Chapter 3 : Gravity

Question 1

Where is the mass seemingly concentrated for any exterior point?

Answer 1

At the center of the mass

Question 2

Where is the mass seemingly concentrated for any interior point?

Answer 2

Gravitational acceleration only due to mass close to the center inside point’s radius

Question 3

Why is earth’s gravitational acceleration not constant over the surface?

Answer 3

Earth is not a perfect sphere but an oblate spheroid (40% variation), earth rotates, reducing gravity due to centrifugal acceleration (60% variation)

Question 4

Where is gravity slightly larger?

Answer 4

0.5% larger at poles relative to equator

Question 5

Geoid

Answer 5

Earth’s shape (reference shape), the equipotential surface corresponding to mean sea level and the level water would lie if imaginary channels were cut across continents

Question 6

Reference spheroid

Answer 6

The oblate spheroid that best approximates the geoid and is a mathematical figure whose surface is an equipotential of the theoretical gravity field of a symmetric spheroidal earth model including centrifugal acceleration

Question 7

Isostasy

Answer 7

The state of gravitational equilibrium between Earth’s crust and mantle such that the crust ‘floats’ at an elevation that depends on its thickness and density

Question 8

Compensation depth

Answer 8

depth below which all pressures are hydrostatic (weight of all columns of same cross-sectional area must be equal at this depth

Question 9

What are the formulations of isostasy?

Answer 9

Airy hypothesis and Pratt hypothesis (or combination)

Question 10

Airy hypothesis

Answer 10

Assumes rigid upper layer with density pu, deformable substatum ps, and isostatic compensation achieved by different column heights

Question 11

Pratt hypothesis

Answer 11

Assumes constant depth for base of upper layer and isostatic equilibrium achieved by different column densities

Question 12

Gravity anomaly

Answer 12

difference from the expected gravity due to sub-surface density variations

Question 13

What corrections to observed gravity are needed to detect gravity anomalies?

Answer 13

Latitude of observation point using reference gravity formula
Elevation above or below reference spheroid - sea level (free-air anomaly)
Excess mass correction
Terrain corrections

Question 14

Bouguer correction

Answer 14

Gravity anomaly of the excess or deficiencies in mass

Question 15

How does topography affect observed gravity?

Answer 15

Too low observed gravity (valley’s lack of mass -> decreased downward pull, mountain’s extra mass -> increased upward pull

Question 16

Isostatic equilibrium

Answer 16

No excess/lack of mass above compensation depth, little free-air gravity anomaly/negative Bouguer anomaly

Question 17

Uncompensated structure

Answer 17

Positive free-air anomaly and zero Bouguer anomaly

Question 18

How do mass deficits affect gravity?

Answer 18

Negative anomaly in gravity, positive anomaly in potential, negative geoid height anomaly (trough)

Question 19

How does mass excess affect gravity?

Answer 19

Positive gravity anomaly, negative potential anomaly, positive geoid height anomaly (bulge)