Displacement Modeling of Volcanic Magma Chambers
Lennox Thompson
Academic Affiliation, Fall 2007: Senior, Coppin State University
RESESS® Summer 2007
Science Research Mentor: Dr.Peter Cervelli
Writing and Communication Mentor: Dr. Dave Phillips
ABSTRACT
Volcanoes can be hazardous if increased pressure in the magma chamber becomes great enough
that magma is forced upward through a crack to the ground surface and erupts. The magma
chamber which lies beneath a volcano is a large underground pool of molten rock lying under the
surface of the earth’s crust. The problem with the magma chamber and why it is significant is
because there are unknown processes occurring inside volcanoes. Researchers have not yet
understood the processes occurring inside of a volcanic magma chamber. My research is to
update a mathematical displacement model which describes the magma chamber properties such
as depth and volume change (e.g. inflation or deflation at surface). So far, the method used to get
the displacement model to work was to move all the file structures along with the displacement
program in one memory storage space in order for the program to work in Matlab. As a result,
the program was able to import and export data in addition to loading geographical features of
the displacement model to better understand the magma chamber for the purpose of prediction of
future volcanic eruptions.
This work was performed under the auspices of the Research Experience in Solid Earth Science for Students (RESESS) program.
RESESS is managed by UNAVCO, Inc., with funding from the National Science Foundation and UNAVCO. RESESS partners
include the Significant Opportunities in Atmospheric Research and Science Program, the United States Geologic Survey, the
Incorporated Research Institutions for Seismology, the United States Geological Survey, and Highline Community College.
1.
Introduction:
The research that I will be focusing on is displacement modeling (or velocities) of the
magma chamber typically found inside active volcanoes. The problem with the magma chamber
is that is unknown processes occurring inside of the volcano. The magma chamber is located
deep down inside of the volcano where the source of magma comes from. Researchers in the past
conducted research on magma chambers in active volcanoes around the world in order to explore
what is occurring in the magma chamber. They were unable to determine how deep, how much
inflation (volume change) or measurements of the uncertainties of displacement of a volcano.
One case study that is relevant to my research is that there have been researchers trying to
determine the source parameters of deformation data with an application to the March of 1997
earthquake swarm off the Izu Peninsula, Japan. The reason why the earthquake swarm that
occurred in Izu Peninsula, located in central Japan, is significant is because of the fact that
researchers have found traces of earthquake swarms that began on March 2, 1997, and continued
for approximately 10 days. The earthquake magnitudes measured by seismometers recorded
earthquake magnitudes as large as M5 and the largest earthquake recorded during March of 1997
time period was M5.3 which occurred exactly on March 4, 1997 (Cervelli P. et al). The
earthquake swarm that occurred in Izu Peninsula is pertinent to what I will be researching
because of the overall emphasis of displacement measurements.
One method researchers use to understand volcano deformation is the
InSAR(Interferometric Synthetic Aperture Radar) method used for analyzing episodic crustal
deformation, with applications to volcanic settings (Hooper, et al). InSAR is a remote sensing
technique that uses radar satellite images. The radar satellites such as ERS1, ERS2, JERS,
ENVISAT, IRS, or RadarSat shoot constant beams of radar waves towards the earth and record
them after they bounced back off the Earth’s surface. Every point in a satellite image (pixel) is
carrying two sets of information: the intensity and the phase. The intensity is the information that
characterizes the material in which what surface the wave bounced off is made of and what
orientation it has. The phase is the information that contains the fractional part of the round trip
distance of a radar signal to travel from the satellite to the ground and back again. When the
radar satellite revisits the exact same portion of the earth, the phase image should be identical.
The combination of these two images can in fact measure how much and where the ground has
moved. Researchers concentrated on modeling volcanic processes of active volcanoes but lack
the data to fully understand the magma chamber inside of volcanoes (Hooper, A et al).
Researchers have discovered that using any volcano interferogram which is a photographic
record made by an apparatus for recording optical interference phenomena, cannot calculate
deformation measurements because certain areas on most volcanoes, signals decorrelate and no
measurements are possible.
As a result of researchers not being able to gather sufficient deformation data from
certain volcanoes, they focused on acquiring deformation data from easily monitored volcanoes
such as Long Valley volcanic caldera in eastern California where they applied InSAR to be able
to model magma chamber processes. Here, researchers were able to gather some promising
results using InSAR which have proven to effectively measure deformation in regions of diverse
elements.
RESESS 2007, Lennox Thompson, 2
Observations from InSAR data can be used to model the characteristics of magma
chambers to allow researchers to be able to understand more about the deformation of active
volcanoes. One model used to interpret active volcanic areas is the point source of dilation
(Mogi’s source) which is used to approximate the behavior of a pressurized spherical magma
chamber. Mogi’s source model is capable of effectively reproducing a computerized
displacement and gravity changes at many volcanoes during either uplift or subsidence in order
for researchers to analyze the behavior of magma chambers of volcanoes (Battaglia M, et al).
What researchers were trying to achieve was to be able to evaluate various deformation
characteristics including elasto-gravitational effects, vertical discontinuities in the earth’s
density, and elastic parameters (Battaglia M, et al). The area where researchers focused their
research was the Long Valley caldera region in California because they have found reoccurring
seismic activity going on over there in the past two decades near that region. They also have
discovered several sources of deformation that have been found in Long Valley caldera,
California (Battaglia M, et al).
In addition to past research efforts into displacement measurements, interpreting the
magma chamber, and modeling crustal deformation in active volcanoes, my research is to update
a mathematical displacement model that describe magma chamber properties such as depth, and
inflation (volume change) of a magma chamber. I will be using old Matlab code in order to
create an updated version of a displacement model on a newer version of Matlab. Input data for
this model will include GPS displacement positions in a 24 hour batch which has x, y , z
measurements of a volcano and also the uncertainty measurements of the x , y ,z coordinates of
the displacement of the magma chamber of a volcano in a SINEX text file.
2. Methods
Deformation models are used to reproduce the behavior of ground deformation and
volcanic activity. Dr. Peter Cervelli developed the deformation model using GPS data
measurements. The GPS data measurements were stored into a SINEX (Solution Independent
Exchange) format text file where the file was used as input data for the deformation model. This
model was developed in a computer language called Matlab. Matlab is a tool for doing numerical
computations with matrices and vectors. Matlab allows easy matrix manipulation, plotting of
functions and data, implementation of algorithms, creation of user interfaces, and interfacing
with programs in other languages. The deformation model (e.g. Dismodel 2.0 Beta 3) is a GUI
(Graphical User Interface) that displays a blank blue screen with a menu option and allows users
to load geographic features, load SINEX files and also display a mesh grid of a 2-D plot.
RESESS 2007, Lennox Thompson, 3
Figure 1. Example of a GUI interface that allows users the option to display different data sets of the displacement
model
The menu options allow users access to files, data, viewing options, and options to change the
coordinate format of the model. Research was conducted on the older version of Matlab because
some things that worked on the older version would not adapt well to the newer version. Matlab
version 5.3 is an older version of Matlab. Research is intended to run the displacement model on
the newer version Matlab 7.0. Uploading the deformation model at first can produce problems
because the old Matlab version has trouble managing GUI. There are newer versions of Matlab
that have more capabilities and are more user friendly than the older versions. Dr. Cervelli
developed the deformation model in the older version of Matlab where it is prone for errors when
a user tries to debug. The problem with the displacement model is that the model does not
function properly. At first, the displacement model did not display anything.
New insights were discovered when the displacement model did not show up when a
user would run the program. The reason why the program did not run was because all the written
functions to display the model were not in the same directory. All the written functions had to be
moved within the same folder as the displacement model program in order for it to work. As a
result, the displacement model began to operate. The program is now able to import data and
export data. The only problem that still remains is loading SINEX text files. The program is able
to open a file and read a data file. It also can upload geographic features along with displaying a
mesh grid view of the model; however, the displacement model is still experiencing some
difficulty with loading SINEX text files. But when the program was uninstalled and then
reinstalled, the Matlab program ran again and the program worked partially. The program still
RESESS 2007, Lennox Thompson, 4
does not function the way it should be, but it is a start. The different methods used to get the
displacement model to work provided new ideas to different methods to use in order for the
program to load the SINEX text files. Once the process is known on how to load SINEX text
files, then a new updated model of a displacement program will be available to the public. Once
the program is updated, the model will enable better understanding of the magma chamber
processes and future prediction of volcanic activity.
3. Results
The program is now able to run on the newer version of Matlab 7.0 but the Dismodel have
problems loading in the SINEX input files. The software displays a 2-D plot of deformation of a
magma chamber. When entering the following model parameters:
Longitude:
Latitude:
Depth (km):
Volume Change (cubic meters):
Lon 121
Lat 14
D 7.7
V -16
The program computed a year worth of velocity measurements from Taal Volcano which is
located in the Philippines. There were eleven GPS antennas positioned at different parts of Taal
Volcano. The eleven GPS stations measure deformation over time. The results below report
deformation of the earth’s surface in units of cm/yr which are velocity measurements of ground
movement with respect to the Mogi source. The Mogi source which is the small green circle in
Fig 2 changes shape when ground deformation occurs. The green circle in the figure below
represents the source of where the deformation is occurring. The black circles in Fig 2 represent
the error ellipses. The error ellipses are the GPS measurement uncertainty. If the red and black
solid lines are close together that means that the observed and modeled measurements are pretty
close agreement with the source of where the deformation occurs. The observed displacements
from the error ellipses are depicted in black. The modeled displacements from the error ellipses
are depicted in red. Displacements are relative to the GPS station labeled TV (Taal Volcano)
followed with a number. The experimental testing of the displacement model reveal that the
reason why the velocities are so small is because of the fact that the GPS station is very far away
with respect to the distance from the estimated displacement field. If a user enters parameters
closer to the Mogi source, then Dismodel would compute larger velocities compared to the
velocities that were calculated below.
RESESS 2007, Lennox Thompson, 5
Output:
Matlab 5.3
E cm/yr
2.6391
-2.0984
-0.8493
0.5593
-2.4714
-2.3795
1.4378
-2.4139
-0.526
-2.0167
-1.8504
N cm/yr
-1.8168
-1.1079
-2.2547
-1.4997
-3.5283
-0.9325
-1.202
-2.8147
-4.7548
-1.6634
-3.3785
Matlab 7.0
Up
cm/yr
-0.2845
-0.6702
-1.8575
-1.4861
-0.0128
0.0735
2.7391
3.0438
2.0178
-1.1265
-1.0721
E cm/yr
2.6391
-2.0984
-0.8493
0.5593
-2.4714
-2.3795
1.4378
-2.4139
-0.526
-2.0167
-1.8504
N cm/yr
-1.8168
-1.1079
-2.2547
-1.4997
-3.5283
-0.9325
-1.202
-2.8147
-4.7548
-1.6634
-3.3785
Up
cm/yr
-0.2845
-0.6702
-1.8575
-1.4861
-0.0128
0.0735
2.7391
3.0438
2.0178
-1.1265
-1.0721
Fig 2 is an example of error ellipses which measure the uncertainty of GPS measurements. Red solid line represents
modeled displacements. Black solid line represents the actual displacements.
RESESS 2007, Lennox Thompson, 6
Fig 3 is a geographical mapped out view of Taal Volcano in the Philippines. A GUI of the region that the
displacement model is taking deformation measurements from. The geographic mapped view is an outline of the
island where the volcano is located.
4. Discussion
The calculations of deformation seem to be accurate because of the fact that the older
version of Matlab 5.3 and the newer version 7.0 were able to compute the same ground
movement velocities that were measured by GPS stations at Taal volcano in the Phillipines. The
Dismodel was able to function properly; however, there were still some uploading issues with
the SINEX input files. The reason why the displacement model does not seem to be functioning
properly is because of version incompatibility between the older version 5.3 and the newer
version 7.0. Some preexisting functions that the older version recognizes is not recognizable on
the newer version of Matlab. Prewritten functions in version 5.3 are obsolete in the newer
version 7.0. It seems that there are conflicting issues with the optimization of the GUI windows.
The reason why the SINEX files are unable to upload the window interface that displays all the
(*mat,*ascii,*fig) files is because of the reason of optimization issues with the newer version of
Matlab. Dr. Cervelli who written the functions that enable the window interface to upload,
written the functions in the older version of Matlab 5.3. When trying to debug the source code of
the displacement model, Matlab debugger identified several source errors with the function
DM_GetSINEXFiles.m. The reason why there were several source errors with the function
DM_GetSINEXFiles.m is because the reason of version incompatibility. The older prewritten
functions that are recognizable on 5.3 is not able to process data using older functions of Matlab
5.3. Matlab 7.0 has more updated functions from the previous functions that Matlab 5.3
recognizes
RESESS 2007, Lennox Thompson, 7
5. Conclusion
Past work that has been done to identify source parameters of deformation such as
researchers conducting research on determining sources of deformation with an application to the
March of 1997 earthquake swarm off the Izu Peninsula is relevant to the findings of what the
Dismodel computed from the Taal Volcano. The model identified the where exactly the source
of the deformation was coming from in the Taal Volcano region off of the Philippines. The past
efforts to understanding deformation in general lead to how to apply different methods for
understanding the magma chamber which lead to the numerical model called Dismodel, which
more effectively helps identify the unknown processes of deformation when a volcano erupts.
The goal of the research presented in this paper was to produce an updated version of
Dismodel on a newer version of Matlab. The process that took place in order to obtain an
updated version of the Dismodel on the newer version of Matlab 7.0 included moving certain file
structures along with the displacement model program within the same directory. This enabled
the program to be able to read in and open files that contain geographical features of the
program. Based on the results of the Dismodel, since modeled velocities computed from Taal
volcano were the same in both Matlab versions 5.3 and 7.0, it is safe to say that the displacement
model deformation calculations are in fact functioning properly in version 7.0. The experimental
testing that occurred in the older and newer version demonstrate the consistency of Dismodel
functions based on testing the displacement model on both versions of Matlab. The primary goal
of this project was therefore successfully achieved.
Overall, from the research that was conducted on updating the Dismodel on a newer
version of Matlab, this research leads to future work that could be conducted on magma
chambers such as Taal Volcano. Since the Dismodel was not able to read in the SINEX text files,
future research could be explored on how the Dismodel would be able to read in the SINEX text
files without Matlab 7.0 having conflicting issues with version incompatibility. If the Dismodel
was able to read in the SINEX files, it would be able to more efficiently describe magma
chamber properties such as depth, and volume change.
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REFERENCES
Cervelli, P., M. Murray, P. Segall, Y. Aoki., and T. Kato, Estimating source parameters from
deformation data, with an application to the March 1997 earthquake swarm off the Izu Peninsula,
Japan, J. Geophys. Res., 106, 11,217-11,237. 2001.
Hooper, A., H. Zebker, P. Segall, and B. Kampes, A new method for measuring deformation on
volcanoes and other natural terrains using InSAR persistent scatterers. Geophys. Res. Lett., 31,
doi: 10.1029/2004GL021737, 2004.
Battaglia M. and P. Segall, The interpretation of gravity changes and crustal deformation in
active volcanic areas Pure and Applied Geophysics, 161, 7, 2004.
Bartel, B.A. 2002. Magma Dynamics At Taal Volcano, Philippines From Continous GPS
Measurements. Master Thesis, Indiana University, Bloomington, IN.
Dzurisin, Daniel. Volcano Deformation: Geodetic Monitoring Techniques, Vancouver:
Washington, 2007.
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