Measureable seismic properties Seismic velocities – P & S – Relationship to elastic moduli...
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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?
Measureable seismic properties Seismic velocities – P & S – Relationship to elastic moduli Seismic anisotropy -- directional variation in seismic velocity
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
Slide 8
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