# Measureable seismic properties

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Seismic Attenuation and Earth Structure

Measureable seismic propertiesSeismic 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?Seismic velocities

= Shear modulus= Lames lambda constant

k = Bulk modulus = density Measuring both Vp and Vs is usefulThe ratio of Vs to Vp depends on Poissons ratio ():

A good approximation is often that = ; then = 0.25 and Vp/Vs = 3 This is called a Poisson solidWe also sometime calculate the Seismic Parameter: = Vp2 - 4/3 Vs2 = k/Shows variations in the bulk modulus (compare to Vs2 = /)

Relationship of anisotropy and strain - xenoliths

Shear velocity of olivineData from Kumazawa & Anderson [1969]Mainprice & Silver [1993]Seismic Anisotropy4Shear Wave Splitting

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 elasticity

Surface wavesWidmer & Laske [2007]

Coutier & Revenaugh [2006]Body wavesNormal Modes

Different Modes show different rates of amplitude decaySo we can determine a Q for each modeDifferent Qs result from how each mode samples the earthAttenuation variation in the Earth

Gung & Romanowicz [2004]Pozgay, Wiens, et al. [2009]8Q 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 frequencies Q = 2 (total energy/energy lost during one cycle)Shear and Bulk QShear wave attenuation results from relaxation of the shear modulus ()P wave attenuation results from the relaxation of both the shear () and bulk () moduliIn general bulk attenuation is thought to be very small in the earth (Q > 1000)If Q ~ and assuming a Poisson Solid ( = ), QP = 2.25 QSAnelasticity

Absorption Band & Velocity DispersionA single relaxation time gives an absorption peak at = 1/Velocity increases from relaxed to unrelaxed values at about the same frequencyA spectrum of relaxation times superposes these effects

Frequency Dependence of Attenuation

Lekic et al. [2009]Q is observed to be weakly frequency dependent in the seismic bandDescribed as Q = Q0 -Interpreted as a broad spectrum of relaxation times

Possible Attenuation MechanismsAnother 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.14Attenuation and Velocity Anomalies are Highly Correlated

Dalton et al. [2009]Q modelS Velocity Model