Geology 5640/6640 Introduction to Seismology 24 Apr 2015 © A.R. Lowry 2015 Last time: Amplitude Effects Multipathing describes the focusing and defocusing of waves by ray-bending in a heterogeneous medium (e.g., basin amplification). The Fresnel Zone corrects ray theory for multipathing (esp. arrivals within a half-period) given a finite frequency Scattering effects occur when velocity varies at even smaller scales where ray theory is no longer usable ( a ~ ) Scattering is responsible for the coda of earthquakes (the long jumble of disturbances that arrive long after the initial phases). Coda energy can be back-projected to the ellipse of possible scatterer locations associated to a given arrival time; interferometry can be used to image changes in velocity structure through time!

Intrinsic Attenuation: Intrinsic attenuation, or anelasticity, describes the process by which elastic energy in the Earth is converted to heat when the seismic wave induces unrecoverable deformation. To examine this, let’s consider a spring: For an idealized spring, has solution with oscillation frequency More realistically though, internal friction in the spring will damp the system resulting in where  is a damping factor and Q   0 /  is called the quality factor. Mass m u Spring constant k

Intrinsic Attenuation: This system has a solution with real and imaginary parts; the actual displacement is the real part and takes the form: i.e., a harmonic oscillator with an exponential decay of amplitude. Here, A 0 is the initial displacement (at time t = 0 ) and Important to note: High frequencies attenuate more than low Harmonic frequency is changed by attenuation Higher Q results in less change to frequency and less intrinsic attenuation for given time Mass m u Spring constant k

Generally, loss of amplitude due to intrinsic attenuation is much greater than that due to partitioning, spreading and the other amplitude effects we have discussed

Intrinsic Attenuation: The wave equation of course is different than that for a simple mass-spring system… For a plane wave, the Amplitude A decreases as where a is the absorption coefficient, a =    / 2Qc Q is generally called Quality factor … Low attenuation implies high Q. For anelastic attenuation, elastic parameters and hence velocity c are complex-valued, i.e. c = c R + ic I, and

So amplitude decay is greater for greater distance x and frequency  0 ; less with higher intrinsic quality factor Q and velocity c. Q differs for P-wave ( Q p ) and S-wave ( Q s ). For sediments, 5 < Q p < 300 (lower if porosity is high) 5 < Q s < 100 For crystalline rocks at shallow depth/low temperature, 100 < Q p < 800

But Q variations can be imaged, and provide additional useful information about a medium! 1 23 V = 1250 m/s f = 250 Hz Q = 5.1 V = 3680 m/s f = 125 Hz Q = 3.2 X X

Seismic attenuation can be particularly useful for imaging of anomalies in melt fraction and free water content in the mantle…

And for resolving potential ambiguities in interpretation of velocity images. Example: Seismic parameters from the Rio Grande Rift region of Colorado (all at 100 km depth)

Pasyanos, BSSA, 2013 Pn-Q P Sn-Q S Measured Modeled