Allied Military Model Making during World War II

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
1Î
Reflectivity and convolution
The seismic wave is sensitive to
the sequence of impedance
contrasts
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
2Spiking deconvolution
Applied Geophysics – Seismic reflection II
Spiking
deconvolution
Recorded
waveform 1-1 ¾ -½
Deconvolution
operator ¼ 1 1
Output 0 1
Recovered
reflectivity
series
Applied Geophysics – Seismic reflection II
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Spiking
deconvolution
Recorded
waveform 1-1 ¾ -½
Deconvolution
operator ¼ 1 1
Output 0 1 0
Recovered
reflectivity
series
Applied Geophysics – Seismic reflection II
Spiking
deconvolution
Recorded
waveform 1-1 ¾ -½
Deconvolution
operator ¼ 1 1
Output 0 1 0 0
Recovered
reflectivity
series
Applied Geophysics – Seismic reflection II
4

Spiking
deconvolution
Recorded
waveform 1-1 ¾ -½
Deconvolution
operator ¼ 1 1
Output 0 1 0 0 0
Recovered
reflectivity
series
Applied Geophysics – Seismic reflection II
Spiking
deconvolution
Recorded
waveform 1-1 ¾ -½
Deconvolution
operator ¼ 1 1
A perfect
deconvolution Output 0 1 0 0 0 ? operator is of
infinite length
Recovered
reflectivity
series
Applied Geophysics – Seismic reflection II
5

Source-pulse deconvolution
Examples
Original Deconvolution:
section 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
6Î
Multiples
Due to multiple bounce paths in the section
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
7Velocity 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
reflection
hyperbolae The reflection traveltime equation
become fatter predicts a hyperbolic shape to
with depth reflections in a CMP gather. The
(i.e. velocity)hyperbolae become fatter/flatter
with increasing velocity
2x2 2T =T +x 0
V1
We want to subtract the NMO
correction from the common depth
point gather 2x
∆T ≈NMO 22TV0 1
But for that we need velocity…
Applied Geophysics – Seismic reflection II
8Î
Î
multiples
Stacking velocity
2x
In order to stack the waveforms we ∆T =NMO 2
need to know the velocity. We find the 2TV0 1
velocity by trial and error:
• 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
V causes the 2
waveforms to
stack on top of
one another
Applied Geophysics – Seismic reflection II
Stacking velocity
Multiple layer case
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
Velocity semblance spectrum
Pick stacking velocities
Applied Geophysics – Seismic reflection II
9Stacking velocity
Note: the sensitivity Multiple layer case
to velocity decreases
with depth
Stacking velocity panels: constant velocity gathers
Applied Geophysics – Seismic reflection II
Multiple layers
zInterval velocity iV =i ti
Average velocity ZV' =
T
0
2
Root-mean- V t∑ i i
V =square velocity RMS
t∑ i
2 2x +4zTwo-way traveltime of ray reflected
t =th noff the n interface at a depth z V
RMS
2 2The interval velocity of layer n (V ) t − (V ) t
RMS,n n RMS,n −1 n −1determined from the rms velocities V =
int
t −tand the two-way traveltimes to the n n −1
th thn and n-1 reflectors
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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