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**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?

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**Seismic velocities k = Bulk modulus μ = Shear modulus ρ = density λ**

= Lame’s lambda constant

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**Measuring both Vp and Vs is useful**

The ratio of Vs to Vp depends on Poisson’s ratio (σ): A good approximation is often that λ = μ; then σ = 0.25 and Vp/Vs = √3 This is called a Poisson solid We also sometime calculate the Seismic Parameter: Φ = Vp /3 Vs2 = k/ρ Shows variations in the bulk modulus (compare to Vs2 = μ/ρ)

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**Seismic Anisotropy Shear velocity of olivine**

Relationship of anisotropy and strain - xenoliths Mainprice & Silver [1993] Data from Kumazawa & Anderson [1969]

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

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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 = 2π (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 (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

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Anelasticity

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**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

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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 = Q0 ω-α 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**

Q model S Velocity Model Dalton et al. [2009]

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