identification of seismic phases 2008, may 12, m7.9, eastern sichuan, china
TRANSCRIPT
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Identification of seismic phases
2008, May 12, M7.9, Eastern Sichuan, China
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A stack of (long period) data from a global network
InterpretationData
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Travel times Ray paths
• Reflected phases include: PcP and PcS.• Refracted phases include: P, S and PKP.
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Snell’s law and the ray parameter: reminder
Flat Earth:
We have seen that:
Thus, the ray parameter may be thought as the horizontal slowness.
Radial Earth:
Similarly, we have seen that:
Thus, the radial ray parameter too is a slowness parameter, and may help to infer Earth velocity structure!
€
Pradial ≡Rsin i
V .
€
Pflat =dT
dXhorizontal
=1
Vhorizontal
.
€
Pflat ≡sin i
V .
€
Pradial =dT
dΔ=
Rmin
Vmin
.
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The ray parameter and the travel-time curves
Pflat and Pradial are the slopes of the travel time curves T-versus-X and T-versus-, respectively.
While the units of the flat ray parameter is S/m, that of the radial earth is S/rad.
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The T-X curves and the velocity structures
Steady increase in wave speed:
The rays sample progressively deeper regions in the Earth, and arrive at progressively greater distances.
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Low velocity layer:
The decrease in ray speed causes the ray to deflect towards the vertical, resulting in a shadow zone.
Question: Were are the low velocity layers in the Earth?
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The outer core is a low velocity layer
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High velocity layer:
The rays are reflected at the layer, causing different paths to cross. For some distance range there are three arrivals: the direct phase, the refracted phase and the reflected phase. This phenomena is referred to as the triplication point.
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Factors affecting seismograms
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• The challenge of source (i.e., earthquake) seismologists is to infer the source time function. Isolation of the source effect is obtained via removal of the propagation, site and instrument effects.
• Global seismologists are interested in imaging earth structure, and their challenge is to remove the source, site and instrument effects.
• The objective of exploration seismologists is to image the subsurface structure on a scale that is relevant for the industry. They use controlled sources, such as dynamite gun shots, weight drop and hammers.
Source, global and exploration seismologists
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Amplitude
In general, the wave amplitude decreases with distance from the source.
Note the reinforcement of the surface waves near the antipodes.
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Also, a major aftershock (magnitude 7.1) can be seen at the closest stations starting just after the 200 minutes mark. Note the relative size of this aftershock, which would be considered as a major earthquake under ordinary circumstances, compared to the mainshock.
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Amplitude
• Energy partitioning at the interface.
• Anelastic attenuation.
• Geometrical spreading.
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Energy partitioning at an interface
Energy:
The energy density, E, may be written as a sum of kinetic energy density, Ek, and potential energy density, Ep.
The kinetic energy density is:
Now consider a sine wave propagating in the x-direction, we have:
where w is the frequency, t is time, and k is the wave-number. The particle velocity is:
and the kinetic energy density is:
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Ek =1
2ρ ˙ U 2 .
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U = Asin(wt − kx) ,
€
˙ U = Aw cos(wt − kx) ,
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Ek =1
2ρ[Aw cos(wt − kx)]2 .
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Since the mean value of cos2 is 1/2, the mean kinetic energy is:
In a perfectly elastic medium, the average kinetic and potential energies are equal, and the mean energy is:
Thus, the average energy density flux is simply:
were C is the wave speed.If the density and the wave speed are position dependent, so is the amplitude. In the absence of geometrical spreading and attenuation, we get:
The product of and C is referred to as the material impedance.
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E k =1
4ρ[Aw]2 .
€
E total = E k + E p =1
2ρ[Aw]2 .
€
˜ E total =1
2ρC[Aw]2 ,
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A1
A2
=ρ 2C2
ρ1C1
.
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In conclusion, the amplitude is inversely proportional to the square root of the impedance.
Reflection and transmission coefficients:
The reflection coefficient of a normal incidence is:
The transmission coefficient of a normal incidence is:
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Areflected
Aincoming
=ρ 2C2 − ρ1C1
ρ 2C2 + ρ1C1
.
€
Atransmitted
Aincoming
=2ρ1C1
ρ 2C2 + ρ1C1
.
Energy partitioning at the interface
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Energy partitioning at the interface
The amplitudes as a function of incidence angle may be computed numerically (see equations 4.81-84 in Fowler’s book).
Figure from Fowler
• Note the two critical angles at 300 and 600.• Phases reflected from the critical angles onwards are of larger amplitude.• For normal incidence, the reflected energy is <1%.
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Energy partitioning at the interface
• Pre-critical angle, i<ic: Reflection and transmission.
• Critical incidence, i=ic: The critically refracted phase travels along the interface, emitting head waves to the upper medium.
• Post-critical incidence, i>ic: No transmission, only reflection. The amplitude of the reflected phase is therefore close to the amplitude of the incoming wave.
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Anelastic attenuation
Rocks are not perfectly elastic; thus, some energy is lost to heat due to frictional dissipation. This effect results in an amplitude reduction with distance, r, according to:
with being the absorption coefficient.
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Amplitude∝ exp−αr ,
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Geometrical Spreading
For surface waves we get :
For body waves, on the other hand, we get:
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Amplitude∝ r−1 .€
Amplitude∝ r−1/ 2 .
Finally, the effect of anelastic attenuation and geometrical spreading combined is:
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Amplitude∝ r−1 exp−αr .