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Page 1: Controlled source seismology: Seismic refraction · Controlled source seismology • Provides for high resolution studies (crustal and smaller scale) • Possible is non-tectonic

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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

Page 2: Controlled source seismology: Seismic refraction · Controlled source seismology • Provides for high resolution studies (crustal and smaller scale) • Possible is non-tectonic

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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

Page 3: Controlled source seismology: Seismic refraction · Controlled source seismology • Provides for high resolution studies (crustal and smaller scale) • Possible is non-tectonic

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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…

Page 4: Controlled source seismology: Seismic refraction · Controlled source seismology • Provides for high resolution studies (crustal and smaller scale) • Possible is non-tectonic

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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

Page 5: Controlled source seismology: Seismic refraction · Controlled source seismology • Provides for high resolution studies (crustal and smaller scale) • Possible is non-tectonic

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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

Page 6: Controlled source seismology: Seismic refraction · Controlled source seismology • Provides for high resolution studies (crustal and smaller scale) • Possible is non-tectonic

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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

Page 7: Controlled source seismology: Seismic refraction · Controlled source seismology • Provides for high resolution studies (crustal and smaller scale) • Possible is non-tectonic

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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:

Page 8: Controlled source seismology: Seismic refraction · Controlled source seismology • Provides for high resolution studies (crustal and smaller scale) • Possible is non-tectonic

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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

Page 9: Controlled source seismology: Seismic refraction · Controlled source seismology • Provides for high resolution studies (crustal and smaller scale) • Possible is non-tectonic

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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!

Page 10: Controlled source seismology: Seismic refraction · Controlled source seismology • Provides for high resolution studies (crustal and smaller scale) • Possible is non-tectonic

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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

Page 11: Controlled source seismology: Seismic refraction · Controlled source seismology • Provides for high resolution studies (crustal and smaller scale) • Possible is non-tectonic

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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