Seismology Flashcards
what are the 3 ways that materials deform
change volume (pressure from all sides)
change shape (shear)
change length (compression)
S wave velocity equation
Vs = sqrt (µ / rho)
µ = shear modulus
rho = density
p wave velocity equation
Vp = sqrt ((K +4/3 µ) / rho))
K = bulk modulus
µ = shear modulus
what is the order of typical seismic velocities
1-10 km/s
what type of waves are faster and what rocks are faster to move through
p faster than s
igneous faster than sediments
what are the 2 body waves and their characteristics
p waves
- pressure/primary
- longitudinal
- arrive first
s waves
- shear/secondary
- transverse (NOT in fluid)
what are the 2 surface waves and their characteristics
love waves
- pure horizontal shear
Rayleigh waves
- similar to ocean waves
- elliptical partical motion
- volume change
both:
velocity 0.9 x body waves
how do body vs surface waves decrease their amplitude with distance
body - decrease with 1/r^3
surface - decrease with 1/r^2
surface decrease less with distance therefore are more destructive
order of seismic wave arrivals
p wave
s wave
love wave
Rayleigh wave
when do standing seismic waves occur
after large earthquakes (>7.5), constructive interference around the earth creates standing waves of frequency = resonant frequency of earth.
shaking + destruction for longer time.
what is the wave equation in 2D
∂2u/∂x2 = c^2 . ∂2u/dt2
what are the factors influencing seismic velocities
stiffness ( k µ )
density
pressure
temperature
melt/volatiles (liquid µ = 0)
what is Snell’s Law
sinθ1/v1 = sinθ2/v2 = constant
formula for Ray Parameter / Horizontal Slowness
p = u . sinθ
= sinθ / v
(θ = angle to normal)
what is the wave slowness, u, formula
u = 1 / v
(v=wave velocity)
equation for critical angle reflection
sin θc = v1 / v2
(can find by subbing θ=90 into snells law)
what is Huygens principle
an interface between mediums acts as a source of waves
what are head waves, how are they generated, and how do they appear on a travel time graph
- generated along the interface upwards due to huygens principle
- appear after critical angle
- are fastest arrival after crossover distance
What does the travel time - distance curve look like for reflected waves and what does this show
- starts at vertical 2 way travel time
- gets closer to direct wave over long distances
What are the 3 components in the ray path
- P -> direction of ray path
- SV (shear vertical)
- SH (shear horizontal)
-> hor/ver oscillations perp. to direction, orthogonal to each other
what happens to P vs SV components of a wave at an interface
SV refracted at a smaller angle due to slower velocity
what should a travel time curve look like on a spherical earth vs a flat reference frame
spherical = looks like getting quicker (gradient decrease) as distance across surface less than actually travelled
flat = straight line constant gradient
how to find apparent velocity of a wave from a travel time curve
v = 1 / slope
Discuss the concept of ‘turning depth’
- velocities increase into earth
- will refract away from the normal when moving into a faster velocity layer
- gradually curve closer to horizontal
- return up as head waves
- depth reached depends on ray parameter
How does the ray parameter dictate geometry of wave path
small p = travel deeper
small p:
= small θ (near vertical), need to be refracted through more layers to get to horizontal
what is the ray parameter for a spherical earth
p = r. u. sinθ
how do anomalous changes in velocity at depth impact the travel time curves
Sudden increase -> triplications (waves taking different paths arrive at the same point at same time)
e.g. transition zone (olivine -> wadsleyite -> ringwoodite) = 2 sudden increases = 2 triplications
decrease (low velocity zone) -> refract other way -> gap in curve
e.g. liquid outer core
what is evidence for a solid inner core
low amplitude waves being discovered in p wave shadow zone.
p waves refracted deeper into liquid, then reflect off boundary to inner core, changing direction, allowing p waves in shadow zone predicted by only liquid core.
what has seismology revealed about the internal structure of the moon
has a fluid outer core and solid inner core like earth. Also has partial melt layer at base of mantle -> little change in density, existence revealed by drop in velocity
what are traveltime residuals and what is generally their pattern across earth
∆T = T(obs) - T(pred)
continents = -Ve = faster
oceans = +ve = slower
How can seismology image downgoing slabs and rising plumes in the earth
slabs = cold = fast velocity anomaly
plume = hot = slow velocity anomaly
anomalies seen in different wavelengths formed in standing waves across the earth in quakes -> fast = shorter wavelength
