Earth's Gravity and Large-Scale Anomalies

Question 1

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

Answer 1

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

Question 2

What is the angular velocity of the Earth?

Answer 2

2π/(24 hrs)

Question 3

What is the equation for centripetal acceleration of Earth?

Answer 3

a = ω^2 * r = ω^2R(earth)sin(θ)

Question 4

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

Answer 4

g(rot) = g - ω^2R(earth)cos^2(λ)

Question 5

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

Answer 5

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

Question 6

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

Answer 6

g(λ) = g(0)*(1+𝛿sin^2(λ)+εsin^4(λ))

𝛿 = 5.279*10^-3
ε = 2.346*10^-5

Question 7

What is a geoid?

Answer 7

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

Question 8

How do we make corrections to the reference gravity formula?

Answer 8

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

Question 9

What is the equation for the gravity anomaly?

Answer 9

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

Question 10

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

Answer 10

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

Question 11

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

Answer 11

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

Question 12

What is the terrain correction? How is it calculated?

Answer 12

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)

Question 13

How can we use gravity corrections to find unknown densities?

Answer 13

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

Question 14

What is isostasy?

Answer 14

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

Question 15

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

Answer 15

V(sub)/V(tot) = ρ(ice)/ρ(water)

Question 16

What is the principle of isostasy?

Answer 16

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

Question 17

What are the two models widely used for isostatic equilibrium?

Answer 17

• Airy model

- Pratt model

Question 18

What happens in the airy model?

Answer 18

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

Question 19

When must r be present in the airy model?

Answer 19

When h pretrudes (out of the water)

Question 20

When must t be present in the airy model?

Answer 20

When the oceanic crust is thinner.

Question 21

What happens in Pratts model?

Answer 21

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