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Physics and chemistry of the Earth’s interior – Seismic refraction
Seismic refractionControlled source seismology:
Reading: Fowler p119-130
Physics and chemistry of the Earth’s interior – Seismic refraction
Seismic methods and scale
Global seismology (earthquakes)
• Provides information on global earth structure and large scale velocity anomalies (100’s to 1000’s km)
• Difficult to image smaller scale structure, particularly away from earthquake source regions
Controlled source seismology
• Allows higher resolution studies (meters to 100’s km)
• Can carry out experiments away from tectonic regions
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Physics and chemistry of the Earth’s interior – Seismic refraction
Controlled source seismology
• Set out a line or array of geophones
• Input a pulse of energy into the ground
• Record the arrival times to interpret velocity structure
Seismic refraction
• Used to study large scale crustal layering: thickness and velocity
Seismic reflection
• “Imaging” of subsurface reflectors
• Difficult to determine accurate velocities and depths
refle
ctio
nre
frac
tion
Physics and chemistry of the Earth’s interior – Seismic refraction
Reflection and refraction
Seismic rays obey Snell’s Law (just like in optics)
The angle of incidence equals the angle of reflection, and the angle of transmission is related to the angle of incidence through the velocity ratio.
2
2
1
1
1
sinsinsinαααeei ==
Note: the transmitted energy is refracted
α1
α2
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Physics and chemistry of the Earth’s interior – Seismic refraction
Reflection and refraction
Seismic rays obey Snell’s Law (just like in optics)
The angle of incidence equals the angle of reflection, and the angle of transmission is related to the angle of incidence through the velocity ratio.
But a conversion from P to S or vice versa can also occur. Still, the angles are determined by the velocity ratios.
where p is the ray parameter and is constant along each ray.
α1 β1
α2 β2
pffeei =====2
2
1
1
2
2
1
1
1
sinsinsinsinsinββααα
Physics and chemistry of the Earth’s interior – Seismic refraction
Reflection and refraction
You can see: a direct wave, reflected and transmitted waves, plus multiples…
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Physics and chemistry of the Earth’s interior – Seismic refraction
Critical incidence
when α2 > α1, e2 > i
we can increase iP until e2 = 90°
When e2 = 90° i = iC the critical angle
2
2
1
sinsinααei =
2
1sinαα=Ci
α1
α2
The critically refracted energy travels along the velocity interface at α2 continually refracting energy back into the upper medium at an angle iC
a head wave
Physics and chemistry of the Earth’s interior – Seismic refraction
Head wave• Occurs due to a low to high velocity interface• Energy travels along the boundary at the higher velocity• Energy is continually refracted back into the upper medium at an angle iC• Provides constraints on the boundary depth e.g. Moho depth
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Physics and chemistry of the Earth’s interior – Seismic refraction
Head wave
You can see: a head wave, trapped surface wave, diving body wave
Physics and chemistry of the Earth’s interior – Seismic refraction
Two-layered model
Energy from the source can reach the receiver via several paths:
1. Direct wave
Energy traveling through the top layer, traveltime:
A straight line passing through the origin
1αxt =
x RS
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Physics and chemistry of the Earth’s interior – Seismic refraction
Two-layered model1. Direct wave
2. Reflected wave
Energy reflecting off the velocity interface, traveltime:
11 ααCRSCt +=
4
221xzCRSC +==
42 2
21
1
xzt +=α
where
so
221
221 4 xzt +=α
or
The equation of a hyperbolae
x RS
Physics and chemistry of the Earth’s interior – Seismic refraction
Two-layered model
x RS
111 αααBRABSAt ++=
222
21
1
1 12αα
αα
xzt +−=
bxat +=ie. the equation of a straight line
1. Direct wave
2. Reflected wave
3. Head wave or refracted wave
Energy refracting across the interface, traveling along the underside and then back up to the surface, traveltime:
with some algebra
where the slope of the line is
and the intercept is
21 α
22
21
1
1 12αα
α−z
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Physics and chemistry of the Earth’s interior – Seismic refraction
Determining model parameters
• α1 determined from the slope of the direct arrival (straight line passing through the origin)
• α2 determined from the slope of the head wave (straight line first arrival beyond xcross)
• Layer thickness z1 determined from the intercept of the head wave (already knowing α1 and α2)
Two-layered model
x RS
Physics and chemistry of the Earth’s interior – Seismic refraction
Multiple-layered models
For multiple layered models we can apply the same process to determine layer thickness and velocity sequentially from the top layer to the bottom
222
21
1
1 12αα
αα
xzt +−=
323
22
2
223
21
1
1 1212αα
ααα
αα
xzzt +−+−=
m
m
j m
j
j
j xzt
ααα
α+
−=∑
−
=
1
12
2
12
Head wave from base of layer 2:
Head wave from base of layer 3:
Head wave from base of layer m:
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Physics and chemistry of the Earth’s interior – Seismic refraction
Some problemsThis analysis works for horizontal flat layers each of which produces a head wave with first arrivals in some distance window
This is not the case for:
Hidden layers do not produce first arrivals
Low velocity layersdo not produce a head wave (need a velocity increase)
Non-horizontal layers?
Physics and chemistry of the Earth’s interior – Seismic refraction
Dipping layers
Dipping layers still produce head waves but the traveltimes are affected by the dip
Shooting up-dip: the velocity appears greater
Shooting down-dip: the velocity is reduced
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Physics and chemistry of the Earth’s interior – Seismic refraction
Reversing lines
For horizontal layers the traveltime curves are symmetrical
For dipping layers layer velocities appear different for each end – the dip and true velocity can be determined from the up-
dip and down-dip velocities
…shooting to a line of geophones from both ends
Physics and chemistry of the Earth’s interior – Seismic refraction
Real Earth “flat” layers
Although the interfaces between real Earth layers are not perfectly flat, head waves still travel along them
Analysis methods:
Best-fit straight line through the points provides an average layer thickness and velocity
Model the data by creating a velocity model and calculating the arrival times: Forward modeling
Trade-off between layer thickness and velocity variations
Ambiguity!
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Physics and chemistry of the Earth’s interior – Seismic refraction
Crustal structure of the Alps
Fowler Fig 9.20
Reduced traveltime
Pg PmP Pn
crust
mantle
Physics and chemistry of the Earth’s interior – Seismic refraction
Amplitudes reflected and transmittedThe amplitude of the reflected, transmitted and converted phases can be calculated as a function of the incidence angle using Zoeppritz’s equations.
Reflection and transmission coefficients for a specific impedance contrast
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Physics and chemistry of the Earth’s interior – Seismic refraction
Summary
Controlled source seismology• Provides for high resolution studies (crustal and smaller scale)• Possible is non-tectonic region • Reflection and refraction seismic techniques
Reflection and refraction at an interface• Snell’s Law allows calculation of ray trajectories• The ray parameter is constant along a ray• Incidence at the critical angle results in a head wave
Refraction (Wide-angle) studies• Provide layer velocity and thickness – crustal structure