Deconvolution
Bryce Hutchinson
Sumit Verma
Objectives:
- Understand the difference between exponential
and surface consistent gain
- Identify power line noise is the frequency
spectrum and remove it
- Grasp what deconvolution is doing to the data
Exponential Gain
Exponential gain multiplies each trace by
an exponential function of the form e(nt)
where we define what the exponential gain
constant (n).
So, according to the formula the gain factor
will increase with increasing time (which
you can think of as increasing depth).
1. Choose the 10-100 band pass volume we
created last week as the input.
2. Set the Exponential Gain Constant to 2
Bandpass
Bandpass with Exp gain
exponential gain : exp(nt) or ent, we kept n=2 and t= time.
See the effect of Exponential gain!
What is this noise ? ///
Have you seen it in exam!
Noise in the frequency spectrum
1. Click the seismic analysis icon
3. There is a
consistent noise at
60Hz in the
frequency spectrum.
Zoom in to see it
better, also take note
of how the noise
looks in both the
trace and frequency
spectrum
3
2. Choose Frequency Analysis Window from the
dropdown menu. Then the green plus to view it.
Zoomed in
Power line noise
Surface consistent (SC) gain
I’ve copied the input windows for each of flow icons in this
slide. I have put the flow icon in the top right of each window
to show you which input it represents.
1. Choose the bandpass
data as the input
Power line noise removal
2. We want to
create a tight
window
around the
power line
noise in the
notch filter
3. Change the
offset bins size
in the Options
tab and select
the Entire
Trace in the
Window tab
4. For SCApply, you will not have a
choice of inputs yet. Be sure the bin size
is set to 220. You must run the SCApply
before these options will appear!
Surface Consistent Scale
Why : Surface-consistent scaling is used on land seismic data in order to
compensate for the effects of the highly variable near-surface layers and variable
source and receiver signatures and coupling.
M. Turhan Taner and Fulton Koehler (1981). ”Surface consistent corrections.” Surface consistent corrections, 46(1), 17-22.
How in this software : In the SCScale the average amplitude (Mean or RMS) of each input trace is
computed. Each trace scalar is assumed to be of the form:
Trace Multiplier = Shot multiplier x Receiver Multiplier x Offset dependent Multiplier x CMP
multiplier.
By utilizing logarithms, this equation becomes a sum of factors rather than a product. The
sum can then be solved by the usual Gauss-Seidel iterative process.
Surface Consistent Gain
1. Run the flow again,
and now you will have
inputs for SCApply
2. Your output should appear something like this. Don’t worry about subtle differences
between this image and yours, we ran our flow in a different order.
Compare the bandpassed data and SC gained data, what differences do you see?
Before sc gain
What is this noise ? ///
Have you seen it in exam!
After sc gain
what step removed it ???
Do you see a better amplitude balance?
• We have done several experiments to change
You can change:
Iterations and offset bin size.
And Time window
We experiment here !
Experiment # 1
Surface Consistent
Scaling
Experiment # 2
Experiment # 3
Surface Consistent
Scaling
Surface Consistent
Deconvolution
Deconvolution
We will complete this part here !
Surface Consistent
Deconvolution
We will upload
this in lab 7b!
Defining a timegate
Define the top and bottom of the timegate. Double click
to end your pick. You can define the window on the raw
data.
Experiment # 1
Surface Consistent
Scaling
Deconvolution
Deconvolution
1. This is the deconvolution flow. Use the
SC gain data as the input.
3
4
This is seismic was
acquired with Vibroseis!
2. Set the Decon Type to Zero-Phase (since
our source was vibroseis)
5
Decon assumptions
1.
The earth is composed of horizontal layers of constant impedance
2. The source generates a compressional wave at normal incidence –
there are no shear waves
3.
The source wavelet does not change as it travels – it is stationary
4. The noise component n(t) is zero
5.
The source waveform is known
6.
The reflectivity is random (autocorrelation and spectra are similar)
7. The seismic waveform is minimum phase and thus has a
minimum phase inverse
Vibroseis has zero phase source wavelet !
15
Dr. Marfurt’s class slide
Decon assumptions
The earth is composed of horizontal layers of constant impedance
decon works if the multiple generators are flat
The source generates a compressional wave at normal incidence – there
are no shear waves
works ok at near offsets
The source wavelet does not change as it travels – it is stationary
use time-variant decon in running windows
The noise component n(t) is zero
design operator on noise-free parts of the data; design decon operators
on stacked traces and then apply to prestack data
16
Dr. Marfurt’s class slide
Decon assumptions
The source waveform is known
If source wavelet is minimum phase, you can obtain a near perfect result
The reflectivity is random (autocorrelation and spectra are similar)
If the source wavelet is not known, you are in serious trouble!
The seismic waveform is minimum phase and thus has a minimum
phase inverse
The result of spiking decon is degraded if the source wavelet is not
minimum phases
In VISTA they have Zero Phase decon , in which
they calculate zero phase decon operator .
17
Dr. Marfurt’s class slide
(Yilmaz, 2001; p 190)
Deconvolution
Spiking Decon:
- Wiener Levinson algorithm
- Auto-correlation of a segment of the
trace which normally varies with
offset (think normal equations) is
computed
Further – Zero Phase:
- Forward Fourier Transform is
calculated giving the amplitude and
phase spectrum
- Phase spectrum is then set to zero
and an inverse transform is performed
- Resulting in a zero phase equivalent
of the spiking (minimum phase)
operator.
- The zero phase operator is then
convolved with the data resulting in
an image showing the reflectors much
tighter
Assume the Earth’s input xt is a series of spikes
approximated by a random Gaussian distribution:
The autocorrelation function looks like:
Input for SC gain
Output
2. Set Compare your output deconvolution to the SC
gained data and to the band pass data. What changes
do you see?
After SC gain
Output
After Zero phase decon
Output
Please check the amplitude spectrum.
Notch filter to remove the
powerline noise
After Deconvolution
Deconvolution shows better balance in frequency spectrum.
After Zero phase decon
Output
Deconvolution generates some artifacts on the higher frequencies
After Zero phase decon and bandpass filter
So we apply band pass filter to remove the noises
Experiment : 2
Surface Consistent
Deconvolution
2
3.2
3
4.2
4
3.3
Experiment 2 Result!
Experiment 1 Result!
After Zero phase decon and bandpass filter
Processor’s dilemma !
Which one do I like better !
Acknowledgement !
• Dr. Kurt Marfurt
• Thang Ha
• Marcus Cahoj for giving inspiration for this lab.