Presentation on theme: "Measureable seismic properties"— Presentation transcript:
1 Measureable seismic properties Seismic velocities – P & SRelationship to elastic moduliSeismic anisotropy-- directional variation in seismic velocitySeismic 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 = √3This is called a Poisson solidWe also sometime calculate the Seismic Parameter:Φ = Vp /3 Vs2 = k/ρShows variations in the bulk modulus (compare to Vs2 = μ/ρ)
4 Seismic Anisotropy Shear velocity of olivine Relationship of anisotropy and strain - xenolithsMainprice & Silver Data from Kumazawa & Anderson 
6 Seismic AttenuationIn a perfectly elastic medium, the total energy of the wavefield is conservedSeismic attenuation is the absorption of seismic energy, or the deviation from perfect elasticitySurface wavesBody wavesCoutier & Revenaugh Widmer & Laske 
7 Normal Modes Different Modes show different rates of amplitude decay So we can determine a Q for each modeDifferent Qs result from how each mode samples the earth
8 Attenuation variation in the Earth Gung & Romanowicz Pozgay, Wiens, et al. 
9 Q – Quality FactorAttenuation 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 frequenciesQ = 2π (total energy/energy lost during one cycle)
10 Shear and Bulk QShear 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) moduliIn 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
12 Absorption Band & Velocity Dispersion A single relaxation time gives an absorption peak at ω = 1/τVelocity increases from relaxed to unrelaxed values at about the same frequencyA spectrum of relaxation times superposes these effects
13 Frequency Dependence of Attenuation Lekic et al. Q is observed to be weakly frequency dependent in the “seismic band”Described as Q = Q0 ω-αInterpreted 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 earthScaling in grain size, temperature, pressure, etc.
15 Attenuation and Velocity Anomalies are Highly Correlated Q modelS Velocity ModelDalton et al.