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. Seismic velocities k = Bulk modulus μ = Shear modulus ρ = density λ
= Lame’s lambda constant

3. 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)

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 = Q0 ω-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]