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Measureable seismic properties

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?. l .

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Measureable seismic properties

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  1. Measureable seismic properties • Seismic velocities – P & S • Relationship to elastic moduli • Seismic anisotropy -- directional variation in seismic velocity • Seismic Attenuation – 1/Qp & 1/Qs -- What is seismic attenuation? -- What causes seismic attenuation?

  2. l = Lame’s lambda constant Seismic velocities k = Bulk modulus  = Poisson ratio = Shear modulus m = density

  3. Measuring both Vp and Vs is useful The ratio of Vsto Vp depends on Poisson’s ratio: A good approximation is often that k = m; then s = 0.25 and Vp/Vs = √3 • We also sometime calculate the Seismic Parameter: • = Vp2 - 4/3 Vs2 = k/r • Shows variations in the bulk modulus (compare to Vs2 = m/r)

  4. Seismic Anisotropy Shear velocity of olivine Relationship of anisotropy and strain - xenoliths Mainprice & Silver [1993] Data from Kumazawa & Anderson [1969]

  5. Shear Wave Splitting

  6. 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 Body waves Coutier & Revenaugh[2006] Widmer & Laske[2007]

  7. 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

  8. Attenuation variation in the Earth Gung & Romanowicz[2004] Pozgay, Wiens, et al. [2009]

  9. 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 = 2π (total energy/energy lost during one cycle)

  10. Shear and Bulk Q • Shear wave attenuation results from relaxation of the shear modulus (μ) • P wave attenuation results from the relaxation of both the shear (μ) and bulk (κ) moduli • In general bulk attenuation is thought to be very small in the earth (Qκ> 1000) • If Qκ~ ∞ and assuming a Poisson Solid (λ = μ), QP= 2.25 QS

  11. Anelasticity

  12. Absorption Band & Velocity Dispersion • A single relaxation time gives an absorption peak at ω = 1/τ • Velocity increases from relaxed to unrelaxed values at about the same frequency • A spectrum of relaxation times superposes these effects

  13. Frequency Dependence of Attenuation Lekic et al. [2009] • Q is observed to be weakly frequency dependent in the “seismic band” • Described as Q = Q0ω-α • Interpreted as a broad spectrum of relaxation times

  14. 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.

  15. Attenuation and Velocity Anomalies are Highly Correlated Q model S Velocity Model Dalton et al. [2009]

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