Seismic Attenuation ---from seismic wave travel times to amplitudes Haijiang Zhang Courtesy of many different sources

Haberland et al., GRL 2003

EARTHQUAKE MAGNITUDE Earliest measure of earthquake size Dimensionless number measured various ways, including M L local magnitude m b body wave magnitude M s surface wave magnitude M w moment magnitude Easy to measure No direct tie to physics of faulting

(4) intrinsic attenuation: due to anelasticity the real earth materials are always “lossy”, leading to reduced wave amplitudes, or intrinsic attenuation. Mechanisms to lose energy: (1) Movements along mineral dislocations (2) Shear heating at grain boundaries These are called “internal friction”. …… (3) Scattering: A way to partition energy of supposedly main arrivals into boundary or corner diffracted, scattered energy. Attnuation Mechanisms : (1) Geometrical spreading: wavefront spreading out while energy per unit area becomes less. (2) Multipathing: waves seek alternative paths to the receiver. Some are dispersed and some are bundled, thereby affecting amplitudes. Key: very wavelength dependent. 4

Geometric spreading: light moves outward from lamp in expanding spherical wave fronts. By conservation of energy, the energy in a unit area of the growing wave front decreases as r -2, where r is the radius of the sphere or distance from the lamp. Analogous to light behavoirs…

Expect minimum at  =90º, and maxima at 0º and 180º GEOMETRIC SPREADING: SURFACE WAVES

From geometric spreading alone, expect minimum at  =90º, and maxima at 0º and 180º Also have effects of anelasticity

For body waves, consider a spherical wavefront moving away from a deep earthquake. Energy is conserved on the expanding spherical wavefront whose area is 4 π r 2, where r is the radius of the wavefront. Thus the energy per unit wave front decays as 1 / r 2, and the amplitude decreases as 1 / r GEOMETRIC SPREADING: BODY WAVES

MULTIPATHING Seismic waves are focused and defocused by variations in velocity.

Idea of Ray Tubes in body waves Ray tube size affects amplitudes, smaller area means larger amplitude Angle dependent: ray bundle expands or contracts due to velocity structure. Also: amplitude varies with takeoff angle Effect of Multipathing 10

Scattering: Scattering occurs when there are velocity heterogeneities in the medium with wavelengths on the order of  of the wave.

Snieder et al., Science, 2002 A simulation of 100 randomly-perturbed scatterers… Moving the scatterers (here, 1/40th of the distance shown, so the perturbation is visible) mostly changes the shapes and amplitudes of the waveforms…

Snieder et al., Science, 2002 Waveforms measured in a granite sample at temperatures of 45°C (blue) and 50°C (red). Changing the matrix velocity, by contrast, introduces a shift (delay or advance) that increases with coda time.

Scattering: Interesting aside: Coda energy in the Earth tends to attenuate much more rapidly than on the Moon! This is partly because lunar regolith is highly fractured by impacts, but mostly because it contains no fluids (and consequently much less intrinsic attenuation !)

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

Definition of the quality factor Energy dissipated in a cycle Energy stored

Putting everything together

Intrinsic attenuation (1) Movements along mineral dislocations (2) Shear heating at grain boundaries Affected by temperature, pressure, frequency, and medium properties

Attenuation property is complementary to velocity.

Haberland et al., GRL 2003

Myers et al., 1995 The key here is to correlate a decrease in Q with fluids in the crust and mantle. The fluid layer again represents melting due to subduction. 23

(Romanowicz & Mitchell, 2007)

Nakajima et al., 2003, GRL

How to estimate Q Code wave Surface wave Body wave Amplitude data …….

Coda wave attenuation Kumar et al., 2005

Estimating Q from body wave using t*

Site Response

Attenuation Model

ABCE Amplitude of horizontal component Period O= /- 0.04s LAT=26.92 N +/- 0.30km LONG= E +/- 0.33km DEPTH= 10 km +/- 0.14km STATIONS USED = 6, STAND DEV= 2.63s ML=2.9/ 6, EYA Pg Sg SMN ML= SME PZH Pn Pg Sg SMN ML= SME XAC Pn Pg Sg SMN ML= SME TCG Pg Sg SMN ML= SME KMI Pg Sg SMN ML= SME ZOT ePg Sg SMN ML= SME Amplitude Q tomography (Shunping Pei)

Theory and Method Source Station Crust Upper mantle

M L Tomography in North China ABCE of 1985 to 1995 (Annual Bulletin of Chinese Earthquakes) 1. Each event was recorded by at least 2 stations, 2. Residuals between -2.0 ~ 2.0, 3. Period T of the Sg wave maximum amplitude (A) is between 0.4~2.0s, 4. Epicentral distance is between 100km-800km. 5. Event depth is less than 20km amplitude data 1732 events 91 stations

10899 Amplitude data 1732 Events (+) 91 Stations (▲)

Histogram of ML distribution

Result Earthquakes with M>7

Phillips et al., 2005 Q from the tomographic inversion of 1 Hz Lg amplitude ratios

Liu et al., 2004

Checkerboard Test 2°× 2°

Checkerboard Test 1.5°× 1.5°

Standard deviation 0.67 Standard deviation 0.41

Summary Crustal attenuation can be reconstructed by tomographic imaging method using amplitude data. Attenuation levels are correlated with regional tectonic structure. High attenuation often occurs in active tectonic areas with significant faulting, while attenuation is low in the stable Ordos Craton. The estimate of attenuation shows a close correlation with topography. Q 0 is generally low in basins, whereas high Q 0 mostly occurs in mountains and uplift regions where crystalline basement appears in the surface. It is possible that low Q 0 in basins is caused by fluid in the upper crust, and deep sediment in basins, while high Q 0 in the mountains and uplift regions results from the presence of old, dense rocks there. (Published in BSSA(2006))