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GE5950 Volcano Seismology

Todays Topics

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

- 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? - ?

- 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 906.487.3554
- 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

- 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).

(No Transcript)

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

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

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)

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

- 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.

(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)

1 hour and 15 minutes

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

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

Scalars and vectors

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

Scalars and vectorsVector addition

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

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

Scalars and vectorsIndex notation

Scalars and vectorsEinstein summation notation

Summation over repeated index, i, is implied

Scalars and vectorsThe Kronecker delta

Matrices

Matrices

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

Matrices identity matrix

Matrices matrix transpose

Matrices inverse matrix

Vectors and Matrices systems of linear equations

Vectors and Matrices systems of linear equations

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.

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