Seismic methods: Seismic reflection - II - Richard...
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1
Applied Geophysics – Seismic reflection II
Seismic reflection - II
Reflection reading: Sharma p130-158; (Reynolds p343-379)
Seismic methods:
Applied Geophysics – Seismic reflection II
Seismic reflection processingFlow overview
These are the main steps in processing
The order in which they are applied is variable
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Applied Geophysics – Seismic reflection II
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
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
…undoing the convolution to get back to the reflectivity series – what we want
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Applied Geophysics – Seismic reflection II
Spiking deconvolution
Applied Geophysics – Seismic reflection II
Spiking deconvolution
1 -1 Recorded waveform
Deconvolution operator
Output 0
¾
1
¼ 1 1
Recovered reflectivity series
-½
4
Applied Geophysics – Seismic reflection II
Spiking deconvolution
1 -1
0
¾
1
¼ 1 1
-½
0
Recorded waveform
Deconvolution operator
Output
Recovered reflectivity series
Applied Geophysics – Seismic reflection II
Spiking deconvolution
1 -1
0
¾
1
¼ 1 1
-½
0 0
Recorded waveform
Deconvolution operator
Output
Recovered reflectivity series
5
Applied Geophysics – Seismic reflection II
Spiking deconvolution
1 -1
0
¾
1
¼ 1 1
-½
0 0 0
Recorded waveform
Deconvolution operator
Output
Recovered reflectivity series
Applied Geophysics – Seismic reflection II
Spiking deconvolution
1 -1
0
¾
1
¼ 1 1
-½
0 0 0
Recorded waveform
Deconvolution operator
Output
Recovered reflectivity series
?A perfect
deconvolution operator is of infinite length
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Applied Geophysics – Seismic reflection II
Source-pulse deconvolution
Deconvolution: Ringing removed
Original section
Source wavelet becomes spike-like
Examples
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.
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Applied Geophysics – Seismic reflection II
MultiplesDue 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 processingFlow overview
These are the main steps in processing
The order in which they are applied is variable
8
Applied Geophysics – Seismic reflection II
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
reflection hyperbolae
become fatter with depth
(i.e. velocity)
1
220
2
VxTTx +=
The reflection traveltime equation predicts a hyperbolic shape to reflections in a CMP gather. The hyperbolae become fatter/flatter with increasing velocity
210
2
2 VTxTNMO ≈∆
We want to subtract the NMO correction from the common depth point gather
But for that we need velocity…
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Applied Geophysics – Seismic reflection II
Stacking velocity
210
2
2 VTxTNMO =∆In order to stack the waveforms we
need to know the velocity. We find the 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
V2 causes the waveforms to
stack on top of one another
Applied Geophysics – Seismic reflection II
Stacking velocityMultiple 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
multiples
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Applied Geophysics – Seismic reflection II
Stacking velocityMultiple layer case
Stacking velocity panels: constant velocity gathers
Note: the sensitivity to velocity decreases
with depth
Applied Geophysics – Seismic reflection II
Multiple layers
Interval velocityi
ii tzV =
0' TZV =
∑∑=
i
iiRMS t
tVV
2
RMSn V
zxt22 4+
=
( ) ( )1
12
1,2
,int
−
−−
−−
=nn
nnRMSnnRMS
tttVtV
V
Average velocity
Root-mean-square velocity
Two-way traveltime of ray reflected off the nth interface at a depth z
The interval velocity of layer n determined from the rms velocities and the two-way traveltimes to the nth and n-1th reflectors Dix equationThe interval velocity can be determined from the rms velocities layer by layer starting at the top
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Applied Geophysics – Seismic reflection II
Velocity sensitivity: ExampleDeep: Two layer model: α1 = 6 km/s, z = 20 km
440031
42 222
1
xxzt +=+=α
4802
2
021
2 xt
xtNMO ==∆α
Equation of the reflection hyperbolae:
Normal move out correction:
For a 5 km offset:α1 = 6.0 km/s then 0.052 sec – correct valueα1 = 5.5 km/s then 0.062 secα1 = 6.5 km/s then 0.044 sec
Are these significant differences?
What can we do to improve velocity resolution?
Shallow: Two layer model: α1 = 3 km/s, z = 5 km
4255.11 2xt +=
60
2xtNMO =∆
For a 5 km offset:α1 = 3.0 km/s then 0.417 secα1 = 2.5 km/s then 0.600 secα1 = 3.5 km/s then 0.306 sec
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
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Applied Geophysics – Seismic reflection II
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 mTherefore 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?
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Applied Geophysics – Seismic reflection II
Fresnel ZoneTells 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:
42
242
2
22
2
λλ
λ
+=
+=
+
dw
wdd
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