# Earth's Gravity and Large-Scale Anomalies Flashcards

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

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

What is the angular velocity of the Earth?

2π/(24 hrs)

What is the equation for centripetal acceleration of Earth?

a = ω^2 * r = ω^2*R(earth)*sin(θ)

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

g(rot) = g - ω^2*R(earth)*cos^2(λ)

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

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

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

g(λ) = g(0)*(1+𝛿sin^2(λ)+εsin^4(λ))

𝛿 = 5.279*10^-3 ε = 2.346*10^-5

What is a geoid?

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

How do we make corrections to the reference gravity formula?

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

What is the equation for the gravity anomaly?

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

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

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

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

Corrects for density differences.

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

What is the terrain correction? How is it calculated?

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)

How can we use gravity corrections to find unknown densities?

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

What is isostasy?

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

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

V(sub)/V(tot) = ρ(ice)/ρ(water)