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 stretched dispersed

PS SS SSS wave packet 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

Period T Phase velocity v = f λ 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 α ⎛ 4 ⎞ K S + µ. = ⎜ 3 ⎟ ⎜ ρ ⎟ ↓v increasing ⎝ ⎠

1/ 2 β ⎛µ ⎞ = ⎜ ⎟ ⎝ 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 of surface waves decays exponentially with depth

Amplitude −Z Z0 A(z) = A0 e Characteristic depth Amplitude at surface of penetration

At Z = Z0 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 -Z A = A /2 exponentially 0 0 with depth

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 Short T Long T Short λ Long λ High f Low f surface 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. Oceanic Dispersion Rayleigh wave

Long T This peak travels at group velocity vG arrives first

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 v Long T arrives fist Long period travelling at high velocity

z Normal dispersion 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 1.5 4 6 8 v km/s water 1.5 km/s 10 km Moho 10 km sediments oceanic crust 6-8 km/s Not Sediments smooth particularly upper mantle 8 km/s z out layering 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” 68 sediments (ignore) v km/s upper crust Conrad 30 km lower crust Distinct mantle 30 km Moho 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

Trapped SH Continental crust → crust 6 km/s waves 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