Seismic methods:
Seismic reflection - II
Reflection reading:
Sharma p130-158; (Reynolds p343-379)
Applied Geophysics – Seismic reflection II
Seismic reflection processing
Flow overview
These are the main
steps in processing
The order in which
they are applied is
variable
Applied Geophysics – Seismic reflection II
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Reflectivity and convolution
The seismic wave is sensitive to
the sequence of impedance
contrasts
Î The reflectivity series (R)
We input a source wavelet (W) which is
reflected at each impedance contrast
The seismogram recorded at the surface
(S) is the convolution of the two
S=W*R
Applied Geophysics – Seismic reflection II
Deconvolution
…undoing the convolution to get back to the
reflectivity series – what we want
Spiking or whitening deconvolution
Reduces the source wavelet to a spike. The filter that best achieves this is
called a Wiener filter
Our seismogram S = R*W
(reflectivity*source)
Deconvolution operator, D, is designed such that D*W = δ
So D*S = D*R*W = D*W*R = δ*R = R
Time-variant deconvolution
D changes with time to account for the different frequency content of
energy that has traveled greater distances
Predictive deconvolution
The arrival times of primary reflections are used to predict the arrival times
of multiples which are then removed
Applied Geophysics – Seismic reflection II
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Spiking deconvolution
Applied Geophysics – Seismic reflection II
Spiking
deconvolution
Recorded
waveform
Deconvolution
operator
Output
1
¼
1
1
0
1
-1
¾
-½
Recovered
reflectivity
series
Applied Geophysics – Seismic reflection II
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Spiking
deconvolution
Recorded
waveform
1
-1
Deconvolution
operator
¼
1
1
Output
0
1
0
¾
-½
Recovered
reflectivity
series
Applied Geophysics – Seismic reflection II
Spiking
deconvolution
Recorded
waveform
1
-1
¾
Deconvolution
operator
¼
1
1
1
0
0
Output
0
-½
Recovered
reflectivity
series
Applied Geophysics – Seismic reflection II
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Spiking
deconvolution
Recorded
waveform
1
Deconvolution
operator
Output
0
1
-1
¾
-½
¼
1
1
0
0
0
Recovered
reflectivity
series
Applied Geophysics – Seismic reflection II
Spiking
deconvolution
Recorded
waveform
1
-1
Deconvolution
operator
Output
Recovered
reflectivity
series
0
1
0
¾
-½
¼
1
0
0
1
?
A perfect
deconvolution
operator is of
infinite length
Applied Geophysics – Seismic reflection II
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Source-pulse deconvolution
Examples
Original
section
Deconvolution:
Ringing removed
Source wavelet becomes spike-like
Applied Geophysics – Seismic reflection II
Deconvolution using correlation
If we know the source pulse
Then cross-correlating it with
the recorded waveform gets
us back (closer) to the
reflectivity function
If we don’t know the source pulse
Then autocorrelation of the waveform gives us something similar to
the input plus multiples.
Cross-correlating the autocorrelation with the waveform then
provides a better approximation to the reflectivity function.
Applied Geophysics – Seismic reflection II
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Multiples
Due to multiple bounce paths in the section
Î Looks like repeated structure
These are also removed with deconvolution
• easily identified with an autocorrelation
• removed using cross-correlation of the
autocorrelation with the waveform
Sea-bottom reflections
Applied Geophysics – Seismic reflection II
Seismic reflection processing
Flow overview
These are the main
steps in processing
The order in which
they are applied is
variable
Applied Geophysics – Seismic reflection II
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Velocity analysis
Determination of seismic
velocity is key to seismic
methods
Velocity is needed to convert the
time-sections into depth-sections i.e.
geological cross-sections
Unfortunately reflection surveys
are not very sensitive to velocity
Often complimentary refraction
surveys are conducted to provide
better estimates of velocity
Applied Geophysics – Seismic reflection II
Normal move out (NMO) correction
The reflection traveltime equation
predicts a hyperbolic shape to
reflections in a CMP gather. The
hyperbolae become fatter/flatter
with increasing velocity
Tx2 = T02 +
reflection
hyperbolae
become fatter
with depth
(i.e. velocity)
x2
V1
We want to subtract the NMO
correction from the common depth
point gather
2
∆TNMO ≈
x
2T0V12
But for that we need velocity…
Applied Geophysics – Seismic reflection II
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Stacking velocity
In order to stack the waveforms we
need to know the velocity. We find the
velocity by trial and error:
∆TNMO =
x2
2T0V12
• For each velocity we calculate the hyperbolae and stack the waveforms
• The correct velocity will stack the reflections on top of one another
• So, we choose the velocity which produces the most power in the stack
V2 causes the
waveforms to
stack on top of
one another
Applied Geophysics – Seismic reflection II
Multiple layer case
s
tiple
mul
Stacking velocity
A stack of multiple horizontal layers is a
more realistic approximation to the Earth
• Can trace rays through the stack using
Snell’s Law (the ray parameter)
• For near-normal incidence the
moveout continues to be a hyperbolae
• The shape of the hyperbolae is related
to the time-weighted rms velocity
above the reflector
Î Velocity semblance spectrum
Î Pick stacking velocities
Applied Geophysics – Seismic reflection II
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Stacking velocity
Note: the sensitivity
to velocity decreases
with depth
Multiple layer case
Stacking velocity panels: constant velocity gathers
Applied Geophysics – Seismic reflection II
Multiple layers
zi
Interval velocity
Vi =
Average velocity
V '= Z
Root-meansquare velocity
ti
T0
∑V t
∑t
2
VRMS =
i
i
i
Two-way traveltime of ray reflected
off the nth interface at a depth z
tn =
The interval velocity of layer n
determined from the rms velocities
and the two-way traveltimes to the
nth and n-1th reflectors
Vint =
x2 + 4z 2
VRMS
(V
) t − (V
2
RMS , n
n
)t
2
RMS , n −1
n −1
t n − t n −1
Dix equation
The interval velocity can be determined from the
rms velocities layer by layer starting at the top
Applied Geophysics – Seismic reflection II
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Velocity sensitivity: Example
Shallow: Two layer model:
α1 = 3 km/s, z = 5 km
Deep: Two layer model:
α1 = 6 km/s, z = 20 km
2
2
2
1
Equation of the
400 + x
t=
z2 + x
=
4 3
4
α1
reflection hyperbolae:
Normal move out
correction:
∆t NMO =
x2
2α t
2
1 0
=
x2
480
For a 5 km offset:
t=
2
1
25 + x
4
1.5
∆t NMO =
x2
60
For a 5 km offset:
α1 = 6.0 km/s then 0.052 sec – correct value
α1 = 3.0 km/s then 0.417 sec
α1 = 5.5 km/s then 0.062 sec
α1 = 2.5 km/s then 0.600 sec
α1 = 6.5 km/s then 0.044 sec
α1 = 3.5 km/s then 0.306 sec
Are these significant differences?
What can we do to improve
velocity resolution?
Applied Geophysics – Seismic reflection II
Frequency filtering
Hi-pass: to remove ground roll
Low-pass: to remove high
frequency jitter/noise
Notch filter: to remove single
frequency
Applied Geophysics – Seismic reflection II
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Resolution of structure
Consider a vertical step in an interface
To be detectable the step must cause an
delay of ¼ to ½ a wavelength
This means the step (h) must be 1/8 to ¼
the wavelength (two way traveltime)
Example:
20 Hz, α = 4.8 km/s then λ = 240 m
Therefore need an offset greater than 30 m
Shorter wavelength signal (higher
frequencies) have better resolution.
What is the problem with very high
frequency sources?
Applied Geophysics – Seismic reflection II
Resolution of structure
When you have been mapping faults in the field what
were the vertical offsets?
Applied Geophysics – Seismic reflection II
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Fresnel Zone
Tells us about the horizontal resolution
on the surface of a reflector
First Fresnel Zone
The area of a reflector that returns energy to
the receiver within half a cycle of the first
reflection
The width of the first Fresnel zone, w:
2
λ

 w
2
d +  = d +  
4

2
w2 = 2dλ +
2
λ2
4
If an interface is smaller than the first Fresnel
zone it appears as an point diffractor, if it is
larger it appears as an interface
Example:
30 Hz signal, 2 km depth where α = 3 km/s then λ = 0.1 km and the width of the
first Fresnel zone is 0.63 km
Applied Geophysics – Seismic reflection II
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