SEISMIC WAVES

ATTENUATE - DECREASE IN AMPLITUDE -

AS THEY PROPAGATE

(S&W 3.7)

Important for earth physics, understanding

earthquake size, and

seismic hazard

MODIFIED MERCALLI

INTENSITY SCALE

Macroscopic measure of

shaking

Estimated for historic

earthquakes from accounts of what

happened

Plot isoseismals - intensity contours

Decays with distance

Proportional to acceleration,

details unclear

0.2 g Damage onset for modern buildings

EARTHQUAKE MAGNITUDE

Earliest measure of earthquake size

Dimensionless number measured various ways, including

ML local magnitude

mb body wave magnitude

Ms surface wave magnitude

Mw moment magnitude

Easy to measure

No direct tie to physics of faulting

CONSEQUENCES OF SHAKING DIFFERENCES

Northridge, M 6.7, was the costliest disaster in U.S. history with economic loss of $40 billion. In contrast, loss in Nisqually earthquake is ~$2 billion. One death, a heart attack victim,

reported in Seattle area, while 57 people died in the Northridge earthquake.

Kirby et al., 1996

NISQUALLY EARTHQUAKE Focal depth 58 km; in subducting Juan

de Fuca plate

AFTERSHOCKS

NORTHRIDGE EARHQUAKE Focal depth 18 km; Los

Angeles Basin shortening

REFLECTION AND TRANSMISSION OF SEISMIC WAVES AT DISCRETE INTERFACES REDUCE THEIR AMPLITUDES.

FOUR OTHER PROCESSES ALSO REDUCE WAVE AMPLITUDES:

- GEOMETRICAL SPREADING- SCATTERING

- MULTIPATHING -ANELASTICITY

THE FIRST THREE ARE ELASTIC PROCESSES, IN WHICH THE ENERGY IN THE PROPAGATING WAVE FIELD IS CONSERVED.

IN CONTRAST, ANELASTICITY, SOMETIMES CALLED INTRINSIC ATTENUATION, INVOLVES CONVERSION OF SEISMIC ENERGY TO

HEAT.

ANALOGOUS BEHAVIORS FOR LIGHT

AS YOU MOVE AWAY FROM A STREET LAMP AT NIGHT, THE LIGHT APPEARS DIMMER FOR SEVERAL REASONS

2) Scattering: light dims as it is scattered by air molecules, dust, and water in the air. Scattering results when objects acting as Huygens' sources scatter energy in all directions. This effect is dramatic on a foggy night because scattered light causes a halo around the lamp.

1) 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.

3) Light is focused or defocused by changes in the refractive properties of the air. This process causes mirages, where light is refracted differently by hot air just above the ground.

Similarly the distorted appearance of the setting sun results from seeing different parts of it through different levels of the atmosphere which refract light differently because of the vertical density gradient.

This effect is termed multipathing in seismology. Focusing and defocusing can be illustrated by looking at the street light through binoculars. Looking through binoculars the usual way, the waves are focused by the lenses, and the lamp appears closer and brighter. Reversing the binoculars makes the lamp appear further and dimmer.

4) Some light energy is absorbed by the air and converted to heat. This process differs from the other three in that light energy is actually lost, not just moved onto a different path.

ALL FOUR PROCESSES ARE IMPORTANT FOR SEISMIC WAVES.

The first three are described by elastic wave theory, and can increase or decrease an arrival's amplitude by shifting energy within the wave field.

In contrast, anelasticity only reduces wave amplitudes because energy is lost from the elastic waves.

So much of seismology is built upon the approximation that the earth responds elastically during seismic propagation that it is easy to forget that

the earth is not perfectly elastic.

However, without anelasticity seismic waves from every earthquake that ever occurred would still be reverberating until the accumulating

reverberations shattered the earth.

Elasticity is a good approximation for the earth's response to seismic waves, but there are many important implications and applications of anelasticity.

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 / r2, and the amplitude decreases as 1 / r

In reality, because body waves travel through an inhomogeneous earth, their amplitude depends on the focusing and defocusing of rays by the velocity

structure.

GEOMETRIC SPREADING: BODY WAVES

MULTIPATHING

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

Although physically this process is the same as the effects of vertical variations, it is often distinguished by the term multipathing.

The distinction reflects our view of the earth as an essentially layered planet with secondary lateral variations.

TRACE RAY PATHS USING SNELL’S LAW

RAYS BEND AS WATER DEPTH CHANGES

FIND WHEN WAVES ARRIVE AT DIFFERENT PLACES

DENSITY OF WAVES SHOWS FOCUSING & DEFOCUSING

Woods & Okal, 1987

1 hour

When multipathing occurs, seismic waves arriving at a receiver can be viewed as having taken ray paths in addition to the direct path, and so sampled a larger region of the earth.

Fermat's principle giving the geometric ray path applies exactly only to waves of infinite frequency. For waves of finite frequency, we view the seismic waveform as a coherent sum of energy that travels all possible paths that arrive within a half-period of the infinite frequency wave, which took the shortest time. These paths form a volume called the first Fresnel zone around the infinite-frequency path. Successive half periods correspond to higher order Fresnel zones.

a = size of heterogeneity

L = distance wave travels

= wavelength

Whether effects of velocity heterogeneity are regarded as scattering depends on the ratio of heterogeneity size to the wavelength and the distance the wave travels in the heterogeneous region.

When the heterogeneity is large compared to the wavelength, we regard the wave as following a distinct ray path distorted by multipathing.

When velocity heterogeneities are close in size to the wavelength, we think of scattered energy rather than distinct ray paths.

When heterogeneities are << than the wavelength, they simply change the medium's overall properties. The further the wave travels in the heterogeneous region, the more useful the scattering description becomes. Hence for longer distances, the wavelength range viewed as scattering increases.

The fact that light scattering in the atmosphere depends on wavelength and the distance traveled has familiar consequences. Because the shortest wavelengths of visible light are the most scattered, blue light reaching us from all directions makes the sky appear blue.

The loss of blue light makes the sun appear yellow, although it would appear white if observed from a spacecraft.

At sunset, when the sunlight passes through a longer path in the atmosphere than at other hours, intermediate wavelengths are also scattered, leaving direct light from the sun enhanced in the longest visible wavelengths (red light) and making the sun appear red.

The unscattered wave travels the shortest distance and gives the initial arrival. Scattered energy lost from this arrival arrives later & could have been scattered from an infinite number of locations that yield the observed travel time. In a constant-velocity medium, the locus of possible scatterers is an ellipsoid with the source and receiver as foci. Larger ellipsoids define the possible scatterers for energy that arrives later. These ellipsoids are distorted by velocity heterogeneity and are analogous to the Fresnel volume used when we consider the waves as following distinct ray paths.

The terrestrial record shows high attenuation,whereas the lunar seismogram shows intense scattering due to thefractured regolith and very weak attenuation due to the lack of intergranular water

SUMATRA EARTHQUAKE:

ANALYZE NORMAL MODE SINGLETS

with time domain fitting

Q and Q-1

The solution for the damped harmonic oscillator incorporated the damping through the quality factor Q.

Attenuation for seismic waves and a variety of other physical phenomena are often discussed in terms of Q or Q -1.

Although Q has more convenient values, Q -1 has the advantage that is directly rather than inversely proportional to the damping.

No attenuation -> Q = ∞ 1/Q =0High attenuation -> Q low 1/Q high

Q OF WAVES VS Q OF THE EARTH

In some cases, Q describes the decay of an oscillation, whereas in others it describes the physical properties of the system that causes a disturbance to attenuate.

For example, the Q of a seismic wave at a given period describes how it decays with time. This decay results from the distribution of material in the earth that causes seismic energy to be lost to heat. This distribution can be described in terms of a Q or anelastic attenuation structure analogous to the elastic velocity structure.

Anelastic structure is analogous to the elastic velocity structure because Q can be viewed mathematically as an imaginary part of

the frequency P = + i* * = / 2Q

or the velocity c = c + i c* Q-1 = 2c*/cHence we define Q and Q for P & S waves

If there is no attenuation, Q = ∞ , the frequency & velocity are purely real

MODEL ANELASTICITY IN THE EARTH

Response to harmonic wave peaked around

natural frequency

Peak width proportional to 1/Q

Schematic model to explain why Q is roughly constant over a wide range of frequencies.

Superposition of absorption peaks for different compositionsat different temperatures and pressuresyields a flat absorption band.

MANY GEOPHYSICAL PROCESSES (MANTLE CONVECTION, PLATE TECTONICS, MAGMATISM, ETC.) INVOLVE LATERAL VARIATIONS IN TEMPERATURE.

Elastic velocities are sensitive to temperature, but are more useful for mapping cold (fast) anomalies like subducting slabs than hot (slow) material like that expected at mantle plumes. Seismic velocities depend nearly linearly upon temperature, whereas attenuation depends exponentially on temperature. Thus combining velocity and attenuation studies can provide valuable information.

LOW-VELOCITY

ANDHIGH-

ATTENUATION REGION

INTERPRETED AS MELT-

FILLEDMAGMA

CHAMBER

Q > 10,000 in the cold and rigid subducting slab but is less than 75 beneath the hot back-arc basin.

ATTENUATION VARIES BOTH WITH DEPTH AND LATERALLY

In the crust, the greatest attenuation (lowest Q or highest Q-1) is near the surface, presumably due fluids. Attenuation is lowest at ~20-25 km, and increases again, presumably due to increasing temperature.Attenuation decreases as a function of frequency.

Attenuation is lower in the eastern U.S. than in the hot, tectonically active, Basin and Range

Attenuation is lower - or wave propagation more efficient -in the eastern U.S. than in the western U.S., which is hotter and

tectonically active

Seismograms from an earthquake in Texasrecorded in Nevada and Missouri.

The MNV record has less high frequencies because the tectonically-active western U.S.is more attenuating than the stable mid-continent.

STRONG GROUND MOTION DECAYS RAPIDLY WITH DISTANCE

1811-12 EARTHQUAKE MAGNITUDES

Largest 1811-1812 earthquakes caused log cabin collapse at New Madrid; minor damage in St Louis, Nashville, Louisville, etc.

Imply low-mid M7 (Hough et al., 2000)

M 7.2 fits observed building damage better (Kochkin &Crandell, 2004)

http://pasadena.wr.usgs.gov/office/hough/east-vs-west.jpg