GE5950 Volcano Seismology

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GE5950 Volcano Seismology
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Todays Topics

• Introductions
• Structure of the course (syllabus)
• Background Materials

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• Why are you taking this course?
• What are your research interests?
• How do you hope to use the knowledge you pick up
  in this class?
• ?

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• GE5950 Volcano Seismology
• Spring semester 2009
• 3 credits
• Description and scope of the course This course
  will prepare students, including those with no
  seismology background, to interpret seismic and
  acoustic signals from volcanoes. Topics basic
  seismology, monitoring techniques, tectonic and
  volcanic earthquakes, infrasound, and deformation
  over a range of time scales.
• Instructor Dr. Greg Waite
• Dow 204
• Office phone [phone]
• e-mail gpwaite_at_mtu.edu
• Teaching Assistant Ingrid Fedde
• e-mail idfedde_at_mtu.edu
• Lecture Monday Wednesday from 1535-1650 in
  EERC B11.
• Lab (required for Michigan Tech students) TBD in
  Dow 211
• Lab help session TBD

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• Texts There is not a required textbook as most
  of the material will be handed out. We will read
  from Stein and Wysession quite extensively
• Stein, S. and M. Wysession, (2003). An
  Introduction to Seismology, Earthquakes, and
  Earth Structure, Blackwell Publishing this is
  an excellent general-purpose seismology textbook
  that also covers advanced topics we wont
  address.
• This is the only volcanic seismology textbook
  that covers most of the topics we will cover in
  the course, but it is hard to find
• Zobin, V.M. (2003), Introduction to Volcanic
  Seismology, Elsevier.
• Prerequisites MA1160/61, GE2000, PH2100, or
  permission from instructor. Labs and homework
  assignments will be done in Matlab, but you need
  not be an expert in Matlab to take the course.
• Readings Journal articles and book sections will
  be assigned.
• Course web page http//www.geo.mtu.edu/gpwaite/t
  eaching/volcanoseismo
• Grades Final grade will be based upon homework
  (25), laboratories (25), mid-term (25) and
  final exams (25).

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Introduction

• Why study seismology?
• One of the best ways to study the Earths
  interior
• Direct observations (drilling) are impossible
  and/or impractical (expensive) in most cases
• Earthquakes are abundant
• Works day or night
• Seismograms record all the complexities
  encountered along the waves path from source to
  receiver (e.g., liquid outer core was discovered
  by seismologist)
• Earth behaves (nearly) elastically at seismic
  frequencies

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Introduction

• Why study volcano seismology?
• Used to evaluate the current state of the
  volcano
• Seismic tomography
• State of stress
• Temporal changes have been observed in both at
  volcanoes
• Primary tool used for eruption prediction
• Dozens of eruptions have been predicted
• Requires years of background monitoring
• Provides quantitative data for modeling of
  eruption dynamics
• Because seismic waves are elastic waves, they can
  be modeled quantitatively relatively easily
• Cheap and easy to maintain a small network of
  stations

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Introduction

• Volcano seismology is extremely complex and
  interesting to study?
• Volcanoes are dynamic with rapidly varying local
  stress regimes, migrating fluids, changing
  topography, etc
• They produce many more earthquakes than a
  typical fault
• Volcanic process produce a wide variety of
  seismic waves with very-long-period earthquakes
  (period 20-60 seconds) up to very small M0 high
  frequency events (100s of Hz)

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Introduction

• Volcano seismology includes nearly all aspects of
  earthquake seismology plus additional
  complexities because of many different types of
  sources
• Must understand the basics of seismology to
  effectively use volcano seismic signals

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• Figure from Garcés, M. A., M. T. Hagerty, and S.
  Y. Schwartz (1998), Magma acoustics and
  time-varying melt properties at Arenal
  Volcano,Costa Rica, Geophys. Res. Lett., 25(13),
  22932296.

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(a) Hour-long record of the east component of
velocity for a station on Stromboli, about 400 m
southeast of the vents. (b) Band-pass filtered
record of (a). Two repeating events were
identified suggesting a repetitive,
non-destructive source process. (after Chouet et
al., JGR 2003)
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1 hour and 15 minutes
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Some mathematical background complex numbers

• A complex number can be written as
• z a bi
• i sqrt(-1)
• a is the Real part of z,
• b is the Imaginary part of z
• r sqrt(a2 b2)
• r is the magnitude of z
• ?? tan-1(b/a)
• ? is the phase angle of z

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Scalars and vectors
Scalars describe a physical property at a point
and are independent of coordinate system
temperature, pressure, mass, etc. Vectors have
both a magnitude and direction displacement u
u1ê1 u2ê2 u3ê3 (u1,u2,u3) ê1 (1,0,0) ê2
(0,1,0) ê3 (0,0,1) hats denote unit vectors,
which have magnitude 1
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Scalars and vectors
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Scalars and vectorsVector scalar multiplication
u (u1,u2,u3) ?u (?u1, ?u2, ?u3) Multiplicatio
n by a positive scalar changes magnitude, but not
direction of the vector
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Scalars and vectorsVector addition
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Scalars and vectorsDot product
Dot product is commutative (aob boa) Dot
product of perpendicular vectors is 0 u o ê1
(u1ê1 u2ê2 u3ê3 ) o ê1 u1
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Scalars and vectorsCross product
Vector resulting from cross product of two
vectors is perpendicular to both Order is
important a x b ? b x a
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Scalars and vectorsIndex notation
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Scalars and vectorsEinstein summation notation
Summation over repeated index, i, is implied
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Scalars and vectorsThe Kronecker delta
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Matrices
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Matrices
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Matrices matrix multiplication
The ijth element of C is the dot product of the
ith row of A and the jth column of B Matrix
multiplication is not commutative
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Matrices identity matrix
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Matrices matrix transpose
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Matrices inverse matrix
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Vectors and Matrices systems of linear equations
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Vectors and Matrices systems of linear equations
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Vectors and Matrices systems of linear equations
If the number of equations (rows of A) and
unknowns (elements of x) is equal, A is square.
If b ? 0, then we have an easy method for
computing the vector of unknowns, x.