Last Time
UNIVERSITY OF SOUTH ALABAMA
Geophysics
GY 305: Geophysics
Lecture 2:
Wave TheoryTheory- Part 2:
Refraction and Reflection
•
•
•
Introductions, class policy etc.
Introduction to geophysics
Start of Wave theory (properties of rocks)
Geophysics
Geophysical analysis is done when…
1) you can’t get direct access to the rocks
2) you want to “model” a large area quickly
3) you know what you are looking for
… but every geophysical technique only
“estimates” geology (lots of interpretation)
Geophysics
There are 2 scales of geophysical analysis:
1) “small-scale” (single well; shallow
penetration seismic etc.)
2) “large-scale” (basin
wide surveys)
Geophysics
So what kind of geophysics is
there?
• Seismology - Study of natural [from
earthquakes] and man-induced seismic
waves
Geophysics
Passive methods
• Seismology - Study of natural [from
earthquakes] and man-induced seismic
waves
• Gravity - Study of variations in earth's
gravitational field
Measuring spatial variations of
static or natural fields of force
• Gravity - Study of variations in earth's
gravitational field
• Electrical Methods - Use of electrical
conductivity / resistance of earth
Active methods
• Electrical Methods - Use of electrical
conductivity / resistance of earth
• Electromagnetics - Study of induced
electromagnetic fields
• Magnetics - Analysis of variations in
earth's magnetic field
http://www.laynewater.com/images/borehole_geophysics1.jpg
Proposed well
• Radioactivity - Study of natural and
induced response to radioactivity
Measurement of wave field
characteristics (i.e. travel times
of elastic waves, and amplitude
and phase of electromagnetic
waves)
• Electromagnetics - Study of induced
electromagnetic fields
• Magnetics - Analysis of variations in
earth's magnetic field
• Radioactivity - Study of natural and
induced response to radioactivity
1
Wave Theory
Wave Theory
This is complex stuff to model, so we need to make a few
assumptions:
This is complex stuff to model, so we need to make a few
assumptions:
1) the media must be considered heterogeneous, but we can
consider this heterogenosity to be the result of stacked horizontal
layers of different homogeneous materials.
2) Seismic disturbances (natural or induced) travel by elastic
displacements of the media.
Homogeneous Shale
Overall,
heterogeneous
Homogeneous Sandstone
Homogenesous Limestone
Lowrie, W., 2007. Fundamentals of Geophysics 2 nd edition, Cambridge
University Press, Cambridge, 381p
Wave Theory
Surface waves spread out over the surface and are analogous to
ripples on the surface of a pool of water. There are 2 categories of
surface wave (collectively called L-waves):
Surface waves spread out over the surface and are analogous to
ripples on the surface of a pool of water. There are 2 categories of
surface wave (collectively called L-waves):
Rayleigh waves (LR) vibrate
in a vertical orientation but in
combination with forward
propagation, forces the
particles that comprise the
media to move in a
retrograde ellipse.
Love waves (LQ) are
vibrations that ore orientated
in a plane horizontal to the
earth’s surface and thus are
more purely shear (SH)
vibrations 90 degrees.
Lowrie, W., 2007. Fundamentals of Geophysics 2 nd edition, Cambridge
University Press, Cambridge, 381p
Today’s Agenda
Lowrie, W., 2007. Fundamentals of Geophysics 2 nd edition, Cambridge
University Press, Cambridge, 381p
Wave Theory
Wave Theory (Continued)
Refraction and Reflection
•
•
•
Wave front mechanics
Wave propagation
Refraction, reflection and Snell’s Law
2
Wave Theory
When a body wave propagates a certain distance from the seismic
source (say out of the damaged zone), the wavefront (the surface
consisting of particles that all vibrate the same) is spherical in
form.
When a body wave propagates a certain distance from the seismic
source (say out of the damaged zone), the wavefront (the surface
consisting of particles that all vibrate the same) is spherical in
form.
Lowrie, W., 2007. Fundamentals of Geophysics 2nd edition, Cambridge University Press,
Cambridge, 381p
Wave Theory
At greater distances, the
spherical shape of the
waveform flattens out
significantly forming a
plane wave.
Lowrie, W., 2007. Fundamentals of Geophysics 2 nd edition, Cambridge
University Press, Cambridge, 381p
When a body wave propagates a certain distance from the seismic
source (say out of the damaged zone), the wavefront (the surface
consisting of particles that all vibrate the same) is spherical in
form.
When a body wave propagates a certain distance from the seismic
source (say out of the damaged zone), the wavefront (the surface
consisting of particles that all vibrate the same) is spherical in
form.
At greater distances, the
spherical shape of the
waveform flattens out
significantly forming a
plane wave.
At greater distances, the
spherical shape of the
waveform flattens out
significantly forming a
plane wave.
P-component
SH-component
(Horizontal)
Lowrie, W., 2007. Fundamentals of Geophysics 2nd edition, Cambridge University Press,
Cambridge, 381p
Wave Theory
Lowrie, W., 2007. Fundamentals of Geophysics 2nd edition, Cambridge University Press,
Cambridge, 381p
Wave Theory
When a body wave propagates a certain distance from the seismic
source (say out of the damaged zone), the wavefront (the surface
consisting of particles that all vibrate the same) is spherical in
form.
In order to be able to interpret geophysical data, some understanding
of mathematical modeling is necessary:
At greater distances, the
spherical shape of the
waveform flattens out
significantly forming a
plane wave.
SV-component
(Vertical)
e.g., this is the one-dimensional
equation of motion
Lowrie, W., 2007. Fundamentals of Geophysics 2nd edition, Cambridge University Press,
Cambridge, 381p
Wave Theory
Lowrie, W., 2007. Fundamentals of Geophysics 2nd edition, Cambridge University Press,
Cambridge, 381p
Wave Theory
3
Wave Theory
In order to be able to interpret geophysical data, some understanding
of mathematical modeling is necessary:
Three dimensional modeling is of course more complex and yet is
still limited due to the assumptions made earlier.
Lowrie, W., 2007. Fundamentals of Geophysics 2nd edition, Cambridge University Press,
Cambridge, 381p
Wave Theory
And this is one-dimensional wave
equation
Chalk Board
Wave Theory
Lowrie, W., 2007. Fundamentals of Geophysics 2nd edition, Cambridge University Press, Cambridge, 381p
Wave Propagation
Passage of a wave (light or
seismic) from one media to
the next across an interface
was first explained in 1678
by Dutch mathematician
Christiaan Huygens.
Fortunately, you do not
have to always fully
understand the math/physics
to be a good geophysicist.
All it takes is practice and
patience
http://www.magiclantern.org.uk/history/history4a.html
Wave Propagation
Huygens’ Principle: “All
points on a wavefront can be
regarded as point sources for
the production of new
spherical waves; the new
wavefront is the tangential
surface (or envelop) of the
secondary wavelets”.
Wave Propagation
Huygens’ Principle: “All
points on a wavefront can be
regarded as point sources for
the production of new
spherical waves; the new
wavefront is the tangential
surface (or envelop) of the
secondary wavelets”.
Lowrie, W., 2007. Fundamentals of Geophysics 2 nd edition, Cambridge
University Press, Cambridge, 381p
Lowrie, W., 2007. Fundamentals of Geophysics 2 nd edition, Cambridge
University Press, Cambridge, 381p
4
Wave Propagation
Huygens’ Principle: “All
points on a wavefront can be
regarded as point sources for
the production of new
spherical waves; the new
wavefront is the tangential
surface (or envelop) of the
secondary wavelets”.
Wave Propagation
Huygens’ Principle: “All
points on a wavefront can be
regarded as point sources for
the production of new
spherical waves; the new
wavefront is the tangential
surface (or envelop) of the
secondary wavelets”.
Lowrie, W., 2007. Fundamentals of Geophysics 2 nd edition, Cambridge
University Press, Cambridge, 381p
Wave Propagation
Now consider what happens when a wavefront encounters an
interface between a second media.
Shale (wave velocity = α1)
Lowrie, W., 2007. Fundamentals of Geophysics 2 nd edition, Cambridge
University Press, Cambridge, 381p
Wave Propagation
Now consider what happens when a wavefront encounters an
interface between a second media.
Shale (wave velocity = α1)
Interface
Sandstone (wave velocity = α2)
Interface
A
B
Sandstone (wave velocity = α2)
Wave Propagation
Now consider what happens when a wavefront encounters an
interface between a second media.
Shale (wave velocity = α1)
Wave Propagation
Now consider what happens when a wavefront encounters an
interface between a second media.
Shale (wave velocity = α1)
Interface
A
B
Sandstone (wave velocity = α2)
Interface
A
B
Sandstone (wave velocity = α2)
5
Wave Propagation
Now consider what happens when a wavefront encounters an
interface between a second media.
Shale (wave velocity = α1)
Wave Propagation
Now consider what happens when a wavefront encounters an
interface between a second media.
Shale (wave velocity = α1)
Interface
A
Interface
A
B
Sandstone (wave velocity = α2)
Sandstone (wave velocity = α2)
Wave Propagation
Reflection of the wave front back into the original media (shale)
B
Wave Propagation
Refraction of the wave front across the interface into the new
media (sandstone)
Lowrie, W., 2007. Fundamentals of Geophysics 2 nd edition, Cambridge University Press, Cambridge, 381p
Lowrie, W., 2007. Fundamentals of Geophysics 2 nd edition, Cambridge University Press, Cambridge, 381p
Wave Propagation
Fermat’s Principle: “Of the many possible paths between 2
points A and B, the ray follows the path that gives the shortest
travel time between the points.”
http://www.york.ac.uk/depts/maths/histstat/people/fermat.gif
The behavior of a wavepath as it
encounters an interface is also
explained by another principle of
optics that was formulated in the
1600’s by Pierre de Fermat, a
French Mathematician
Wave Propagation
Reflection using
Fermat’s
Principle (this
can also be done
for refraction)
A
B
Lowrie, W., 2007. Fundamentals of Geophysics 2 nd edition, Cambridge University Press, Cambridge, 381p
6
Wave Propagation
This brings us back to
elementary wave theory and in
particular, Snell’s Law
Wave Propagation
This brings us back to
elementary wave theory and in
particular, Snell’s Law
sin(i) = sin(r)
Vi
Vr
sin(i) = sin(r)
Vi
Vr
Sheriff, R.E., 1978. A First Course in Geophysical Exploration and
Interpretation. IHRDC, Houston, TX. 313p
Wave Propagation
Most optical concepts (e.g., critical angle) also apply to
geophysical techniques (e.g., seismology).
For seismology, it is more common to
call this the Law of Refraction. Snell’s
Law is more commonly applied to
optical waves (e.g., XRD).
Sheriff, R.E., 1978. A First Course in Geophysical Exploration and
Interpretation. IHRDC, Houston, TX. 313p
Wave Propagation
And that also goes for standard wave terminology:
•Amplitude
•Frequency
•Period
•Wavelength
Sheriff, R.E., 1978. A First Course in Geophysical Exploration and Interpretation. IHRDC, Houston, TX. 313p
Lowrie, W., 2007. Fundamentals of Geophysics 2 nd edition, Cambridge University Press, Cambridge, 381p
Wave Propagation
Wave Propagation
It aids us in planning geophysical surveys like seismic lines.
Why should we care?
24 group split spread
24 group off-end split
Sheriff, R.E., 1978. A First Course in Geophysical Exploration and Interpretation. IHRDC, Houston, TX. 313p
7
Wave Propagation
Wave Propagation
It aids us in planning geophysical surveys like seismic lines.
It aids us in planning geophysical surveys like seismic lines.
Sheriff, R.E., 1978. A First Course in Geophysical Exploration and Interpretation. IHRDC, Houston, TX. 313p
Sheriff, R.E., 1978. A First Course in Geophysical Exploration and Interpretation. IHRDC, Houston, TX. 313p
Upcoming Stuff
Thursday’s Lab:
Calculations: Bring a scientific calculator.
Monday Lecture:
Petroleum Geology (ONLINE)
8