 # Measureable seismic properties

## Presentation on theme: "Measureable seismic properties"— Presentation transcript:

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?

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

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)

Seismic Anisotropy Shear velocity of olivine
Relationship of anisotropy and strain - xenoliths Mainprice & Silver  Data from Kumazawa & Anderson 

Shear Wave Splitting

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  Widmer & Laske 

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

Attenuation variation in the Earth
Gung & Romanowicz  Pozgay, Wiens, et al. 

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)

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

Anelasticity

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

Frequency Dependence of Attenuation
Lekic et al.  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

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.

Attenuation and Velocity Anomalies are Highly Correlated
Q model S Velocity Model Dalton et al.