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Elastic Waves
1. Introduction to Seismology-KFUPM
Introduction to Seismology
Chapter 3
Body Elastic Waves
http://faculty.kfupm.edu.sa/ES/oncel/geop204chap3.htm
Chapter 4, Bullen and Bolt
Ali Oncel
oncel@kfupm.edu.sa
Department of Earth Sciences
KFUPM
Introduction to Seismology-KFUPM
http://faculty.kfupm.edu.sa/ES/oncel/geop204presenta.htm
http://faculty.kfupm.edu.sa/ES/oncel/oncellinks.htm
Some Links
http://faculty.kfupm.edu.sa/ES/oncel/geop204link.htm
Introduction to Seismology-KFUPM
Recall: Wave
crests (high points)
equilibrium
(middle)
troughs (low points)
wave speed = wavelength/period = wavelength x frequency.
We often express this as v=fλ
1
2. Introduction to Seismology-KFUPM
Wave Equation
α and β are termed for the P-wave and S-wave
velocities. Often, the symbols Vp and Vs are used
instead of α and β.
Θ is the scalar displacement potential.
Where µ,λ are the Lamé coefficients
where λ is bulk modulus (incompressibility), µ shear
modulus (rigidity) and r density.
Introduction to Seismology-KFUPM
Seismic velocities
P wave velocity α and S wave velocity β depend on
physical properties of medium through which they
travel:
k + ( 4/3)µ λ + 2µ
V = α = = ρ
p
ρ
µ Question: How α and β depend
Vs = β =
ρ on density ρ?
Where µ,λ are the Lamé coefficients and λ is
λ = k - 2µ = νE
3 ( 1 + ν ) ( 1 - 2ν )
Introduction to Seismology-KFUPM
Elastic Coefficients and Seismic
Velocities
Rock Type Density Young's Modulus Poisson's Ratio Vp Vs Vp/Vs Vs as %Vp
r E m (m/s) (m/s)
Shale (AZ) 2.00 0.120 0.040 2454 1698 1.44 69.22%
Siltstone (CO) 2.00 0.120 0.040 2454 1698 1.44 69.22%
Limestone (PA) 2.00 1.100 0.156 7640 4877 1.57 63.84%
Limestone (AZ) 2.00 1.100 0.180 7728 4828 1.60 62.47%
Quartzite (MT) 3.00 0.636 0.115 4675 3083 1.52 65.96%
Sandstone (WY) 3.00 0.140 0.060 2169 1484 1.46 68.42%
Slate (MA) 3.00 0.487 0.115 4091 2698 1.52 65.96%
Schist (MA) 3.00 0.544 0.181 4440 2771 1.60 62.41%
Schist (CO) 2.70 0.680 0.200 5290 3239 1.63 61.24%
Gneiss (MA) 2.64 0.255 0.146 3189 2053 1.55 64.38%
Marble (MD) 2.87 0.717 0.270 5587 3136 1.78 56.13%
Marble (VT) 2.71 0.343 0.141 3643 2355 1.55 64.65%
Granite (MA) 2.66 0.416 0.055 3967 2722 1.46 68.62%
Granite (MA) 2.65 0.354 0.096 3693 2469 1.50 66.85%
Gabbro (PA) 3.05 0.727 0.162 5043 3203 1.57 63.51%
Diabase (ME) 2.96 1.020 0.271 6569 3682 1.78 56.05%
Basalt (OR) 2.74 0.630 0.220 5124 3070 1.67 59.91%
Andesite (ID) 2.57 0.540 0.180 4776 2984 1.60 62.47%
Tuff (OR) 1.45 0.014 0.110 996 659 1.51 66.20%
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3. Introduction to Seismology-KFUPM
Velocity and Density “Birch’s law”
Crust and mantle rock observations
A linear relationship between density and seismic velocity
where a and b are constants (Birch, 1961). V = a ρ + b
Three pressures
6km 18km 30km
Introduction to Seismology-KFUPM
Nafe-Drake Curve
An important empirical relation, used in joint
interpretation of wide angle reflection and refraction
data and gravity data, exists between P wave velocity
and density.
Cross-plotting velocity and density values of crustal
rocks gives the Nafe-Drake curve after its
discoverers.
Only a few rocks such as salt (unusually low density)
and sulphide ores (unusually high densities) lie off
the curve.
Introduction to Seismology-KFUPM
Nafe-Drake Curve
Sediments and
sedimentary rock
Igneous and
metamorphic rock
Figure 3.10 of Lillie, 1999, modified from Birch, 1960 Reference
L=limestone; Q=quartz; Sh=shale; Ss=sandstone.
3
4. Introduction to Seismology-KFUPM
Factors affecting P-wave velocity
Increases with
mafic mineral content (Nafe-Drake curve)
pressure (modulus change > density change)
Decreases with
temperature (modulus change > density
change)
Introduction to Seismology-KFUPM
Factors affecting S-wave velocity
Increases with
mafic mineral content (Nafe-Drake curve)
with pressure (modulus change > density
change)
Decreases due to
presence of fluid, e.g. porous sand or
partial melt
No S waves in
fluids, e.g. water of molten rock. Velocity
zero
Introduction to Seismology-KFUPM
Velocity-Geology
Grifts and King, 1981
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5. Introduction to Seismology-KFUPM
Amplitude Changes of Particle Motion
Reference
Maximum amplitude of particle motion occurs along
the 90 degree phase wave front. Other wave
fronts correspond to positions where the wave goes
from positive to negative amplitude (180 degree)
and at the minimum amplitude (270).
Introduction to Seismology-KFUPM
Wave Fronts and Raypaths
Initial wavefronts for
compressional (P),shear
(S), and Rayleigh ( R )
waves.
Changes in velocity cause segments of wave fronts to
speed up or slow down, distorting the wave fronts
from perfect spheres.
Reference
Ray paths thus bend (refract) as velocity changes.
Seismic energy travels along trajectories perpendicular
to wave fronts.
Introduction to Seismology-KFUPM
Seismic Trace
Reference
Seismic waves radiating from a source to one receiver.
Seismic trace recording ground motion by the
receiver, as a function of the travel time from the
source to the receiver. For controlled source studies
(seismic refraction and reflection), the travel time is
commonly plotted positive downward.
5
6. Introduction to Seismology-KFUPM
Introduction to Seismology
Chapter 3
Body Elastic Waves
http://faculty.kfupm.edu.sa/ES/oncel/geop204chap3.htm
Chapter 4, Bullen and Bolt
Ali Oncel
oncel@kfupm.edu.sa
Department of Earth Sciences
KFUPM
Introduction to Seismology-KFUPM
Previous Lecture
Wave equation
Elastic Coefficients and Seismic Waves
Birch's Law
Nafe-Drake Curve
Factors affecting P-wave and S-wave velocity
Seismic velocities for Geological Materials
Amplitude Changes of Particle Motions
Animation: Particle Motion in Seismic Waves
Wavefronts and RayPaths
Seismic Trace
Introduction to Seismology-KFUPM
Recall: Wavefronts and raypaths
nt
fro ular
v e erpendic t3
P
a
le
ang
W
t2
Ray
p ath t1
t0 Com pressional
Source (P) m otion
Shear (S)
m otion
From: http://web.ics.purdue.edu/~braile/edumod/slinky/slinky.htm
6
7. Introduction to Seismology-KFUPM
http://www.geol.binghamton.edu/faculty/jones/SeismicWavesSetup.exe
Seismic Waves A program for the visualization of
wave propagation contributor: Alan Jones
Year: 2006
Introduction to Seismology-KFUPM
From: http://www.citiesoflight.net/AlaskaQuake.html
Introduction to Seismology-KFUPM
Solution for Homework 2
Write up phases of
from 1 to 6?
1
2
3
6
5 4
7
8. Introduction to Seismology-KFUPM
Body Wave Propagation
P- and S- Waves (propagation along raypath)
Earth’s surface
Seismograph X
Y
Source
* SH
SV P-wave particle
motion -- parallel
to direction of
S-wave particle propagation
motion -- perpendicular
to direction of propagation (usually
approximately in SV and SH
Z (down) directions)
Modified from http://web.ics.purdue.edu/~braile/edumod/slinky/slinky.htm
Introduction to Seismology-KFUPM
Introduction to Seismology-KFUPM
Identify the waves of Body and Surface?
8
9. Introduction to Seismology-KFUPM Introduction to Seismology-KFUPM Introduction to Seismology-KFUPM
coast of Chile earthquake recorded at NNA
Three-component seismograms for the M6.5 west
9
10. Introduction to Seismology-KFUPM
Recall: Seismic Wave Types
“body waves” travel in Earth’s interior
P-waves (“P” for primary)
Expansion/compression:
push/pull motion
S-waves (“S” for secondary)
Shear:
side-to-side motion
“surface waves” travel on Earth’s surface
Surface Waves - Body Waves
Introduction to Seismology-KFUPM
Reference
Introduction to Seismology-KFUPM
Seismic Body Waves
Wave Type Particle Motion Other Characteristics
(and names)
P, Alternating compressions P motion travels fastest in
Compressional (“pushes”) and dilations materials, so the P-wave is the
Primary, (“pulls”) which are directed in first-arriving energy on a
Longitudinal the same direction as the seismogram. Generally smaller and
wave is propagating (along the higher frequency than the S and
raypath); and therefore, Surface-waves. P waves in a liquid
perpendicular to the or gas are pressure waves,
wavefront. including sound waves.
S, Alternating transverse S-waves do not travel through
Shear, motions (perpendicular to the fluids, so do not exist in Earth’s
Secondary, direction of propagation, and outer core (inferred to be
Transverse the raypath); commonly primarily liquid iron) or in air or
approximately polarized such water or molten rock magma). S
that particle motion is in waves travel slower than P waves in
vertical or horizontal planes. a solid and, therefore, arrive after
the P wave.
From: www.eas.purdue.edu/~braile/edumod/waves/WaveDemo.htm
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11. Seismic Surface Waves
Introduction to Seismology-KFUPM
Wave Particle Motion Other Characteristics
Type
(and names)
L, Transverse horizontal Love waves exist because of the Earth’s
motion, perpendicular surface. They are largest at the surface
Love, to the direction of and decrease in amplitude with
Surface propagation and depth. Love waves are dispersive, that is,
waves, Long generally parallel to the the wave velocity is dependent on
waves Earth’s surface. frequency, generally with low frequencies
propagating at higher velocity. Depth of
penetration of the Love waves is also
dependent on frequency, with lower
frequencies penetrating to greater depth.
R, Motion is both in the Rayleigh waves are also dispersive and the
Rayleigh, direction of propagation amplitudes generally decrease with depth in
Surface and perpendicular (in a the Earth. Appearance and particle motion
waves, Long vertical plane), are similar to water waves. Depth of
waves, and “phased” so that penetration of the Rayleigh waves is also
Ground roll the motion is generally dependent on frequency, with lower
elliptical – either frequencies penetrating to greater depth.
prograde or Generally, Rayleigh waves travel slightly
retrograde. slower than Love waves.
From: www.eas.purdue.edu/~braile/edumod/waves/WaveDemo.htm
Downloading the AmaSeis software
Introduction to Seismology-KFUPM
The Using AmaSeis Tutorial:
http://web.ics.purdue.edu/~braile/edumod/as1lessons/UsingAmaSeis/UsingAmaSeis.htm
http://www.geol.binghamton.edu/faculty/jones/AmaSeis.html
Homework due to March, 19: Plot Seismic Trace for one of
available recent earthquakes given by program and try to
explain your observations for Seismic Waves such as Picking
Body Waves, time for S-P and values of maximum amplitude?
11
12. Introduction to Seismology-KFUPM
Seismic Waves of Argentina EQ
Introduction to Seismology-KFUPM
Next Class: Class Presentation
Introduction to Seismology-KFUPM
Introduction to Seismology
Chapter 3
Body Elastic Waves
http://faculty.kfupm.edu.sa/ES/oncel/geop204chap3.htm
Chapter 4, Bullen and Bolt
Ali Oncel
oncel@kfupm.edu.sa
Department of Earth Sciences
KFUPM
12
13. Introduction to Seismology-KFUPM
Previous Lecture
Seismic Wave Types
Revisit: Wavefronts and raypaths
Seismic Waves A program for the visualization of
wave propagation contributor: Alan Jones
Body Wave Propagation
Example: M6.5, 1998 West Coast of Chile Earthquake
Example: Ms7.8, 1999 Izmit Earthquake, Turkey
Revisit: Seismic Wave Types
Downloading the AmaSeis Software
Homework: Seismic Trace Exercise by AmaSeis, Due
to March, 19
Introduction to Seismology-KFUPM
Term Paper:
Refraction
Seismology
Due to March 21
For more detail,
visit to Project
Page of Geop204
http://faculty.kfupm.edu.sa/ES/oncel/geop204termproject.htm
Introduction to Seismology-KFUPM
Travel-Time
Graph
Initial wave fronts for P, S and R waves, propagating
across several receivers at increasing distance from the
source. •Travel time graph. The seismic
traces are plotted according to the
distance (X) from the source to
each receiver. The elapsed time
after the source is fired is the
travel time (T). T=X/V
X distance from source to the receiver,
T total time from the source to the Reference
receiver
V seismic velocity of the P, S, or R
arrival.
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17. Introduction to Seismology-KFUPM
Reflected/Refracted Waves
A) A compressional wave,
incident upon an interface at
an oblique angle, is split into
four phases: P and S waves
reflected back into the original
medium; P and S waves
refracted into other medium.
See pp.140-152 of Bullen&Bolt
Introduction to Seismology-KFUPM
Seismic Refraction
•Wave fronts are distorted
from perfect spheres as
energy transmitted into
material of different
velocity. Ray paths thus
bend (“refract”) across an
θ1 interface where velocity
θ2
changes.
The angles for incident and refracted are measured from
a line drawn perpendicular to the interface between the
two layers.
Introduction to Seismology-KFUPM
Behavior of
Refracted Ray on
Velocity Changes
17
18. Behavior of Seismic Waves
Introduction to Seismology-KFUPM
Penetrating the Earth
At the mantle-outer core (fluid)
boundary the decrease in
velocity causes those rays
refracted into the core to bend
towards the normal
In the mantle and inner core,
the velocities increase with
depth, so the ray bend away
from the normal
Introduction to Seismology-KFUPM
Recall
Modules of Bulk (k) and Shear (µ)
Bulk Modulus
where Θ = dilatation = ∆V/V
and P = pressure
k= (∆P/Θ)
Ratio of increase in pressure to associated volume change
shear stress = (∆F /A)
shear strain = (∆l /L)
shear modulus
shear stress
µ = shear strain
Force per unit area to change the shape of the material
Introduction to Seismology-KFUPM
Recall
Poisson’s Ratio/Young Module
Poisson’s Ratio
∆L
εxx = σ= ( εyy / εxx )
L
∆W Young Module
εyy = W (∆F /A)
Ε = (∆L/L)
Ratio Vp and Vs depends on Poisson ratio:
where
Poisson’s ratio varies from 0 to ½. The elastic constants E, σ, µ are
Poisson’s ratio has the value ½ for mostly used in works of engineering
fluids seismology because they are easily
measured by simple experiments.
See pp.32 of Bullen&Bolt
18
19. Introduction to Seismology-KFUPM
Recall
Seismic Velocities (P-wave)
See pp.318 and 471 of Bullen&Bolt
Introduction to Seismology-KFUPM
Rock Velocities (m/sec)
pp. 18-19 of Berger
See pp.319 of Bullen&Bolt
Introduction to Seismology-KFUPM
Recall
Influences on Rock Velocities
• In situ versus lab measurements
• Frequency differences
• Confining pressure
• Microcracks
• Porosity
• Lithology
• Fluids – dry, wet
• Degree of compaction
•……………
19
20. Introduction to Seismology-KFUPM
Introduction to Seismology
Refraction and Reflection
Ali Oncel
oncel@kfupm.edu.sa
Department of Earth Sciences
KFUPM
Introduction to Seismology-KFUPM
Previous Lecture
Travel-time Graph
Estimates of Seismic Velocity
Huygens's Principle
Fermat's Principle
Calculation of Travel Times
Snell's law-Critically Refracted Arrival
Reflection/Refraction
Reflected/Refracted waves
Seismic Refraction
Behavior of refracted ray on velocity changes
Behavior of seismic waves refracted ray penetrating
the Earth
Representative P-wave Velocities for various Rocks
Influences on Rock Velocities
Introduction to Seismology-KFUPM
Refracted Ray and Angle
The angle of refraction increases as
the angle of incidence increases.
20
22. Introduction to Seismology-KFUPM
Travel time for
Direct/Refracte
d Waves
Xc=critical distance
Xcr=crossover distance V1 +V 2
T1= Intercept time xcr = 2h1
V2 −V 1
Introduction to Seismology-KFUPM
Seismic
=Z1
Reflection
=Z2
Lillie, Whole Earth Geophysics, Fig 3.28
Reflection occurs when Z1 differs from Z2, where Z
Acoustic impedance which is product of density and velocity
V-shaped ray paths for a compressional wave from a
source to 6 receivers, reflected from a horizontal interface.
Introduction to Seismology-KFUPM
Reflection equation for a reflection hyperbolae:
(X 2
+ 4h 2
)1 / 2
tr =
V 1
22
23. Introduction to Seismology-KFUPM
?
ed
?
ct
fle
ave
Re ad W
Time
do r He
acte
Refr
ti ?
Crossover distance
?
ct
re
Di
Distance
Introduction to Seismology-KFUPM
Introduction to Seismology-KFUPM
IRIS Deployment in Venezuela, 2001
"line" of fifteen Reftek 125 "Texan" recorders
The source of energy:
Betsy M3 Seisgun
From: http://www.passcal.nmt.edu/%7ebob/passcal/venezuela
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24. Introduction to Seismology-KFUPM
That is what named as “Model 130-01” which was ordered
for ESD in 2006. From: http://www.reftek.com/productshome.html#Seismic%20Recorders
Introduction to Seismology-KFUPM
21 “Texans” from Refraction
Technology, Inc.
From: http://www.seismo.unr.edu/geothermal/
Introduction to Seismology-KFUPM
200 “Texans”
From: http://www.seismo.unr.edu/geothermal/
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25. Introduction to Seismology-KFUPM
The N. Walker Lane Experiment, 2002
From: http://www.seismo.unr.edu/geothermal/
Introduction to Seismology-KFUPM
How Thick is the Crust?
?
Horizontal Rays
Refraction ?
“Tunneling”
7.2 km/s Moho
Journal Publication: Louie, J. N., W. Thelen, S. B. Smith, J. B. Scott, M. Clark, and S.
Pullammanappallil, 2004, The northern Walker Lane refraction experiment: Pn arrivals
and the northern Sierra Nevada root: Tectonophysics, 388, 253-269.
Introduction to Seismology-KFUPM
The length of profile, which is 180 meter in this case, provided a depth of resolution
to 60 meter but note that velocity in shallow is not detailed due to increased spacing
of receivers (=15 meter)?
KFUPM BEACH-2005
Elevation (m)
180 meter
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26. Introduction to Seismology-KFUPM
In this case, the receiver distance is about 0.4 meter but provided detail information
in depth of very shallow even we could not have info about the detail.
KFUPM-2006
Elevation, m
10 meter
Introduction to Seismology-KFUPM
Class Feedback
What is the most important thing you
learned this week?
What is one thing you still do not
understand?
Respond to me anonymously over a piece of
small paper within 1 or 2 minutes.
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