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Geo 3010 > Exam 3 Review > Flashcards

Exam 3 Review Flashcards

1
Q

Newton’s Law of Gravitation Equation

A

F = -Gm1m2/r2​

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2
Q

Centrifugal acceleration:

A

|a| = w2REcosλ

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3
Q

The Universal Constant of Gravitation (G)

A

G=6.67*10-11 N*m2 / kg2​

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4
Q

gravitational acceleration (g):

A

9.8 m/s2​

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5
Q

Compositional Layers of the Earth & Thicknesses

A

Crust

  • Oceanic (gabbro, basalt) (~7km)
  • Continental (granitoids) (20-70 km)

Upper Mantle (peridoite, 75% olivine, 25% pyroxyene) (70-660 km)

Transition Zone (Mg2SiO4, spinel structure, 10% more dense) (410-660 km)
Lower Mantle (pyrovskite) (660 km-2891 km)
D" (post pyrovskite (more dense)) (2541 - 2741 km)
Outer Core (Fe, S, Ni, liquid) (2891 km to 5150 km)
Inner Core (Solid Fe, Ni) (5150 to 6371 km)
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6
Q

What is the oceanic crust made of?

A

Gabbro (basalt)

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7
Q

What is the thickness of the oceanic crust?

A

~7 km

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8
Q

What is the continental crust made of?

A

Granitoids

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9
Q

What is the thickness of the contiental crust?

A

20-70 km

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10
Q

What is the upper mantle made of?

A

peridotite (75% olivine, 25% pyroxene)

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11
Q

What is the thickness of the upper mantle?

A

70 km to 660 km

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12
Q

What is the transition zone made of?

A

Mg2SiO4 (spinel structure 10% more dense)

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13
Q

What is the thickness of the transition zone?

A

410-660 km

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14
Q

What is the lower mantle made of?

A

Pyrovskite

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15
Q

What is the thickness of the lower mantle?

A

660 to 2891 km

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16
Q

What is the D’’ layer made of?

A

post pyrovskite (more dense)

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17
Q

What is the thickness of the D’’ layer?

A

~2541 - 2741 km to 2891 km

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18
Q

What is the outer core made of?

A

Liquid Fe, S, Ni

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19
Q

What is the thickness of the outer core?

A

2891 to 5150 km

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20
Q

What is the inner core made of?

A

Solid Fe, Ni

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21
Q

What is the thickness of the inner core?

A

5150 to 6371 km

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22
Q

Draw the setup for the Wenner Array

A

See L12-9

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23
Q

What is unique about the spacing for the Wenner Array?

A

Equal spacing, a

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24
Q

What is the equation for resistivity for the Wenner Array?

A

p = 2πaΔV/I

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25
Q

What is ra equal to for the Wenner Array?

A

a

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26
Q

What is rb equal to for the Wenner Array?

A

2a

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27
Q

What is Ra equal to for the Wenner Array?

A

2a

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28
Q

What is Rb​ equal to for the Wenner Array?

A

a

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29
Q

What is the procedure for the Wenner Array? (Draw diagram)

A

The procedure is to make measurements of ΔV where we keep enlarging the array (always keeping an even distance a), centered above a central point in the field. (DRAW DIAGRAM L12-10)

30
Q

What is the convention on how we determine the spacing, a, for each increase in overall width of the array?

A

a is equally spaced on a logarithmic scale with 6 points per decade.

31
Q

What is the drawback to the Wenner Array?

A

all four electrodes (battery & voltmeter) have to be moved in between each measurement, tedious.

32
Q

What is the resistivity technique based on?

A

Based on artificially generating a current beneath the ground.

33
Q

How to do the resistivity technique?

A

Essentially, hook up a battery with electrodes stuck into the ground.

Then, using a voltmeter we measure the potential differences between different points in the ground.

34
Q

What does the resistivity technique tell you and what can that information be used to infer?

A

It tells you the variations in the measured potential differences and that is used to infer electrical properties of the subsurface.

35
Q

What does the resistivity technique aim to do?

A

Measure the resistivity of materials beneath the surface.

36
Q

What is conducting when resistivity is measured?

A

In rocks and soil, current is mostly carried by the passage of ions in pore waters (electrolytic conduction)

37
Q

What happens with multiple layers each having a different resistivity? (where does the current want to flow?)

A

Basically, the current wants to flow where the resistance to flow is the smallest.

38
Q

Draw the diagram for multiple layers wit the electrode set up and the corresponding resistivity measurement graph.

A

L13-4

39
Q

See figure on L13-5, read over, draw a bunch

A
40
Q

How is G measured experimentally? (with a diagram)

A

DRAW DIAGRAM L14-2

The experiment used a torsion balance.

Basically, you attach two masses (with mass m) at the end of a bar hanging from a string. This way the bar and masses are allowed to rotate as indicated by the arrow.

Now, if you bring into place two larger masses (with mass M) at a fixed location, the two smaller masses will be attracted and will rotate on the pendulum to be closer to the larger masses.

Next, if we balance the torque exerted on the string to the gravitational force, we can measure G.

41
Q

How was g measured experimentally?

A

ag= -G*(ME/RE2​)

42
Q

What is a gal?

A

cm/s^2

43
Q

What is the gravitational acceleration?

A

9.8 m/s^2 or 981 gal

44
Q

Why is earth shaped the way that it is?

A

Centrifugal Acceleration

Centripetal acceleration is directed radially inward.

But, in the earth’s reference frame, the object experiences a centrifugal acceleration outward.

If we measure the acceleration of an object on a rotating body, we need to take both the gravitation and centrifugal acceleration into account.

  • That is, what we measure, g, is actually a vector sum of the gravitational and centrifugal accelerations and is not directed radially inward.

FINALLY. Because of the effect of centrifugal acceleration, the Earth is not shaped like a sphere.

  • The outward force makes the earth shaped like an ellipsoid, where it bulges out more at the equator.
45
Q

How is the shape of the Earth defined?

A

As an equipotential surface of gravity.

46
Q

What equipotential surface is used to define the shape of the Earth?

A

An equipotential surface that coincides with the mean sea level.

47
Q

Why is the earth’s equipotential surface closer to an ellipsoid than a sphere?

A

Centrifugal acceleration

48
Q

How is the precise determination of the shape of the earth determined?

A

Through gravity measurements

49
Q

What is the procedure to determine the shape of the earth?

A

Try and fit gravity measurements to a best fitting ellipsoid

50
Q

What does a, the semimajor axis, of the ellipsoid represent?

A

equatorial radius

51
Q

What does c, the semiminor axis represent?

A

polar radius

52
Q

What is the international reference ellipsoid and what does it give?

A

It’s the best fitting ellipsoid that gives a close approximation to the equipotential surface at mean sea level (math convenience)

53
Q

What can the reference ellipsoid be used to calculate?

A

The gravitational acceleration on a rotating oblate spheroid.

54
Q

What is the geoid?

A

The true equipotential surface at mean sea level

55
Q

What is elevation dependent on?

A

Different models

56
Q

What is it sometimes better to do with the ellipsoid when dealing with smaller regions of the Earth?

A

Define an ellipsoid that fits the local geoid better

57
Q

What affects the geoid?

A

Small scale variations like seamounts, trenches, etc.
Large scale variations, much deeper mass anomalies

58
Q

What is an ellipsoid?

A

oblate spheroid

59
Q

How is the ellipsoid and geoid related?

A

The ellipsoid is a mathematical model, but the geoid is the true equipotential surface

60
Q

What are the six corrections you have to make to gravity data?

A

Tidal corrections, Instrumental Drift, Rotating Earth, Free Air correction, Bouger Correction, Terrain Correction

61
Q

What is the Tidal Correction and what is it for?

A

This is the correction on the gravitational pull of the sun and the moon. You have to take the time and location of each measurement into account as the tides are well known and can be corrected for.

62
Q

What is instrumental drift and what is it used for?

A

Need to account for changes in g that resulted in changes in the instrument. Temperature changes induce elastic changes in the spring but this is minimized by keeping important bits in vacuum chamber at constant temp.

63
Q

How is a drift correction performed?

A

Measurements are made at the same station at different times in the day.

The most basic correction assumes that drift between measurements is linear between each reading.

So we find the linear trend between measurements at the same station and fit the same linear trend to the rest of the stations.

64
Q

What is the rotating earth correction and what is it used for?

A

Variable centrifugal acceleration that is latitude dependent, so g is latitude dependent, but we can correct this by using the reference gravity formula.

65
Q

What is the free air correction and what is it used for?

A

This is an elevation correction (accounts for measurement not being taken at sea level), but assuming vacuum in between sea level and the measurement point.

66
Q

What is the Bouguer correction and what is it used for?

A

With the free air correction, we assumed a vacuum existed between sea level and the elevation we took our measurement at, but this accounts for mass in between sea level and our measurement point. This is done be estimating the mass’s extra gravitational pull as an infinite sheet.

67
Q

What is the terrain correction and what is it used for?

A

The terrain correction accounts for extra or no mass with respect to the Bouguer slab. The Bouguer slab does not take topography into account. This is done by plotting points on a topo map and using a hammer circle to compute average elevation in an area.

68
Q

What kind of gravity anomalies do we get from a buried sphere?

A

A sphere could result in what looks like a normal curve or an upside down normal curve, depending on if the sphere had a greater or less than density than the surrounding material.

69
Q

What kind of gravity anomaly do we get from a buried cylinder?

A

The gravity anomaly looks very similar in shape to that of a buried sphere, except that the anomaly extends infinitely in the direction of the long axis of the cylinder

70
Q

What kind of gravity anomaly do we get from a buried semi-infinite sheet?

A

With a semi-infinite sheet, the gravity anomaly looks like a pH curve, with a shallower gradient the deeper the slab.

Geo 3010 (7 decks)

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