Surface Waves

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Observational Seismology

Lecture 4Surface Waves and Dispersion


Surface Wave Dispersion


Observationsstretched stretched dispersed

P S SS SSSsurface waveswave packet

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).


Reminder

Phase velocity v = f Amp

t

Period T

f frequency = 1/T (s-1)

- wavelength (m)

But a whole spectrum of different period or frequency waves are emitted from an earthquake because earthquake rupture is a complex fracture process.


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).

v increasing2/1

.34

+=

SK

2/1

=

Reminder

Velocity just depends on local elastic properties, e.g, of core or mantle


Types of surface waves

Love wave

Rayleigh wave


Surface waves

Amplitude

Surface waves travel close to surface

Amplitude of surface waves decays exponentially with depth

00)(

ZZeAzA = Characteristic depth of penetrationAmplitude at surface

At Z = Z0 A(z) = A0 / e ~ A0 / 2

i.e., the amplitude at the characteristic depth of penetration is approx. half surface amplitude

depth z


Particle motion of Rayleigh wavesrolling surface wave

amplitude decays

exponentially with depth

Retrograde ellipse

- Z0 A = A0/2

Characteristic depth of penetration is proportional to wavelength of surface wave

Z0 T 1/f - the longer wavelength the deeper it will penetratee.g., for T = 20s, v 4km/s, then 80km, c.f. lithospheric thickness


Dispersion

surface

MohoLow speed

lithosphere

Penetrates deeply into high speed layer so will travel faster

High speed

Short T Short High f

Long T Long Low f

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


Dispersion measured from seismograms

OceanicRayleigh wave

Long T arrives first

This peak travels at group velocity vG

Surface waves are a complex superposition of simple harmonic waves. Complex because earthquake source and lithospheric structure are complex.

Dispersion

They travel at a group velocity because each peak can represent a group of S.H.M.


Types of dispersion

a) v gradually increasing with depthLong T arrives fist

Long period travelling at high velocity

Normal dispersion

b) v gradually decreasing with depth

Long period travelling at low velocity

v

v

z

z Reverse dispersion

Short T arrives first


Types of dispersion

c) velocity constant

Impulsive arrival - all frequencies arrive together

v

z


Types of dispersion

d) Oceanic dispersion

Large change in velocity in just 10 km - lots of dispersion

z

v km/s

10 km

1.5 4 6 8

Moho

Not particularly sharp

Sediments smooth out layering

water 1.5 km/ssedimentsoceanic crust 6-8 km/s

upper mantle 8 km/s

10 km

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.)

P wave velocity


Types of dispersion

e) Continental dispersion

z

v km/s

30 km

6 8

Distinct Moho

Not seensediments (ignore)upper crust

mantle

30 km lower crustConrad

P wave velocity

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

Airy phase responding to 6 km/s thick continental crust

Some low frequency, long period responding to gradual increase in v beneath Moho


Types of dispersion

d) Continental dispersion

crust 6 km/s

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.

Trapped SH waves

Continental crust distinct layer trap for Love waves


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

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Surface Waves