Introduction to Geophysics
Exam 3 Review Sheet
GLY3160 / PHY3160
This sheet provides a general outline of the topics covered on your upcoming exam. This is not an exhaustive list, but is
simply a general list of key points. In other words, most exam questions will be based on the topics listed here, but I
reserve the right to also include questions about topics from the textbook and items not specifically on this list.
Disclaimer:
I will never provide equations that can be easily figured out by dimensional analysis
e.g.
𝑑
𝑣= ,
𝑡
𝑣
𝑓= ,
𝐹 = 𝑚𝑎 ,
𝜆
𝑚
𝐷=
𝑣
, etc...
I also will not provide any unit conversion factors (e.g. 1 in = 2.54 cm). You should know how to convert units from the
dimensional analysis lab. I also assume that everyone knows their metric abbreviations e.g.
m = 10-3, c = 10-2, k = 103, M = 106, G = 109, etc…
Materials covered on this exam:
 Textbook Chapters 8, 9, and 12
I will provide the following potentially useful equations on your exam:
(I assume that all science majors know Newton’s second law of motion, i.e. 𝐹 = 𝑚𝑎)
Resistivity Equations
𝑅=
𝑉
𝐼
𝑙
𝑉
𝐼
𝜌Wenner = 2𝜋𝑎 ( )
Gravity Equations
1
1 −1
𝑅𝑒𝑞 = ∑𝑛𝑖=1 𝑅𝑖
𝑅 = 𝜌𝑎
𝜌Schlumberger = 𝜋
𝑅𝑒𝑞 = (∑𝑛𝑖=1 𝑅 )
𝐿2 𝑉
( )
2𝑙 𝐼
𝐺 = 6.672 𝑥 10−8 𝑚3 ⋅ 𝑀𝑔−1 ⋅ 𝑠 −2
𝑑𝑧 = 2 𝑔𝑡 2
𝐹=𝐺
𝛿𝑔sphere = 𝐺
∆𝑚 𝑧
𝑚1 𝑚2
𝑟2
𝜌1 𝑡𝑎𝑛𝜃1 = 𝜌2 𝑡𝑎𝑛𝜃2
𝑖
𝑉
𝐼
𝜌DipoleDipole = 𝜋𝑛(𝑛 + 1)(𝑛 + 2) ( )
1 𝑚𝐺𝑎𝑙 = 1 x 10−5
4
𝑉sphere = 3 𝜋𝑟 3
𝑚
𝑠2
SurfAreasphere = 4𝜋𝑟 2
3
(𝑥 2 +𝑧 2 )2
𝛿𝑔slab = 2𝜋𝐺∆𝜌𝑡
𝛿𝑔𝜆 = 978031.8(1 + 0.0053024 𝑠𝑖𝑛2 𝜆 − 0.0000059 𝑠𝑖𝑛2 2𝜆) (𝑚𝐺𝑎𝑙)
𝛿𝑔Eötvös = 4.040𝑣 𝑠𝑖𝑛𝛼 𝑐𝑜𝑠𝜆 + 0.00121𝑣 2 (𝑚𝐺𝑎𝑙)
𝑑𝑔
≈ 0.3086ℎ (𝑚𝐺𝑎𝑙)
𝑑𝑅
𝑚
𝛿𝑔Bouguer = 2𝜋𝐺𝜌ℎ ( 2 ) ≈ 0.04192𝜌ℎ (𝑚𝐺𝑎𝑙)
𝑠
𝛿𝑔free−air =
1
𝑀excess = 2𝜋𝐺 𝑉anomaly
𝑛
𝑖=1
body −𝜌surroundingRock
𝑛
(∑ 𝜌𝑖 ℎ𝑖 )
𝐵𝑙𝑜𝑐𝑘 𝐴
𝜌body
𝑀body = 𝑀excess (𝜌
𝑛
= (∑ 𝜌𝑖 ℎ𝑖 )
𝑖=1
𝐵𝑙𝑜𝑐𝑘 𝐵
𝑛
(∑ ℎ𝑖 )
𝑖=1
)
𝐵𝑙𝑜𝑐𝑘 𝐴
= (∑ ℎ𝑖 )
𝑖=1
𝐵𝑙𝑜𝑐𝑘 𝐵
Introduction to Geophysics
Exam 3 Review Sheet
GLY3160 / PHY3160
Chapter 8: Gravity on a Small Scale
Know the law of universal gravitation and be able to use this equation to solve simple problems
about forces and accelerations between two massed bodies.
The gravitational forces due to a uniform sphere and a hollow spherical shell…in what cases would
they be different or the same?
Can two spherical bodies of different size and density produce the same gravity anomalies?
Why is the acceleration due to gravity, g, only dependent on the mass of Earth and not our mass?
E.g. why does a feather fall with the same acceleration as a brick (if both are in a vacuum)?
The Earth can be approximated as a point source in terms of its gravitational behavior. What is
required for this approximation to remain true?
Using the law of universal gravitation, how do geophysicists calculate the mass of the Earth?
Would the following geologic scenarios produce a local gravity anomaly? Why?
Horizontal layers of sandstone on top of a horizontal basalt flow
A vertical basaltic dike cutting through horizontal sandstone layers
Horizontal layers offset by a strike-slip fault
Horizontal layers offset by a reverse fault
A granitic intrusion (ρ=2.7) into sedimentary rocks (ρ=2.7)
Know how to calculate the size of a gravity anomaly directly above and around a buried sphere.
Why are gravity anomalies typically measured in mGal and not m/s2?
I will provide 1 mGal = 1x10-5 m/s2 so, you should be able to give gravity calculations in either m/s2
or mGal.
If given a geologic sketch, you should be able to sketch the approximate gravity anomaly that will be
produced. E.g. how would the anomaly look different for a deep and shallow sphere or dike?
Know the details of all of the gravity corrections covered in lecture. Know:
Why they are needed
What they correct for
In what situations they are not needed
What is the Free-Air Anomaly? What can this anomaly tell us?
How is the Free-Air Anomaly different from the Free-Air Correction?
What is the Bouguer Anomaly? What can this anomaly tell us?
How is the Bouguer Anomaly different from the Bouguer Correction?
What are regional and residual anomalies and why/when must they be separated?
Know the general caveats of gravity surveying
Introduction to Geophysics
Exam 3 Review Sheet
GLY3160 / PHY3160
Chapter 9: Gravity on a Large Scale and Isostasy
What is isostasy?
What does it mean if the free-air anomaly is nearly zero over a large continental mountain range?
What if the free-air anomaly is negative?
What if the free-air anomaly is positive?
What does it mean if the Bouguer anomaly is negative over large continental mountain range?
What if the Bouguer Anomaly is zero?
What if the Bouguer Anomaly is positive?
In what ways do mountains follow Archimedes principle?
What is isostatic equilibrium? What does it mean to be isostatically compensated?
What is the weight equation? The height equation? Know how to use both to solve basic isostatic
problems. Be sure to know how to set up the blocks properly.
What is the Airy model of isostasy?
What does it require of crustal blocks and mountains?
Where does the Airy model agree best with geologic and geophysical data?
What is the Pratt model if isostasy?
What does it require of crustal blocks and mountains?
Where does the Pratt model agree best with geologic and geophysical data?
Why are both the Airy and Pratt models not the only two choices for isostasy models?
Chapter 12: Resistivity
What is resistivity? Conductivity? Resistance? Voltage? Potential Difference? Current?
How are resistivity and conductivity related?
What is Ohm’s Law and what is it useful for?
What does resistance depend on? What does resistivity depend on?
Is resistance or resistivity a material property?
Know the mathematical rules for resistors in series and parallel and know how to apply them
Why does adding a voltmeter and an ammeter not change the resistance of a circuit?
What is the relative resistance of a voltmeter (very high or very low)?
Why is this required?
How must a voltmeter be connected to a circuit? (series/parallel)
What is the relative resistance of an ammeter (very high or very low)?
Why is this required?
How must a voltmeter be connected to a circuit? (series/parallel)
What controls the resistivity of geologic materials?
In general what kind of rocks (sed, Ig, Meta) have low resistivity? Why?
In general what kind of rocks (sed, Ig, Meta) have high resistivity? Why?
How does a resistivity meter work? What does the resistivity device actually measure?
Introduction to Geophysics
Exam 3 Review Sheet
GLY3160 / PHY3160
Why are four electrodes necessary? Be able to draw the setup and explain it.
What path does current take in the subsurface between two electrodes?
How does refraction affect subsurface current path lines?
What is a geometrical correction factor and why is it necessary?
Know the general setup of a Wenner array. If I ask questions about the other type of arrays I will
describe their setup.
In general, what parameter controls the depth of penetration of an electrical resistivity survey?
How can a survey be adjusted to ‘see’ deeper or shallower?
Why are the resistivities calculated in a resistivity survey referred to as ‘apparent resistivity?’
I will not make you fit an apparent resistivity curve to a master curve, but you should know what a
master curve is and why this is done.
Be able to visually inspect a multi-layer VES apparent resistivity curve to determine the number of
layers present
What are some limiting factors for resistivity surveys?
What is equivalence?
Don’t worry about the mathematical details. Just know what equivalence is and why it is an
issue that we should be aware of in a resistivity survey.
What is electrical profiling? Electrical imaging? Vertical Electrical Sounding (VES)?
What are pseudosections and why are they not ‘true’ sections? Are ‘true’ sections really true?
Do resistivity surveys produce non-unique results?
Be able to discuss this with a couple of simple examples
Lab Stuff
Be able to do problems similar to what was given in the labs.
Make sure to practice resistivity stuff on your own, since we didn’t have a full lab assignment on
that technique.