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Teaching introductory geophysics: what our students don’t know, need to,
and what we can do
Seth Stein
Department of Earth and Planetary SciencesNorthwestern University Evanston IL 60208
This presentation athttp://www.earth.northwestern.edu/people/seth/Lectures/teachinggp.ppt
Solid earth concepts can be taught purely descriptively at the
100-level
But this is teaching science as magic, not
geophysics
AGI: “Geophysics is a branch of experimental
physics dealing with the earth”
Davidson et al
NU introductory geophysics:
-First geophysics class (200-level) for geology majors, engineers, or other science folk
-Typically sophomores or juniors
- Some have descriptive (100-level) intro to earth science
- Math, physics, chemistry prerequisite or corequisites
- Global/planetary perspective
- Course goes beyond descriptive
- Try to challenge students & prepare them for higher level classes
GEOLOGY
PHYSICSMATH
GEOPHYSICS
Intro geophysics classes integrate topics that we’d like students to know from other classes, but often don’t
know well (or at all). These can include
Earth structure Earth processes Geologic time
Mechanics E&M Waves Heat & temperature How we measure these
Vectors & vector diff. operators ( )
Spherical geometry
Calculus
Simple ODE & PDE (wave, heat)
∆
Problem solving (not just plug in)
GEOLOGY
PHYSICSMATH
GEOPHYSICSEarth structure Earth processes Geologic time
∆
In practice, we need to “review” - or teach - much of these This is OK since many students learn them better in context
We can’t do detailed derivations, but can give intuition & contexts (often common to different applications)
Vectors & vector diff. operators ( )
Spherical geometry
Calculus
Simple ODE & PDE (wave, heat)Problem solving (not just plug in)
Mechanics E&M Waves Heat & temperature How we measure these
GEOLOGY
PHYSICSMATH
GEOPHYSICSEarth structure Earth processes Geologic time
∆
Seek to improve students’ understanding of both underlying concepts & geophysical application
Vectors & vector diff. operators ( )
Spherical geometry
Calculus
Simple ODE & PDE (wave, heat)Problem solving (not just plug in)
Mechanics E&M Waves Heat & temperature How we measure these
GEOLOGY
PHYSICSMATH
GEOPHYSICSEarth structure Earth processes Geologic time
∆Vectors & vector diff. operators ( )
Spherical geometry
Calculus
Simple ODE & PDE (wave, heat)Problem solving (not just plug in)
Mechanics E&M Waves Heat & temperature How we measure these
Tradeoff between breath of topics covered & depth of each (underlying math & physics) depends on class
goals & composition
VECTORS
Physics independent of coordinate system (F=ma)
Magnitude-angle vs components
Vector operations (sum, gradient, curl, etc.)
Magnetic field Plate motion
Stein et al, 2007
SPHERICAL GEOMETRY
Latitude & longitude
Vector components: (r,, ), (N-S, E-W, up-down), (x,y,z)
Unit vectors in non-Cartesian system
VDOs in spherical coordinates
Operations must be done in Cartesian
Magnetic fieldPlate motion Stein et al, 2007
Stein & Wysession,
2003
SYSTEMS OF EQUATIONS/LEAST SQUARES
Can motivate w/o math or w/simple algebra
Davidson et al, 2002
GPS receiver finds position with radio signals from different satellitesLocating earthquake from arrivals at multiple seismometers
Tomography
MECHANICS
F=ma
Weight vs mass
Gravity on different planets
Objects of different mass fall at same
speed
Torque
Magnetic surveys
Paleomagnetism
Need to understand cross product
Magnetic field torque on
magnetic dipole causes
ThermalRemnantMagnetization
Stein et al, 2007
Compass to work
ROTATION (CIRCULAR MOTION)
Torque, angular velocity & momentum, moment of
inertia
Need to understand cross product & vector nature of
acceleration
L=IPrecession magnetometer Plate motion Moment of inertia
Stein et al, 2007
ELECTROMAGNETISM
How fields arise
Columb’s law
B from moving charges
Lorentz force
Maxwell’s equations
How we measure & use fields
Spinner magnetometer V=-d flux B/dt
Mass spectrometer (age dating)
F=q(E + v x B)
Circular motion
Stein et al, 2007
B
V
SEISMOLOGY
Waves in space & time
Observe as either
Period, wavelength, speed (c=/T) &
dimensions
Relation between wave fronts and rays
U(x,t)
Stein & Wysession,
2003
Wavefront Rayt
x
Idea of geometric optics: when we can use rays, when we need waves
Travel time vs amplitude
SEISMOLOGY
Huygens’ principle graphic
Inquiring minds want to know
Like boat’s wake wavefront -> ray
Stein & Wysession,
2003
To
T1
T2
Non-geometric optical arrivals
Frequency dependent (hear but not see around corners)
DIFFRACTION
Single slit
D/2d core
Migration undoesdiffraction
Interface end diffraction
DEPTH TIME
Stein & Wysession,
2003
earth.leeds.ac.uk/.../ active_tectonics/vlbi.gif
CONSTRUCTIVE & DESTRUCTIVE INTERFERENCE
http://comet.nerc.ac.uk/schoolssar_how.html
VLBI
INSAR
X-ray diffraction
CMP stacking
Michelson–Morley experiment (1887)
Phase difference between waves
Distance & time measurement
http://www.eserc.stonybrook.edu/ProjectJava/Bragg/
Stein & Wysession, 2003
Potential
GEOTHERMICS
Conservation of energy (science
vs popular usage)
Potential, kinetic, chemical, heat,
electrical…
Most energy available to humans &
natural systems is ultimately
nuclear from sun or other stars
Chemical
Planets are heat engines Stein et al, 2007
Nuclear
HEAT & TEMPERATURE
Explain physically (towel)Heat transfer modes
Use partial derivative (don’t have to call it grad) Time dependant solutions
Cooling halfspace solution
Lava lake
Stein et al, 2007
Stein & Wysession, 2003
Simple models of spreading & subduction
Tie to observations
Density anomalies
Plate driving forces
THERMAL EVOLUTION OF LITHOSPHERE
Stein & Wysession,
2003
Forsyth & Uyeda, 1975
THERMAL CONVECTION
Buoyancy force
Adiabat
Convection cell
Solid & fluid earth
Tie to weather & climate
change
Stein et al, 2007
VISCOSITY
Define w/o tensor
Magma & mantle flow
Stokes’ problem
Rayleigh number
Reflects magma chemistry; tie to hazard
GPSStratovolcano
Shield volcano
Tie to glacial geologyStein et al, 2007
How & why it occurs
Why nuclear energy released
Age dating
Radioactive heating of earth
RADIOACTIVITY
E=mc2
Nucleus
Stein et al, 2007
Meteorites from early solar system
SUGGESTIONS
Identify math, physics, chemistry concepts implicitly or explicitly needed
in course
Assess which students are shaky on
“Review” - or teach - these at level suitable for class curriculum &
composition
Seek to improve students’ understanding of both underlying
concepts & geophysical application
Develop problems & labs for this goal
Accept that some students will benefit more than others
“You come in here with a skull full of mush and you leave thinking like a lawyer.”