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