Seismology

Question 1

What is seismology?

Answer 1

The study of seismic waves passing through the Earth (body wave) or along its surface (surface wave).

Question 2

What is the Laplacian version of the wave equation?

Answer 2

d^2u/dt^2 = c^2 * ∇^2u

Question 3

What is a general solution to the wave equation?

Answer 3

Plane waves: u(r,t) = u0*exp(i(kr-ωt))

Question 4

What is the bulk modulus?

Answer 4

The ratio of hydrostatic pressure increase to resulting relative decrease in volume: K = -dP/(dV/V) [Pa]

Question 5

What is the shear modulus?

Answer 5

Distorts the material without changing the volume (amount of distortion per unit stress: μ = (F/A)/(Δ
x/l) [Pa]

Question 6

How does the bulk modulus compare to the shear modulus in normal materials?

Answer 6

K > μ > 0

Question 7

What is the wave equation for compressional waves?

Answer 7

d^2Ф/dt^2 = α^2*∇^2Ф, where α = sqrt((K+4μ/3)/ρ)

Question 8

What is the wave equation for shear waves?

Answer 8

d^2Ψ/dt^2 = β^2*∇^2Ψ, where β = sqrt(μ/ρ)

Question 9

What can compressional waves travel in? What can shear waves travel in?

Answer 9

Compressional - solids and liquids

Shear - solids only

Question 10

What can measuring the propagation speeds α and β give us?

Answer 10

Can tell us about properties of deeply buried layers and earthquake location (focus).

Question 11

What is a compressional and shear wave?

Answer 11

Compressional is a longitudinal wave whereas shear is a transverse wave

Question 12

What are the two main types of surface waves?

Answer 12

• Rayleigh waves: no transverse particle motion

- Love wave: only transverse motion

Question 13

What is the epicentre and focus of an earthquake?

Answer 13

The focus is the centre of the earthquake. The epicentre is the position on the earths surface vertically above the focus.

Question 14

How is energy distributed in a wave?

Answer 14

Equally distributed across wavefront.

Question 15

What is the equation for energy of a 2D wave (surface wave)?

Answer 15

E ∝ 1/2πr

Question 16

What is the equation for energy of a 3D wave (body wave)?

Answer 16

E ∝ 1/4πr^2

Question 17

What are shadow zones?

Answer 17

Zones where certain waves generally are not seen.

Question 18

What is snells law in 3 different versions?

Answer 18

n1*sin(θ1) = n2*sin(θ2)
sin(θ2)/β2 = sin(θ1)/β1
sin(θ2)/α2 = sin(θ1)/α1

Question 19

What is the principle of least time?

Answer 19

Smoothly varying refractive index causes wave to follow path that minimises travel time.

Question 20

What does the principle of least time mean we can do?

Answer 20

If we smoothly vary the refractive index, the wave with smoothly curve around, changing direction. We can use this to estimate the angle of the transmitted wave as things like the inner core do not have a uniform refractive index.

Question 21

What do we use to make direct measurements of seismic waves?

Answer 21

Use a seismometer with the displacement if the Earth’s surface.

Question 22

What are compressional waves denoted by in the mantle, outer core and inner core?

Answer 22

Mantle = p-wave
Outer core = K-wave
Inner core = I-wave

Question 23

What are shear waves denoted by in the mantle and inner core?

Answer 23

Mantle = s-wave

Inner core = J-wave

Question 24

What i the equation for x, the displacement of the wave at time t?

Answer 24

x = Δt/(1/β - 1/α)

Question 25

What is traingulation?

Answer 25

Using 3 or more seismometers to take different readings, and can use this to find the focus of the earthquake.

Question 26

What is seismic wave travel time inversion?

Answer 26

Can obtain travel times for many different ray paths between different places, and refine out models of seismic wave speeds α(r) and β(r) as a function of depth.

Question 27

What is the pressure increase equal to as we move further into the Earth?

Answer 27

dP = -g(r)ρ(r)dr

Question 28

What is g(r) equal to for the earth?

Answer 28

GM/r^2

Question 29

What is the Adams-Williamson Equation?

Answer 29

dP/dr = -GMρ(r)/(r^2*(α(r)^2 - 4/3 * β(r)^2))