Examples of Spreadsheets in Introductory Geophysics Courses

Sarah Kruse, USFBorrowing heavily from SSAC: Len Vacher, Laura Wetzel, and

others

Outline

• Why spreadsheets?

• When?

• What?

• How? Good practices.

Why Spreadsheets?

Geophysical context

Plan for how to solve the

problemPractical tool

Why Spreadsheets?

Spreadsheets Across the Curriculum

serc.carleton.edu/sp/ssac

When to use spreadsheets?

• Introductory Geophysics

– ~100% of students say they know how to do calculations using a spreadsheet

• *survey at beginning of semester

When to use spreadsheets?

from K.F. Kim, 2004, A survey of first-year university students ability to use

spreadsheets, 1(2), Spreadsheets in Education.

“… instrument measures the level of student confidence in ICT usage, which according to academic staff who teach ICT courses, over-estimates the actual level of ICT skill. (Note that the ability of students to use technology, and their willingness to persevere in the face of difficulty is governed by their confidence, that is on their perceived ability, rather than their actual ability.)”

When to use spreadsheets?

…and then after Intro Geophysics, STOP.

Programming

treats your data with more respect

improves with practice

What?

• Students write their own– SSAC, “full benefits”

– But in geophysics, the equations can be complicated!

What?

• Students use existing spreadsheets to explore significance of variables

– Burger et al. textbook Introduction to Applied Geophysics: Exploring the Shallow Subsurface

– Steve Sheriff http://www.umt.edu/geosciences/faculty/sheriff/Sheriff_Vita_abstracts/Sheriff_software.htm

What?

• Hybrid: – Students complete partially developed spreadsheets

How? Good practices

• Keep connected to geophysics context

start in class, continue as homework

How? Good practices

• In the beginning, in the written assignment give some equations in “Excel” language

v = 2*sqrt((x/2)^2+h^2)/t

How? Good practices

• Have intermediate deadlines on longer assignments

How? Good practices

• Wrap some non-quantitative material around the assignment– Do in class

– Incorporate into assignment SSAC modules

• Example from Len Vacher’s SSAC spreadsheet module on Earth’s density

SSAC2004.QE539.LV1.5

Earth’s Planetary Density – Constraining What We Think

of the Earth’s Interior

Prepared for SSAC by Len Vacher – University of South Florida, Tampa

© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2006

Supporting Quantitative IssuesUnit conversionsSolid geometry: Volume of spherical shellForward modeling: Inverse problem by trial and errorIntegral: Concept

Core Quantitative Issue Weighted average

Any model for the thickness and density of Earth’s constituent shells must be consistent with the planetary density (5.5 g/cm3), which is known from the value of g (9.81 m/sec2).

Version 10/04/06

Density as a function of depth

• Before seismology it was known

– The Earth is a sphere with circumference 40,000 km, and therefore a radius of 6370 km.

– The average density of the planet is 5.5 g/cm3.

– Nearly all rocks we see at or near the surface are less dense than the planet as a whole. In fact, except for unusual rocks such as ores, rocks that we experience first hand are about half as dense as the Earth as a whole.

– Therefore, the Earth must be denser in the interior than it is near the surface.

• With early seismology it was known that the density of the interior changes abruptly at certain depths, that the interior of the Earth is structured into layers. The boundaries between the layers are named discontinuities, because they register as discontinuities in the graph of P and S velocity – and hence density – as a function of depth. The three boundaries are:

– The Mohorovicic Discontinuity (1909), at 5-70 km depth.– The Gutenberg Discontinuity (1914), at 2890 km.– The boundary between liquid and solid discovered by Inge Lehmann in 1936 -- at

5150 km. (End note 4)

How? Good practices

• Help students through the how-to-solve-it process (Polya, see SSAC website)

give guidance in planning give sample layouts (simpler problems) or give incomplete spreadsheets (complicated problems)

• Example from an assignment Estimating Magnetic Anomalies Associated with Subsurface Features

Problem

Solve the problem by treating the cannonball as a dipole that consists of two equal and opposite monopoles. The dipole field is the vector sum of the fields from each of the monopoles.

Calculate the magnetic anomalies you would measure by collecting a grid of total field magnetic readings over a cannonball

buried one meter deep at Fort DeSoto.

(Photo from www.pinellascounty.org).

Note our work is made easier because we can neglect declination (currently) here.

So we only need to consider the• N-S (x) component of anomalous field • vertical (z) component of the anomalous field

Background

• In this example, background primarily comes from textbook….

• Students are given a partially completed spreadsheet, with a lot of the work of setting up the structure of multiple worksheets already done. For example, plots are set to work if equation cells are filled in properly.

Designing a Plan, Part 1a

For each of the two monopoles, and each of the points on the grid, we can set:

the measurement position

the monopole position (and depth)

the pole strength

Notes: We will set up a grid of measurement

positions. The STARTING POINT spreadsheet has this done for you.X (N-S) positions of each grid point are given in column B. Y (E-W) positions are given in row 8._

Designing a Plan, Part 1b

For each of the two monopoles, and each of the points on the grid, we can set:

the measurement position

the monopole position (and depth)

the pole strength

Notes: We will simplify the equations (a bit)

by assuming the negative pole is at the horizontal position x=0, y=0. The positive pole position can then be adjusted to account for the direction of magnetization and the approximate size of the cannonball.

Effective position of negative pole

Designing a Plan, Part 1c

For each of the two monopoles, and each of the points on the grid, we can set:

the measurement position

the monopole position (and depth)

the pole strength

Notes: We will need to compute the pole

strength from the susceptibility and dimensions of the cannonball and the strength of the Earth’s field.

m = k*A*Fe

Designing a Plan, Part 2a

For each of the two monopoles, and each of the points on the grid, we will need to compute:

the N-S horizontal component HA of the anomalous field

the vertical component ZA of the anomalous field

Notes: The horizontal and vertical

components for each monopole will be calculated on separate worksheets. These can then be graphed separately.

For example this worksheet (sheet HA –m) only shows the horizontal component of the anomalous field for the negative pole.

Designing a Plan, Part 2b

For each of the two monopoles, and each of the points on the grid, we will need to compute:

the N-S horizontal component HA of the anomalous field

the vertical component ZA of the anomalous field

Watch out!

HA = mx/(x2+y2+z2)(3/2) wherex = (xmeasurement point – xpole)Similarly for y and z

So the anomaly depends on the relative positions of the measurement point and the pole

(Remember for the negative pole only, we are assuming xpole = 0.)

Designing a Plan, Part 2c

For each of the two monopoles, and each of the points on the grid, we will need to compute:

the N-S horizontal component HA of the anomalous field

the vertical component ZA of the anomalous field

In each worksheet make a plot of the field component throughout the grid

etc. etc.

How? Good practices

• Assessment– Make notes for changes for the next time you teach it.

• Fun example from SSAC (Len Vacher)