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Tom Wilson, Department of Geology and Geography
Environmental and Exploration Geophysics II
Department of Geology and GeographyWest Virginia University
Morgantown, WV
TimeTime--distance relationshipsdistance relationshipsRayRay--tracingtracing
Don’t forget to visit the web site for slides and other info -http://www.geo.wvu.edu/~wilson/geol554/lect2/lec2.pdf
Tom Wilson, Department of Geology and Geography
I’m often in my office, so feel free to drop by. To be sure I’m not tied up with
something send me an e-mail in advance.
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Tom Wilson, Department of Geology and Geography
Grading25% on computer labs,
30% problem sets,
10% mid term exam,
20% Expl project/term report and class presentation,
15% final exam.
Questions about class content and grading? The exploration project?
Have you tried using your class accounts? Go ahead and give that a try now if you already haven’t.
Tom Wilson, Department of Geology and Geography
Different kinds of waves … Body Waves
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Tom Wilson, Department of Geology and Geography
Surface Waves
Tom Wilson, Department of Geology and Geography
Body vs. “Surface” Waves
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Tom Wilson, Department of Geology and Geography
In general VR <VL <VS <VP
But this is not strictly true. The Love wave is a surface wave and its velocity will be equal to the shear wave velocity in the upper medium. The Love wave like the Rayleigh wave is also a dispersive wave. That means that deeper Love wave motion usually propagates more rapidly since velocity increases with depth.
Shear waves beneath the surface layers are generally much faster than those in the surface, so in application, the shear waves that we are concerned with generally have higher velocity than the Love waves.
Tom Wilson, Department of Geology and Geography
Love waves tend not to be recorded in the conventional seismic survey where the interest is primarily in the recording of P-waves. The geophones used in such surveys respond to vertical ground motion and thus do not respond to the side-to-side vibrations produced by Love waves.
Rayleigh waves produce large vertical displacements and are a significant source of “noise” in the conventional P-wave reflection seismic survey.
Single component vertical motion detectors
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Tom Wilson, Department of Geology and Geography
Breaking seismic disturbances down into their component parts
Some nomenclature
Tom Wilson, Department of Geology and Geography
time and frequency
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Tom Wilson, Department of Geology and Geography
wavelength and wavenumber
Tom Wilson, Department of Geology and Geography
Sinusoid arguments
2 2Amplitude = sin or sin
through substitution for or =v , we get two additional forms
2 2Amplitude = sin or sin
x t
x vtvt x
v
π πλ τ
λ τπ πλ τ
=
Temporal
form
Spatial
form
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Tom Wilson, Department of Geology and Geography
Some examples of the seismic source
Tom Wilson, Department of Geology and Geography
The seismic wavelet
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Tom Wilson, Department of Geology and Geography
The wavelet or pulse is a transient disturbance – it comes and goes
Tom Wilson, Department of Geology and Geography
Spatial view
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Tom Wilson, Department of Geology and Geography
A Wave Packet or Wavelet
Time domain and frequency domain a different way of viewing the time series
Tom Wilson, Department of Geology and Geography
Creating a wavelet using a sum of sinusoids
See http://www.geo.wvu.edu/~wilson/geol554/SumofCosines.xls
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Tom Wilson, Department of Geology and Geography
The wavelet
Any time series can be represented as a sum of sinusoids
Tom Wilson, Department of Geology and Geography
How do mechanical waves get from point A to B
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Tom Wilson, Department of Geology and Geography
You can go straight there or …
Tom Wilson, Department of Geology and Geography
The reflection events we see in a seismic section don’t start off looking like this
The geologist usually immediately starts to see layers, stratigraphy, depositional history, structure…
Fruitland coals-
San Juan Basin, NM
The
migrated
stack
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Tom Wilson, Department of Geology and Geography
When we bang on the ground, the reflection events are mixed together with a variety of other events
This time-distance record shows everything coming in with different shapes, sometimes almost at the same time and sometimes earlier,
sometimes later. A real mess!
Tom Wilson, Department of Geology and Geography
Our initial goal is to develop an understanding of the different types of events that appear in a shot record and how to extract information from these observations
and to understand how their travel times (t) vary with source receiver offset (x).
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Tom Wilson, Department of Geology and Geography
Some shallow high res data from Marshall Co. WV
Pentolite charges
Tom Wilson, Department of Geology and Geography
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Tom Wilson, Department of Geology and Geography
Another record from the Marshall Co. site
Tom Wilson, Department of Geology and Geography
Migrated stack display-The “geological” display
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Tom Wilson, Department of Geology and Geography
Routine logs (ρ, γ, resistivity, July, 07). Sonic Scanner for Acoustic and
Mechanical Properties (March, 08)
Geophysical CharacterizationLogging Effort
Tom Wilson, Department of Geology and Geography
Schematic Schlumberger Sonic Scanner
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Tom Wilson, Department of Geology and Geography
Pittsburgh Coal
Geophysical CharacterizationMechanical Properties
Tom Wilson, Department of Geology and Geography
For the seismic work we take information from sonic and density logs and create a synthetic seismogram
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Tom Wilson, Department of Geology and Geography
Migrated stack display-The “geological” display
Tom Wilson, Department of Geology and Geography
A shot record is a recording of ground movements produced by a single shot (mechanical disturbance created at some point on or near the earth’s surface).
The recording is made at several locations ideally along a straight line extending in either or both directions away from the source.
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Tom Wilson, Department of Geology and Geography
How will the travel times of the direct arrival vary with offset? What will a direct arrival look like in a time distance plot?
Tom Wilson, Department of Geology and Geography
Direct Arrival
shot record
Also need to consider the type of direct arrival ...
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Tom Wilson, Department of Geology and Geography
Time Distance Plot
Direct Arrival
Tom Wilson, Department of Geology and Geography
The reflection event and its time distance relationships-The reflection law
These chalk board slides are just for reference. I’ll set this up independently in class and you’ll find prettier notes in the text.
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Tom Wilson, Department of Geology and Geography
The image point
Tom Wilson, Department of Geology and Geography
V1
The image point
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Tom Wilson, Department of Geology and Geography
( ) ( )212 2hxd +=
Triangles come in quite handy in geophysics
Tom Wilson, Department of Geology and Geography
Seismic reflections have a hyperbolic shape in their time-distance representation.
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Tom Wilson, Department of Geology and Geography
Reflection time distance curve in basic hyperbolic form
Tom Wilson, Department of Geology and Geography
Some basic math probably worth seeing again
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Tom Wilson, Department of Geology and Geography
Location of the apex in time
Tom Wilson, Department of Geology and Geography
As time goes by reflection events approach start to come in linearly with time. They approach the asymtotes of the hyperbola
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Tom Wilson, Department of Geology and Geography
The direct arrival has the relationship of an asymptote to the arrival times of the reflection event.
Tom Wilson, Department of Geology and Geography
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21
21
22 4
Vh
Vxt +=From the basic time-distance relationship
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21
212 2or 4
Vht
Vht ==When x = 0, which is the time intercept.
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Tom Wilson, Department of Geology and Geography
121
22 or
Vxt
Vxt ≈≈
When x becomes very large with respect to the thickness of the reflecting layer, the x2/V2 term
becomes much larger than the 4h2/V2 term so that
Tom Wilson, Department of Geology and Geography
The single layer refraction time-distance relationship - but first -
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Tom Wilson, Department of Geology and Geography
The c’s cancel out and we have ...
1 1 2 2 1 21 2
sin sin ; sin sinc cn nV V
θ θ θ θ= =
Tom Wilson, Department of Geology and Geography
One of our assumptions -
Assume V1 < V2 < V3
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Tom Wilson, Department of Geology and Geography
Tom Wilson, Department of Geology and Geography
because sin(π/2) = 1
11 2
2
sin sinVV
θ θ=
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Tom Wilson, Department of Geology and Geography
For next time
• Hand in problems 2.1 and 2.2
• Continue your reading of Chapter 2
• Review background on the refraction time-distance relationship
• Look over problems 2.3 and 2.6 for next Monday. These problems will be due next Wednesday,
January 20th.