Slide 1

Measureable seismic properties Seismic velocities P & S Relationship to elastic moduli Seismic anisotropy -- directional variation in seismic velocity Seismic Attenuation 1/Q p & 1/Q s -- What is seismic attenuation? -- What causes seismic attenuation?

Slide 2

Seismic velocities = Shear modulus = Lame s lambda constant k = Bulk modulus = density

Slide 3

Measuring both V p and V s is useful The ratio of V s to V p depends on Poissons ratio (): A good approximation is often that then and V p /V s = This is called a Poisson solid We also sometime calculate the Seismic Parameter: V p 2 - 4/3 V s 2 = k Shows variations in the bulk modulus (compare to V s 2 =

Slide 4

Relationship of anisotropy and strain - xenolithsShear velocity of olivine Data from Kumazawa & Anderson [1969] Mainprice & Silver [1993] Seismic Anisotropy

Slide 5

Shear Wave Splitting

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

Slide 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

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Attenuation variation in the Earth Gung & Romanowicz [2004]Pozgay, Wiens, et al. [2009]

Slide 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 = 2 (total energy/energy lost during one cycle)

Slide 10

Shear and Bulk Q Shear wave attenuation results from relaxation of the shear modulus () P wave attenuation results from the relaxation of both the shear () and bulk () moduli In general bulk attenuation is thought to be very small in the earth (Q > 1000) If Q ~ and assuming a Poisson Solid ( = ), Q P = 2.25 Q S

Slide 11

Anelasticity

Slide 12

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

Slide 13

Frequency Dependence of Attenuation Lekic et al. [2009] Q is observed to be weakly frequency dependent in the seismic band Described as Q = Q 0 - Interpreted as a broad spectrum of relaxation times

Slide 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.

Slide 15

Attenuation and Velocity Anomalies are Highly Correlated Dalton et al. [2009] Q model S Velocity Model