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Rayleigh wave particle motion (ipython notebook) Let us visualize Rayleigh wave particle motion in the x-z plane

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Seismologie Oberflächenwellen

1. The 2002 Denali earthquake recorded GEOSCOPE station SPB (vertical component) in Brazil at an epicentral distance of 115.4 deg. Time is from the earthquake origin time.

Love or Rayleigh waves? Why?

Measure the average time and the separation between successive waveform troughs over the interval 3200 to 3600 s. Make a table of velocity as a function of wave period.

Compare with the dispersion curve predicted for PREM.

From Shearer.

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2. Rayleigh wave particle motion (ipython notebook)

Let us visualize Rayleigh wave particle motion in the x-z plane. The equation of motions for a Rayleigh wave in a homogeneous half space in x-direction is given by

) ( cos ) 4679

. 1 8475

. 0 (

) ( sin ) 5773

. 0 (

3933 . 0 8475

. 0

3933 . 0 8475

. 0

x ct k e

e C

u

x ct k e

e C u

kz kz

z

kz kz

x

+

=

=

At first assume phase velocity c=3 km/s; period T = 1s.

Plot the maximum displacements ux and uz as a function of depth, plot also the (normalized) elastic energy (ux2 + uz2) in the same plot. Discuss the behaviour with depth.

Plot the elastic energy as a function of depth for a representative range of periods for surface waves. Discuss the results.

Plot the time-varying particle motion (i.e., ground displacement) in the x.z plane for a fixed depth and given period of T=1 s. Discuss the characteristics of the particle motion as a function depth. Find – by trial and error – the depth at which the particle motion properties change. How does this depth depend on period?

3. Love waves (ipython notebook) (From Shearer)

Model the crust as a simple layer over a half-space as in Figure 8.2, with h = 40 km, ρ1= 2.7 g/cm3, ρ2= 3.3 g/cm3, β1 = 3.5 km/s, and β2 = 4.5 km/s. Find the lowest value of ω (i.e., the fundamental mode) that satisfies the equation below at values of phase velocity (c = 1/p) between β1 and β2 . Convert ω to period, T, and plot your results as c(T) which corresponds to a Love wave dispersion curve (fundamental mode) . Hint: Solve the equation for ω. Make sure that you use consistent units in computing the μ values the equation.

2 2 1 1

2 2 2 2 2

2

1 1/ 1/

/ 1 / ) 1

/ 1 / 1 tan(

c c c

H

=

µ β

β β µ

ω

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Free oscillations

Drei starke Erdbeben wurden an der Station WET beobachtet. Die Seismogramme wurden in die transversale Richtung rotiert.

Die schwarzen Spuren sind die transversalen Beschleunigungen (rot sind die Rotationen).

a. Mw9:0 Tohoku (2011) b. Mw = 8:8 Maule,Chile (2010) c. Mw8:1 Samoa. Alle Beben wurden in Wettzell aufgezeichnet. Erklären Sie die Unterschiede der Zeitintervalle zwischen GN und GN+1. Welche Konsequenzen für die Antipoden von großen Erdbeben (oder Meteoriteneinschlägen)?

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Die folgenden Spektren wurden aus den obigen Zeitreihen ermittelt:

1. Chile, b. Samoa. Woran liegt die unterschiedliche Breite der Spektrallinien? Was beeinflusst die relativen Amplituden der Spektrallinien?

2. Die Translations und Rotationsspektren sehen – obwohl am gleichen Ort aufgezeichnet – unterschiedlich aus, was könnte der Grund sein?

3. Welche tiefenabhängige physikalische Eigenschaft des Erdinneren ist am schlechtesten bestimmt und lässt sich fast nur aus Eigenschwingungen ableiten?

4. Welche Phänomene führen zum Aufsplitten einzelner Spektrallinien in so genannte Multiplets?

5. Der Ton A hat eine Frequenz von 440 Hz. Der tiefe Ton C hat bereits eine „Hilfslinie“. Pro Oktave braucht man 3.5 Linien. Wo müsste der Erd-„Ton“ für 0S2 im Violinschlüssel notiert werden (wieviele Hilfslinien)? Zur Erinnerung: Die Frequenz des ersten Obertons (erste Oktave) ist zweimal die Frequenz des Grundtons. Wie viele Oktaven, bis Sie zum A kommen?

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