The Reflection Method

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06 Feb 2008
Read For Fri Ch 4.0-4.1 (pp 149167)
The Reflection Method

• Recall from last time
• Refraction Method Recognize velocity change
  within a
• layer as a break in slope of refraction
  that has the
• same slope both forward reversed
• Offset of layer boundary Offsets (change in
  intercept) of
• refractions in opposite directions similar
  slopes either side
• Delay-time or plus-minus method for thickness
• velocity of an irregular layer interface
• where m- is slope of a plot of t1it2i vs
  xi for SP1, 2 and
• geophones i

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The Reflection Seismic Method
Consider a single layer over a half-space, with
layer thickness h1 and velocity V1
x/2
V1
h1
The travel-time for a reflected wave to a
geophone at a distance x from the shot is given
by
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Hyperbola
The Reflection Seismic Method
Recall from earlier in the course that
this travel-time for a reflection corresponds
to the equation of a hyperbola. If we re-write
intercept a asymptote m b/a
water
shale
gas sand
shale
this implies an intercept at 2h1 and
asymptotes with slope 1/V1
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Some quick observations Changing only depth of
the layer changes intercept of the hyperbola but
not the slope or intercept of the asymptotes,
so reflection from a shallower interface appears
more pointy
h1 15 m V1 1500 m/s
h1 45 m V1 1500 m/s
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Changing velocity of the layer changes intercept
of the hyperbola and the slope of the
asymptotes, so reflection in a layer with higher
velocity arrives sooner and appears more flat
h1 45 m V1 1500 m/s
h1 45 m V1 4000 m/s
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Normal Move-Out or NMO is the difference in
reflection travel times at distance x versus
relative to the intercept (x 0), i.e., NMO
emphasizes changes in curvature of the
hyperbola (NMO is greater for shallower depth of
reflection and for lower velocity of the layer).
It is particularly important to correct for
move-out if one wants to use the reflection
energy in imaging the subsurface
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Reflection from a second layer interface over
half-space
x/2
V1
h1
V2
h2

• Can derive using Snells law but easier to
  consider that
• For x 0, ? intercept of
  hyperbola 2(h1h2)
• For x ? ?, asymptotic to the refraction from
  layer 2

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Equation for the hyperbola then is
After some algebra we have
And you might see where this could start to get
complicated for 3, 4, layers This is part of
why industry seismic reflection processing
historically did not go after full seismic
velocity analysis but instead took shortcuts to
imaging of structures
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A Dipping Reflector
V1
h1
?
?
Geometrically, this is equivalent to rotating the
axis of the reflector by the dip angle ?. This
rotates the hyperbola on the travel-time curve
by ? tan-1(-2h1sin?) and has equation
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Getting velocity structure The x2 t2
method If we have travel-times from a
reflection, can plot t2 vs x2 to get parameters
of thickness velocity from slope and intercept
of the resulting line fit