Teaching Gp

8/9/2019 Teaching Gp

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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

[email protected]

This presentation athttp://www.earth.northwestern.edu/people/seth/Lectures/teachinggp.ppt

mailto:[email protected]

http://www.earth.northwestern.edu/people/seth/Lectures/teachinggp.ppt

http://www.earth.northwestern.edu/people/seth/Lectures/teachinggp.ppt

mailto:[email protected]



Solid earth conceptscan be taught purelydescriptively at the

100-level

But this is teachingscience as magic, not

geophysics

AGI: “Geophysics is abranch of experimentalphysics 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

PHYSICS

MATH

GEOPHYSICSEarth structure

Earth processes

Geologic time

∆

In practice, we need to “review” - or teach - much of theseThis is OK since many students learn them better in contextWe 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&MWaves

Heat & temperature

How we measure these



GEOLOGY

PHYSICS

MATH


Earth processes

Geologic time

∆

Seek to improve students’ understanding of bothunderlying concepts & geophysical application

Vectors &

vector diff.

operators ( )

Spherical

geometry

Calculus

Simple ODE

& PDE


Mechanics

E&MWaves

Heat & temperature




GEOLOGY

PHYSICS

MATH


Earth processes

Geologic time

∆

Vectors &

vector diff.

operators ( )

Spherical

geometry

Calculus

Simple ODE

& PDE


Mechanics

E&MWaves

Heat & temperature


Tradeoff between breath of topics covered & depth ofeach (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,Θ,φ),

(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 massGravity on different

planets

Objects of differentmass fall at same

speed

Torque

Magnetic surveys

Paleomagnetism

Need to understand

cross product

Magnetic field

torque onmagnetic dipole

causes

Thermal

Remnant

Magnetization

Stein et al, 2007

Compass to work



ROTATION(CIRCULAR MOTION)

Torque, angular velocity &

momentum, moment ofinertia

Need to understand crossproduct & vector nature of

acceleration

L=Iω

Precession 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 & usefields

Spinnermagnetometer 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 wavefronts 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’principlegraphic

Inquiring mindswant to know

Like boat’s wake

wavefront -> ray

Stein & Wysession,

2003

To

T1

T2



Non-geometricoptical arrivals

Frequency

dependent (hearbut not see aroundcorners)

DIFFRACTION

Singleslit

λD/2d core

Migration undoes

diffraction

Interface

end

diffraction

DEPTH TIME

Stein & Wysession,

2003



earth.leeds.ac.uk/.../

active_tectonics/vlbi.gif

CONSTRUCTIVE & DESTRUCTIVE INTERFERENCE

http://comet.nerc.ac.uk/sc

hoolssar_how.html

VLBI

INSAR

X-raydiffraction

CMP stacking

Michelson–Morleyexperiment(1887)

Phase differencebetween waves

Distance & timemeasurement

http://www.eserc.stonybrook.edu/ProjectJava/Bragg/

Stein & Wysession, 2003



RAYS ARE

APPROXIMATIONSTO WAVES

Stein & Wysession,

2003



Potential

GEOTHERMICS

Conservation ofenergy (science

vs popularusage)

Potential, kinetic,chemical, heat,

electrical…

Most energyavailable tohumans &

natural systemsis ultimately

nuclear from sunor other stars

Chemical

Planets are heat engines Stein et al, 2007

Nuclear



HEAT & TEMPERATURE

Explain physically (towel)

Heat transfer modesUse 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 ofspreading & subduction

Tie to observations

Density anomalies

Plate driving forces

THERMAL EVOLUTION OF LITHOSPHERE

Stein & Wysession,

2003

Forsyth &

Uyeda, 1975



THERMALCONVECTION

Buoyancyforce

Adiabat

Convectioncell

Solid & fluidearth

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 geology

Stein et al, 2007

H & h it



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, chemistryconcepts 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 applicationDevelop problems & labs for this goal

Accept that some students will benefitmore than others

“You come in

here with askull full ofmush and youleave thinkin

like a lawyer!"



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Teaching Gp