Seismology Flashcards
What is seismology?
The study of seismic waves passing through the Earth (body wave) or along its surface (surface wave).
What is the Laplacian version of the wave equation?
d^2u/dt^2 = c^2 * ∇^2u
What is a general solution to the wave equation?
Plane waves: u(r,t) = u0*exp(i(kr-ωt))
What is the bulk modulus?
The ratio of hydrostatic pressure increase to resulting relative decrease in volume: K = -dP/(dV/V) [Pa]
What is the shear modulus?
Distorts the material without changing the volume (amount of distortion per unit stress: μ = (F/A)/(Δ
x/l) [Pa]
How does the bulk modulus compare to the shear modulus in normal materials?
K > μ > 0
What is the wave equation for compressional waves?
d^2Ф/dt^2 = α^2*∇^2Ф, where α = sqrt((K+4μ/3)/ρ)
What is the wave equation for shear waves?
d^2Ψ/dt^2 = β^2*∇^2Ψ, where β = sqrt(μ/ρ)
What can compressional waves travel in? What can shear waves travel in?
Compressional - solids and liquids
Shear - solids only
What can measuring the propagation speeds α and β give us?
Can tell us about properties of deeply buried layers and earthquake location (focus).
What is a compressional and shear wave?
Compressional is a longitudinal wave whereas shear is a transverse wave
What are the two main types of surface waves?
- Rayleigh waves: no transverse particle motion
- Love wave: only transverse motion
What is the epicentre and focus of an earthquake?
The focus is the centre of the earthquake. The epicentre is the position on the earths surface vertically above the focus.
How is energy distributed in a wave?
Equally distributed across wavefront.
What is the equation for energy of a 2D wave (surface wave)?
E ∝ 1/2πr
What is the equation for energy of a 3D wave (body wave)?
E ∝ 1/4πr^2
What are shadow zones?
Zones where certain waves generally are not seen.
What is snells law in 3 different versions?
n1*sin(θ1) = n2*sin(θ2) sin(θ2)/β2 = sin(θ1)/β1 sin(θ2)/α2 = sin(θ1)/α1
What is the principle of least time?
Smoothly varying refractive index causes wave to follow path that minimises travel time.
What does the principle of least time mean we can do?
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.
What do we use to make direct measurements of seismic waves?
Use a seismometer with the displacement if the Earth’s surface.
What are compressional waves denoted by in the mantle, outer core and inner core?
Mantle = p-wave
Outer core = K-wave
Inner core = I-wave
What are shear waves denoted by in the mantle and inner core?
Mantle = s-wave
Inner core = J-wave
What i the equation for x, the displacement of the wave at time t?
x = Δt/(1/β - 1/α)
What is traingulation?
Using 3 or more seismometers to take different readings, and can use this to find the focus of the earthquake.
What is seismic wave travel time inversion?
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.
What is the pressure increase equal to as we move further into the Earth?
dP = -g(r)ρ(r)dr
What is g(r) equal to for the earth?
GM/r^2
What is the Adams-Williamson Equation?
dP/dr = -GMρ(r)/(r^2*(α(r)^2 - 4/3 * β(r)^2))
