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

seth@earth.northwestern.edu

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

RAYS ARE APPROXIMATIONS TO WAVES

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.”