# Earth's Gravity and Large-Scale Anomalies Flashcards

1
Q

What should we expect when we measure Earth’s gravity across the Earths surface?

A

Equipotential surface, with r = R(Earth) all the way round.

2
Q

What is the angular velocity of the Earth?

A

2π/(24 hrs)

3
Q

What is the equation for centripetal acceleration of Earth?

A

a = ω^2 * r = ω^2R(earth)sin(θ)

4
Q

What is the equation for the corrected gravity due to earths rotation?

A

g(rot) = g - ω^2R(earth)cos^2(λ)

5
Q

What is the shape of the Earth and what does this mean for the gravity?

A

It is an oblate spheroid, and this means it has changes in g due to your z-position on Earth (due to centripetal acceleration)

6
Q

What is the reference gravity formula? What are the values of the letters?

A

g(λ) = g(0)*(1+𝛿sin^2(λ)+εsin^4(λ))

```𝛿 = 5.279*10^-3
ε = 2.346*10^-5```
7
Q

What is a geoid?

A

Surface on which gravity is equal everywhere, and to which the direction of gravity is perpendicular to its surface

8
Q

How do we make corrections to the reference gravity formula?

A

Use accurate gravimetres to measure local variations in gravity to ~ 10^-6 g

9
Q

What is the equation for the gravity anomaly?

A

g(A) = g(0) - (g(λ) +/- sum over i of 𝛿(gi))

10
Q

What is the free air correction? What is 𝛿(gF) equal to for this?

A

Accounts for height of measurement above sea level. 𝛿(gF) = 2g(λ)h/R(earth) = 2gh/R(Earth) ~ 0.31 mgal m^-1

11
Q

What is the Bouguer correction? What is 𝛿(gB) equal to for this?

A

Corrects for density differences.

𝛿(gB) = 2πG(ρ1 - ρ0)*t, where t is the thickness of the slab, ρ1-ρ0 is the difference in density

12
Q

What is the terrain correction? How is it calculated?

A

Correct for true lateral density profiles. Can make a full digital terrain model and numerically integrate to obtain the full terrain correction. (full bouguer correction)

13
Q

How can we use gravity corrections to find unknown densities?

A

Find the corrected gravity equation and rearrange the equation for ρ(unknown).

14
Q

What is isostasy?

A

Lithosphere floats on the asthenosphere, which behaves like a liquid on a geological timescale.

15
Q

What is the equation relating volume and density of ice in water?

A

V(sub)/V(tot) = ρ(ice)/ρ(water)

16
Q

What is the principle of isostasy?

A

Over a region of isostatic equilibrium the total mass per unit area of the lithosphere should be constant.

17
Q

What are the two models widely used for isostatic equilibrium?

A
• Airy model

- Pratt model

18
Q

What happens in the airy model?

A

Vary crust thickness with constant ρ, ρ(s)>ρ(L), where ρ(s) is the density of the asethenosphere and ρ(L) is the density of the lithosphere

19
Q

When must r be present in the airy model?

A

When h pretrudes (out of the water)

20
Q

When must t be present in the airy model?

A

When the oceanic crust is thinner.

21
Q

What happens in Pratts model?

A

Vary density at constant substrate depth, can calculate mass/area using different densities and multiplying by the height.