Geophysics/Tectonics

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Geophysics/Tectonics

• GLY 325

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(No Transcript)
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Geophysical Surveys Active or Passive-- Passive
geophysical surveys incorporate measurements of
naturally occurring fields or properties of the
earth (i.e., earthquake seismology, gravity,
magnetics, radiometric decay products, Self
Potential (SP), Magnetotelluric (MT), and heat
flow). Active geophysical surveys impose a
signal on the earth, and then the earths
response to this signal is measured (i.e.,
seismic reflection/refraction, DC resistivity,
Induced Polarization (IP)and Electromagnetic
(EM)).
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Geophysical Technique
Measured Earth Property
Earth Property Effecting Signal
Natural Source Earthquake
Seismic Velocity (V ) and Attenuation (Q )
Ground Motion (Displacement, Velocity or
Acceleration)
Refraction
Seismic
Seismic Velocity (V )
Controlled Source
Acoustic Impedance (Seismic Velocity, V, and
Density, r)
Reflection
Gravitational Acceleration (g )
Density (r)
Potential Field
Gravity
Magnetic Susceptibility (c) and Remanent
Magnetization (Jrem)
Strength and Direction of Magnetic Field (F )
Magnetics
Thermal Conductivity (k ) and Heat Flow (q )
Geothermal Gradient (dT/dz )
Heat Flow
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Elastic Waves Elastic Behavior -- the ability
of a material to immediately return to its
original size, shape, or position after being
squeezed, stretched, or otherwise deformed. The
material follows Hookes Law (s Ce). Plastic
(Ductile) Behavior -- a permanent change in the
shape, size, etc., of a solid that does not
involve failure by rupture. Stress -- force
per unit area (s) Strain -- change in shape or
size (e)
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Elastic Waves A materials behavior can be
plotted on a stress/strain diagram
Ductile Behavior
Elastic Limit
Elastic Behavior
Increasing Stress
Hookes Law (s µ e)
Increasing Strain
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Elastic Waves However, an important factor we
havent talked about is strain rate ( e ). A
material will have a different stress/strain
diagram with varying e .
Slow rate of shape change (low strain rate)
Fast rate of shape change (high strain rate)
Stress
Stress
Strain
Strain
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Elastic Waves The deformation of the
lithosphere (folding) is a slow strain-rate
process (ductile), while the propagation of
seismic waves is a fast strain-rate process
(elastic).
Fast rate of shape change (High strain rate)
Slow rate of shape change (Low strain rate)
Stress
Stress
Strain
Strain
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Elastic Waves So in general, all seismic waves
are elastic waves and propagate through material
through elastic deformation. We can design
computer models of earth materials to behave
elastically, and demonstrate not only how seismic
waves propagate, but also the form in which they
propagate. The following models plot in color
the displacement of material as seismic energy
passes.
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Elastic Waves, as waves in general, can be
described spatially...
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or temporally.
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Elastic Waves The controlling factors in the
propagation of seismic wave are the physical
properties of the material through which the
seismic energy is travelling. The specific
properties are called the elastic constants Bulk
Modulus (k) -- describes the ability to resist
being compressed. Shear Modulus (µ) -- describes
the ability to resist shearing.
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Elastic Waves It turns out that k and µ can be
difficult to measure, so other elastic constants
relating the two were derived Youngs Modulus
(E) -- describes longitudinal strain in a body
subjected to longitudinal stress. Poissons Ratio
(n) -- describes transverse strain divided by
longitudinal strain in a body subjected to
longitudinal stress.
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Elastic Waves Lames Constant (l) --
interrelates all four elastic constants and is
very useful in mathematical computations, though
it doesnt have a good intuitive meaning.
Its important for you to know the terms and what
they represent (when appropriate) because we will
be using them in labs.
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The Wave Equation Well look at the scalar wave
equation to mathematically express how elastic
strain (dilatation, D) propagates through a
material r d2D (l 2m) 2D dt2
where D exx eyy ezz and 2 is the
Laplacian of D, or d2D/dx2 d2D/dy2 d2D/dz2
D
D
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Elastic Waves When solving the wave equation
(which describes how energy propagates through an
elastic material), there are two solutions that
solve the equation, Vp and Vs . These solutions
relate to our elastic constants by the following
equations
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Elastic Waves It turns out that Vp and Vs are
probably familiar to you from your introductory
earthquake knowledge, since they are the
velocities of P-waves and S-waves,
respectively. So, now you know why there are P-
and S-waves--because they are two solutions that
both solve the wave equation for elastic media.
S
P
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The Wave Equation The wave equation can be
rewritten as 1 d2D 2D a2
dt2 where a2 (l 2m)/r, or alternatively
as 1 d2Q 2Q b2 dt2 where b2
m/r And youll recognize the physical
realization of these equations as a P-wave and
b S-wave velocity.
D
D
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The Wave Equation Since the elastic constants
are always positive, a is always greater than b,
and b/a m/(l2m)1/2 (0.5-s)/(1-s)1/2 S
o, as Poissons ratio, s, decreases from 0.5 to
0, b/a increases from 0 to its maximum value
1/v2 thus, S-wave velocity must range from 0 to
70 of the P-wave velocity of any material.
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The Wave Equation These first types of
solutionsP-waves and S-wavesare called body
waves. Body waves propagate directly through
material (i.e. its body). I. Body Waves
a. P-Waves 1. Primary wave (fastest
arrive first) 2. Typically smallest in amplitude
3. Vibrates parallel to the direction of
wave propagation. b. S-Waves 1.
Secondary waves (moderate speed arrives
second) 2. Typically moderate amplitude 2.
Vibrates perpendicular to the direction of wave
propagation.
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The Wave Equation The other types of solutions
are called surface waves. Surface waves travel
only under specific conditions at an interface,
and their amplitude exponentially decreases away
from the interface. II. Surface waves
(slowest) 1. Arrives last 2. Typically
largest amplitude 2. Vibrates in vertical,
reverse elliptical motion (Rayleigh) or
shear elliptical motion
(Love)
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The Wave Equation The three types of surface
waves are 1) Rayleigh Wavesform at a
free-surface boundary. Air closely approximates
a vacuum (when compared to a solid), and thus
satisfies the free-surface boundary condition.
Rayleigh waves are also called ground roll. 2)
Love Wavesform in a thin layer when the layer is
bound below by a seminfinite solid layer and
above by a free surface. 3) Stonely Wavesform
at the boundary between a solid layer and a
liquid layer or between two solid layers under
specific conditions.
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The Wave Equation For a typical homogeneous
earth material, in which Poissons ratio s 0.25
(also called a Poisson solid), the following
relationship should be remembered between P-wave,
S-wave, and Rayleigh wave velocities VP VS
VR 1 0.57 0.52 In other words, VS is
about 60 of VP, and VR is about 90 of VS. But
remember, this only is a guide...
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The Wave Equation Modeled The wave equation
explains how displacements elastically propagate
through material. In models, colors represent
the displacement of discrete elements (below
yellowpositive, purplenegative) away from their
equilibrium position.