other choices, "B" was the most likely answer.
Earth and their representation zones on maps. This expands on traditional representations of the shadow zone
in standard geology texts by giving students the opportunity to explore the impact of the shadow zone concept
to seismograph recordings of distant earthquakes and
furthers understanding of the structure of the Earth. The
authors would like to explore ways to integrate more
universal and quantitative assessments, such as the
Geoscience Concept Inventory (GCI) (Libarkin and An derson 2005) into introductory classes with a focus on
both the visual and conceptual understanding of
geospatial phenomenon like shadow zones. The CGI
uses a variety of diagrams including Mercator-type
world projections and cross sections of the globe and
these questions are available at http://newton.bhsu.edu/eps/gci.html. Questions about plate tectonics and the earth's interior tend to use cross sections of
the globe as in numbers 7, 20, 22, and 24. Two questions
use Mercator-type world projections, number 65, about
the shape of the ocean basins and number 13, about the
distribution of the world's active volcanoes. Considerable research in student learning about the Earth's Interior has been undertaken recently in the CGI and in
through model-based conceptual change (Steer et al
1995). Our research provides geospatial support for
larger scale initiatives of student learning in the
geosciences.
The digital and paper-based mapping techniques
here can be successfully applied to determine shadow
zones for any other location to make earth science classes
relevant to individual students. These activities have
been successfully implemented in undergraduate Earth
Science classes by using a pre-activity assessment using
four hypothetical representations of the shadow zone for
an earthquake and post activity questionnaire about both
seismic waves and the Earth's interior and how three
dimensional Earth phenomena are distorted on two
dimensional maps. Students indicate that hands-on
experiences increase their ability to understand spatial
representation of difficult geoscience data and concepts.
GIS can be used as an effective learning tool but there are
still some aspects of the technology that may interfere
with student learning when compared to using
traditional paper exercises. Observations of student
CONCLUSIONS
behavior during the GIS activity indicated that student's
Mapping P-S shadow zones enhance students' under- were highly focused on the script in the activity, and
standing of shadow zones on the three dimensional rightfully so as to proceed through the activity. Research
Kroll and Dobosiewicz - Mapping Theoretical Shadow Zones
601
in GIS exclusively as an educational tool (Hall-Wallace
Wadsworth Group/Brooks-Cole, Pacific Grove, CA,
and McAuliffe 2002) indicates that with GIS experience,
733p.
students would not only be able to reach the intended Murphy, B., and Nance, D., 1999, Earth Science Today,
learning objectives but could engage in higher order
The Wadsworth Group/Brooks-Cole, Pacific Grove,
thinking skills and the transfer of knowledge for
CA, 684p.
application to other areas in earth science.
Oldham, R.D., 1906, The constitution of the earth,
Quarterly Journal of Geological Science, v. 62, p.
456-473.
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