tom wilson, department of geology and geography environmental and exploration geophysics ii...
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Tom Wilson, Department of Geology and Geography
Environmental and Exploration Geophysics II
tom.h.wilsontom.wilson@mail.wvu.edu
Department of Geology and GeographyWest Virginia University
Morgantown, WV
Time-distance Time-distance relationshipsrelationshipsRay-tracingRay-tracing
Don’t forget to visit the web site for slides and other info -http://www.geo.wvu.edu/~wilson/geol554/lect3/lec3.pdf
Tom Wilson, Department of Geology and Geography
Different travel paths
Tom Wilson, Department of Geology and Geography
Reflection events in the shot record are completely different from those in the stack section
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 for general perspective
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
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
21
21
21
22 4
Vh
Vxt From the basic time-distance relationship
1
12
1
212 2or 4
Vht
Vht When x = 0, which is the time intercept.
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
When we bang on the ground, the Earth speaks back in a variety of ways
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
The shot record does not portray subsurface structure The differences in travel times are associated with differences in source receiver offset
Tom Wilson, Department of Geology and Geography
The geology of the area is nearly flat lying
Tom Wilson, Department of Geology and Geography
The single layer refraction time-distance relationship - but first -
1 1 2 2 sin sinwhere n is the index of refraction
velocity of light in vacuumvelocity of light in medium
n n
cnv
Snell’s law
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
Tom Wilson, Department of Geology and Geography
One of our assumptions -
Assume V1 < V2 < V3
Tom Wilson, Department of Geology and Geography
Tom Wilson, Department of Geology and Geography
because sin(/2) = 1
11 2
2
sin sinVV
Tom Wilson, Department of Geology and Geography
Critical Refraction
Tom Wilson, Department of Geology and Geography
With the direct arrival and the single layer reflection we travel from point A to B with constant velocity
The critical refraction problem is still a simple distance over velocity function, but the velocity changes on us.
Tom Wilson, Department of Geology and Geography
V1
V2
Isolating travel paths based on velocity
Tom Wilson, Department of Geology and Geography
The slant path length
Tom Wilson, Department of Geology and Geography
The path along the interface
Tom Wilson, Department of Geology and Geography
Sum them together
Tom Wilson, Department of Geology and Geography
Variables and constants
Tom Wilson, Department of Geology and GeographyDirect Arrival
2
1
Which of the two lines have the correct relationship of the critical refraction to the direct arrival?
time
x – source receiver offset distance
Trig simplifications
Tom Wilson, Department of Geology and Geography
Basic properties of the critical refraction
c
sin()1
21 sin
c
V1
2 22 1V V
V2
sin()=V1/V2
Tom Wilson, Department of Geology and Geography
11
2 1 2
2 tan2cos
c
c
hhxtV V V
Trig transformations
The critical or minimum refraction distance
c
xmin
The refraction time-intercept
The single layer refraction
Skip to 39
h1
Tom Wilson, Department of Geology and Geography
Trig functions and velocity ratios
Tom Wilson, Department of Geology and Geography
Snell's law gives us an easy way to look trig functions in the critical triangle
Tom Wilson, Department of Geology and Geography
Going through the algebraic substitution the constants in our earlier expression are represented in terms of velocity instead of critical angle.
Tom Wilson, Department of Geology and Geography
The critical or minimum distance
Tom Wilson, Department of Geology and Geography
Determining the critical distance
Tom Wilson, Department of Geology and Geography
Putting all these events together in the time-distance plot reveals useful information content in the shot record.
Tom Wilson, Department of Geology and Geography
Basic time-distance relationships for the refracted wave - Single horizontal interface
1) straight line 2) Refraction and reflection arrivals coincide at one offset (xcross).3) Refraction arrivals follow a straight line with 4) slope 1/V2, where 5) 1/V2 is less than 1/V1
Tom Wilson, Department of Geology and Geography
Questions about the shot record
Given that the geophone interval is 10 feet determine the velocities of events A, B and C
Tom Wilson, Department of Geology and Geography
Density range 2 to 3; Y, 0.12 to 1.1 (x1011N/m2);, 0.04 to 0.3. Which have the greatest influence on Vp. Use Table 1 (see H:Drive also see table linked on
class web page) to help you assess this problem.
(1 )(1 2 )(1 )p
EV
Problem 2.6
• How will you handle this problem ?
Get together in groups and talk about this. Describe your approach and hand in. 2.6 will be due next Monday and should – from here
out – be worked independently.
Tom Wilson, Department of Geology and Geography
For next time
• Continue your reading of Chapter 2, pages 65 -77 (Chapter 3) and pages 149 - 164 (Chapter 4).
• Hand in problems 2.3 and 2.6 (next Monday)
• Look over problems 2.7, 2.12 for Monday
• Look over the absorption problem handed out today.
• Bring your questions to class next Monday.
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