# measureable seismic properties seismic velocities – p & s – relationship to elastic moduli...

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- Slide 1
- Measureable seismic properties Seismic velocities P & S Relationship to elastic moduli Seismic anisotropy -- directional variation in seismic velocity Seismic Attenuation 1/Q p & 1/Q s -- What is seismic attenuation? -- What causes seismic attenuation?
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- Seismic velocities = Shear modulus = Lame s lambda constant k = Bulk modulus = density
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- Measuring both V p and V s is useful The ratio of V s to V p depends on Poissons ratio (): A good approximation is often that then and V p /V s = This is called a Poisson solid We also sometime calculate the Seismic Parameter: V p 2 - 4/3 V s 2 = k Shows variations in the bulk modulus (compare to V s 2 =
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- Relationship of anisotropy and strain - xenolithsShear velocity of olivine Data from Kumazawa & Anderson [1969] Mainprice & Silver [1993] Seismic Anisotropy
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- Shear Wave Splitting
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- Seismic Attenuation In a perfectly elastic medium, the total energy of the wavefield is conserved Seismic attenuation is the absorption of seismic energy, or the deviation from perfect elasticity Surface waves Widmer & Laske [2007] Coutier & Revenaugh [2006] Body waves
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- Normal Modes Different Modes show different rates of amplitude decay So we can determine a Q for each mode Different Qs result from how each mode samples the earth
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- Attenuation variation in the Earth Gung & Romanowicz [2004]Pozgay, Wiens, et al. [2009]
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- Q Quality Factor Attenuation is quantified by 1/Q, in analogy to the damped harmonic oscillator (underdamped) Smaller Q results in faster damping (greater deviation from elastic case) Frequency-independent Q damps high frequencies more than low frequencies Q = 2 (total energy/energy lost during one cycle)
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- Shear and Bulk Q Shear wave attenuation results from relaxation of the shear modulus () P wave attenuation results from the relaxation of both the shear () and bulk () moduli In general bulk attenuation is thought to be very small in the earth (Q > 1000) If Q ~ and assuming a Poisson Solid ( = ), Q P = 2.25 Q S
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- Anelasticity
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- Absorption Band & Velocity Dispersion A single relaxation time gives an absorption peak at = 1/ Velocity increases from relaxed to unrelaxed values at about the same frequency A spectrum of relaxation times superposes these effects
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- Frequency Dependence of Attenuation Lekic et al. [2009] Q is observed to be weakly frequency dependent in the seismic band Described as Q = Q 0 - Interpreted as a broad spectrum of relaxation times
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- Possible Attenuation Mechanisms Another Mechanism: Dislocation Damping (Farla et al., 2012) Identification of mechanism is necessary to scale results from lab to earth Scaling in grain size, temperature, pressure, etc.
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- Attenuation and Velocity Anomalies are Highly Correlated Dalton et al. [2009] Q model S Velocity Model