Download 4 Surface Waves

Observational Seismology
Lecture 4
Surface Waves and Dispersion
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Surface Wave Dispersion
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Observations
stretched
P
S
SS
stretched
SSS
wave packet
dispersed
surface waves
Body waves
Impulsive, short period (but later arrivals are stretched
out due to attenuation). Higher frequencies make waves “sharper”.
Surface waves Dispersed, arrive in wave packets. But note a wave
packet might be a single wavelet (oceanic arrivals).
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Reminder
Phase velocity v = f λ
Period T
Amp
f – frequency = 1/T (s-1)
λ - wavelength (m)
t
But a whole spectrum of different period or frequency waves are emitted
from an earthquake because earthquake rupture is a complex fracture
process.
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Body waves
Body waves all travel at the same velocity even if they are different
frequencies, as travelling through the body of the Earth where
velocity changes are gradual (except for major discontinuities).
Reminder
1/ 2
⎛ K S + 4 .µ ⎞
3 ⎟
α = ⎜⎜
⎟
ρ
⎝
⎠
↓v increasing
1/ 2
⎛µ⎞
β = ⎜⎜ ⎟⎟
⎝ρ⎠
Velocity just depends on local elastic properties, e.g, of core
or mantle
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Types of surface waves
Love wave
Rayleigh wave
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Surface waves
Surface waves travel close to surface
depth z
Amplitude
Amplitude of surface waves decays
exponentially with depth
A( z ) = A0 e − Z Z 0
Amplitude at surface
At Z = Z0
Characteristic depth
of penetration
A(z) = A0 / e ~ A0 / 2
i.e., the amplitude at the characteristic depth of penetration is
approx. half surface amplitude
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Particle motion of Rayleigh waves
rolling surface wave
Retrograde ellipse
amplitude
decays
exponentially
with depth
- Z0
A = A0/2
Characteristic depth of penetration is proportional to wavelength of surface wave
Z0 ∝ λ ∝ T ∝ 1/f - the longer wavelength the deeper it will penetrate
e.g., for T = 20s, v ∼ 4km/s, then λ ∼ 80km,
c.f. lithospheric thickness
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Dispersion
surface
Short T
Short λ
High f
Long T
Long λ
Low f
Low speed
Moho
lithosphere
High speed
Penetrates deeply into high speed layer so will travel faster
So long period waves, as they penetrate deeply into the Earth travel at
higher velocities; short period waves travel at slower velocities
This is normal dispersion
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Dispersion measured from seismograms
Surface waves are a complex superposition of simple harmonic waves.
Complex because earthquake source and lithospheric structure are complex.
Dispersion
Oceanic
Rayleigh wave
Long T
arrives first
This peak travels at group velocity vG
They travel at a group velocity because each peak can
represent a group of S.H.M.
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Types of dispersion
a) v gradually increasing with depth
Long T arrives fist
v
Long period
travelling at high
velocity
Normal dispersion
z
b) v gradually decreasing with depth
v
Short T arrives first
Long period
travelling at low
velocity
z
Reverse dispersion
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Types of dispersion
c) velocity constant
v
z
Impulsive arrival - all
frequencies arrive together
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Types of dispersion
P wave velocity
d) Oceanic dispersion
water
10 km sediments
oceanic crust
upper mantle
1.5 km/s
1.5
4
6
8
v km/s
Moho
10 km
6-8 km/s
8 km/s
z
Sediments smooth
out layering
Not
particularly
sharp
Large change in velocity in
just 10 km - lots of dispersion
1) Lot of Rayleigh waves because big change in velocity in short depth.
Wave train very dispersed.
2) Less Love waves because no distinct layering (no distinct Moho),
thinner crust. (No shear waves in water anyway.)
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Types of dispersion
e) Continental dispersion
P wave velocity
“Not seen”
6
8
sediments (ignore)
upper crust
30 km
v km/s
Conrad
lower crust
mantle
Distinct
Moho
30 km
z
1) Less Rayleigh because smaller change in velocity in greater depth.
Continents do not provide big enough velocity difference for great dispersion.
not so dispersed
Some low frequency,
long period responding
to gradual increase in v
beneath Moho
Airy phase responding to 6
km/s thick continental crust
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Types of dispersion
d) Continental dispersion
crust
6 km/s
Trapped SH
waves
Continental crust →
distinct layer “trap” for
Love waves
mantle 8 km/s
Before advent of exploration and use of aftershock seismic arrays, surface
waves were the main means for determining the structure of the lithosphere
on a regional scale. Surface waves directly sample the lithosphere.
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD
Dispersion
Note that phase and group velocity are strongly
dependent on period especially at low frequency
Note that the phase velocity is faster than the group
velocity
GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD