Environmental%20and%20Exploration%20Geophysics%20II

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Environmental and Exploration Geophysics II
Extracting Physical Properties from the Shot
Record and The Two Layer Refraction Problem
tom.h.wilson tom.wilson_at_mail.wvu.edu
Department of Geology and Geography West Virginia
University Morgantown, WV
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Questions?
Ray Trace Exercise I
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Graphical presentation
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In ray-trace exercises I-III
1) label all plotted curves, 2) label all
relevant points and 3) Note (comment on) basic
relationships between events observed in the
time-distance plots (see following)
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Ray Trace Exercise II

• Do Exercise II and III using Excel.
• In exercise II comment on the origins of the
  differences in the two reflection hyperbola?
  What is their relationship to corresponding
  direct arrivals.

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Ray Trace Exercise III
For Exercise III, explain the differences
observed in the arrival times of the reflection
and diffraction observed in the shot record. Why
does the diffraction event drop below the
reflection?
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For the Barrel Interpreter
The following references will be provided on a
sign out basis Brown AAPG Memoir 42, 1986 3D
Interp Brown, 2004, more recent volume on 3D
interp (6th ed) Neidel, 1979, strat
modeling Yilmaz, 2001, seismic data analysis,
volumes 1 and 2 Lines and Newrick, 2004,
fundamentals of seismic interp. Biondi, 2007,
Concepts and apps in 3D imaging We can be more
focused once we know where the project area is
For now the basics
You will first want to research the AAPG bulletin
and Journal Geophysics for publications related
to the project area
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SOFAR Channel sound fixing and ranging channel
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Absorption
When we set a spring in motion, the spring
oscillations gradually diminish over time. In the
same manner, we expect that as a seismic wave
propagates through the subsurface, energy will be
consumed through the process of friction and
there will be conversion of mechanical energy to
heat energy. We guess the following - there will
be a certain loss of amplitude dA as the wave
travels a distance dr and that loss will be
proportional to the initial amplitude A. i.e.
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? is a constant referred to as the attenuation
factor
In order to solve for A as a function of distance
traveled (r) we will have to integrate this
expression -
In the following discussion,let
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Mathematical Relationship
Graphical Representation
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The physical significance of ?
? - the attenuation factor is also a function of
additional terms -
? is wavelength, and Q is the absorption constant
1/Q is the amount of energy dissipated in one
wavelength (?) - that is the amount of mechanical
energy lost to friction or heat.
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? is also a function of interval velocity, period
and frequency
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? is just the reciprocal of the frequency so we
can also write this relationship as
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Smaller Q translates into higher energy loss or
amplitude decay.
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increase f and decrease A
Higher frequencies are attenuated to a much
greater degree than are lower frequencies.
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When we combine divergence and absorption we get
the following amplitude decay relationship
The combined effect is rapid amplitude decay as
the seismic wavefront propagates into the
surrounding medium. We begin to appreciate the
requirement for high source amplitude and good
source-ground coupling to successfully image
distant reflective intervals.
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But we are not through - energy continues to be
dissipated through partitioning - i.e. only some
of the energy (or amplitude) incident on a
reflecting surface will be reflected back to the
surface, the rest of it continues downward is
search of other reflectors.
The fraction of the incident amplitude of the
seismic waves that is reflected back to the
surface from any given interface is defined by
the reflection coefficient (R) across the
boundary between layers of differing velocity and
density.
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Z1 and Z2 are the impedances of the bounding
layers.
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The transmitted wave amplitude T is
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Consider the following problem
At a distance of 100 m from a source, the
amplitude of a P-wave is 0.1000 mm, and at a
distance of 150 m the amplitude diminishes to
0.0665 mm. What is the absorption coefficient of
the rock through which the wave is
traveling? (From Robinson and Coruh, 1988)
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Group Problem 1
Set up the equation that needs to be solved in
the foregoing problem. Write it down on a piece
of paper and hand in.
Group Problem 2
Write down the Excel equation you would use to
solve for the diffraction time-distance
relationship as portrayed in ray trace exercise II
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The critical distance and the crossover distance.
To determine the crossover distance set the
direct arrival time equal to the critical
refraction arrival time and solve for Xcross
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This is a new one, but pretty simple see 3.2.4
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We now have several equations which contain
quantities that we can measure directly from the
shot record and use to determine layer thickness
- h1.
XCross
Refraction Time intercept
V1
V2
Reflection Time intercept
Knowns
Xcrit
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Ways to solve for layer thickness

• Reflection time intercept
• Refraction time-intercept
• Crossover distance
• Critical Distance

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The two-layer refraction problem (see 3.3.1)
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Time distance traveled/velocity
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For the details see 3.3.1
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Snells law for multiple layers
?C
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The velocity triangle
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Expressing trig functions in terms of velocities
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The end result, where
and
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Interrelationships

• What is the critical distance
• What is the relationship of the reflection from
  the base of layer 2 to the critical refraction
  from the top of layer 2

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As x gets larger and larger the reflection from
the base of layer 2 and the refraction across the
top converge
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• In the three layer problem the number of possible
  terms that could potentially be measured directly
  from the shot record includes -
• V1, V2 and V3
• two reflection time intercepts
• two refraction time intercepts
• one crossover distance, and
• two critical distances

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How would you determine the thickness of layer 2
(h2)?

• From reflection arrivals
• From refraction events?

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What variables can be determined from an analysis
of the shot record
V1, V2, V3, ti1, ti2, where the tis refer to
the reflection time intercepts
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What variables can be determined from an analysis
of the shot record
V1, V2, V3, ti1, ti2, where the tis refer to
the refraction time intercepts
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Pitfalls
1) We have assumed that our layers have
successively higher and higher velocity. What
happens if we have a velocity inversion - lets
say V2 is less than V1 and V3? 2) Another
assumption we have made here is that the
refraction from the top of the third layer, for
example, will actually show itself, and not get
buried somewhere beneath the earlier refraction
and reflections. This can happen if the 2nd
layer is too thin.
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Assignments

• Today turn in problem 2.6, 2.7 and 2.12

• Please read through Chapter 3, pages 95 to top
  of 114.
• Chapter 4, pages 149 to 164 (as assigned
  previously.

• Continue working Exercises I-III and bring
  questions to class next Monday (due next
  Wednesday)
• Also consider the attenuation problem and be
  prepared to discuss further on Monday (due next
  Wednesday).