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EARTH 260
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Tony Endres
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Lecture

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University of Waterloo

Earth Sciences

EARTH 260

Tony Endres

Fall

Description

Earth 260-Applied Geophysics 1
II.) SEISMIC METHODS
Mechanical energy can travel through a medium as a wave,
such as sound waves in air or water.
Seismic waves are waves of mechanical energy that travel
through the Earths interior. The traveltime and amplitude of
these waves are measured to determine the structure of the
subsurface.
A.) Basic Concepts for Seismic Wave Propagation
1.)Stress and Strain
a.)Stress a measure of the intensity of the mechanical
force applied to a material.
Consider the force applied uniformly across the face of a
cube, the stress would be
Force / Surface Area of the Face
SI Units of stress:
2 2
Newtons / meter ( N / m ) = Pascal (Pa)
There are different types of stress that can be applied to a
material (e.g., pressure, traction or shear stress).
b.)Strain a measure of the deformation (i.e., changes in
shape and size) caused by an applied stress.
1 Earth 260-Applied Geophysics 1
Different types of strain correspond to differing types of
stress (e.g., dilatational (or volumetric) strain, shear
strain).
Strain is a dimensionless quantity.
2.) Elastic Moduli
a.)If the stress and strain are small in magnitude (which they
generally are for seismic waves), there is a proportional
relationship between them.
Stress = Constant Strain (1)
This proportionality constant is an elastic modulus that is
a physical property of the material.
Elastic moduli have the same SI units as stress (i.e., Pa).
Note: This relationship is analogous to Hookes Law for springs.
b.) The elastic modulus used is in this equation is
determined by the stress and strain type.
1.) Bulk modulus K relates pressure P to volumetric
strain .
P = K (2)
2 Earth 260-Applied Geophysics 1
2.) Shear modulus (or Rigidity) relates shear stress
to shear strain .
= (3)
There is no volume change associated with shear
stress and strain; the deformation is a distortion in
shape.
Fluids (i.e., water and air) cannot support a shear
stress; their shear modulus = 0.
3.)Types of Seismic Waves
When the stress-strain relationships (i.e., constitutive
relationships) are combined with the equations of motion
nd
(the generalized version of Newtons 2 Law: Fa= m ),
we get the elastic wave equation that describes the
propagation of mechanical waves through a material.
From this equation, we find there are different types of
seismic waves with distinctive characteristics.
There are two groups of seismic waves: body and
surface waves.
3 Earth 260-Applied Geophysics 1
a.) Body Waves
1.) These waves travel/propagate through the body (or
interior) of a medium.
2.) There are two types (i.e., modes) of body waves that
differ in terms of their particle motion relative to the
propagation (i.e., travel) direction of the wave.
Particle motion is determined by tagging a particle in
the material; its movement as the wave passes is the
particle motion.
3.) Compressional (longitudinal, primary or P-) waves
a.)Particle motion is in the same direction as the wave
propagates.
b.)These waves have regions of dilatation/rarefraction
and compression due to volume changes.
c.) P-wave velocity:
4
K + 3
VP = = (4)
3
where is the density (in kg / m ) of the material.
Note #1: SI units for velocity are m / s or km / s.
Note #2: Density is introduced through the inertia terms in the
equations of motion.
4

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