Transcript Does It Matter What Kind of Vibroseis Deconvolution is Used?

Does It Matter What Kind of
Vibroseis Deconvolution is Used?
Larry Mewhort*
Husky Energy
Sandor Bezdan
Geo-X Systems
Mike Jones
Schlumberger
Outline
• Introduction
• Description of Pikes Peak
141/15-06-50-23W5M VSP
• Filtering elements of the
Vibroseis system
• Down hole wavelets before and
after deconvolutions
• Conclusions
• Acknowledgements
Introduction I
• Effective stratigraphic seismic
interpretation is aided by having a constant
and known phase in the final section.
• Removal of the transfer function between
the vibrator pilot sweep and the far-field
velocity signature is needed to achieve
such high quality seismic.
• The downgoing wavefield extracted from a
Vertical Seismic Profile (VSP) represents
the far-field signature at the discrete depths
sampled by the geophones.
Introduction II
• Vibroseis deconvolution attempts to
remove the transfer function knowing only
the pilot sweep; the impulse responses of
the geophones and the recording
instruments; and usually assuming white
reflectivity in the Earth.
• The VSP is an ideal tool to test the
effectiveness of deconvolutions.
Pikes Peak VSP Experiment
• A 3C, five-level ASI tool was used to
acquire data from 66 depths 27.0 to 514.5
meters (depth increment of 7.5 meters).
• A Mertz HD18 Vibrator located 23 meters
from the well head generated an 8 to 200
Hz linear sweep.
• The weighted-sum estimate of the ground
force (WSEGF) was used as the phase lock
signal.
• The WSEGF was maintained in phase with
the pilot sweep as per the SEG standard.
Filters that Deconvolution must
remove to recover the reflectivity
of the Earth
Klauder Wavelet
Vibrator Electronic and
Hydraulic Distortions
Baseplate Flexing
Differential Filter
Geophone Impulse
Response
Instrument Impulse
Response
Attenuation of the
Earth ‘Q’
Reflectivity Scattering
Attenuation
If these were all minimum phase then
perhaps all that would be needed would be
conventional spiking deconvolution?
Convert the Klauder wavelet into
its minimum phase equivalent
with the Vibop operator
Klauder
Wavelet
Minimum phase
equivalent of the
Klauder wavelet
Vibop
Filters that Deconvolution must
remove to recover the reflectivity
of the Earth
Klauder Wavelet
Vibrator Electronic and
Hydraulic Distortions
Baseplate Flexing
Differential Filter
Geophone Impulse
Response
Instrument Impulse
Response
Attenuation of the
Earth ‘Q’
Reflectivity Scattering
Attenuation
The recorded weighted-sum
ground force estimates
200 ms
Wavelets
Amplitude
0 Hz
200 Hz
200 degrees
Phase
-200 degrees
Filters that Deconvolution must
remove to recover the reflectivity
of the Earth
Klauder Wavelet
Vibrator Electronic and
Hydraulic Distortions
Baseplate Flexing
Differential Filter
Geophone Impulse
Response
Instrument Impulse
Response
Attenuation of the
Earth ‘Q’
Reflectivity Scattering
Attenuation
50
Phase (degrees)
0
-50
Filters that Deconvolution must
remove to recover the reflectivity
of the Earth
Klauder Wavelet
Vibrator Electronic and
Hydraulic Distortions
Baseplate Flexing
Differential Filter
Geophone Impulse
Response
Instrument Impulse
Response
Attenuation of the
Earth ‘Q’
Reflectivity Scattering
Attenuation
Standard Vibroseis Theory
• The P-wave far-field particle
displacement is proportional to
the applied force.
• Equivalently, the far-field
particle velocity is the time
derivative of the true ground
force.
• In the frequency domain the
derivative filter boosts the
amplitude spectrum 6 dB/octave
and applies a +90 degree phase
shift.
Proof that the first derivative is
minimum-phase (from Cambois)
The first derivative in the Fourier domain is
expressed as i. The modulus is ¦ ¦ and the
phase is /2 or –/2 depending on the sign of .
To show that the derivative is minimum-phase,
we have to show that the Hilbert transform of
log¦ ¦ is /2 sgn().
First, we consider that:

  
H 2
 2
2 
2








(1)
Where H stands for the Hilbert transform.
Integrating equation (1) with respect to we
find:
1
 
2
2 
H  log      arctan  
2

 

As  goes to zero:
H log   


2
(2)
sgn(  )
(3)
Test of whether a
differential filter is
minimum phase
Input Wavelets
Derivative Wavelet
Wavelet
After Wiener Deconvolution
Derivative Wavelet
Wavelet
Filters that Deconvolution must
remove to recover the reflectivity
of the Earth
Klauder Wavelet
Vibrator Electronic and
Hydraulic Distortions
Baseplate Flexing
Differential Filter
Geophone Impulse
Response
Instrument Impulse
Response
Attenuation of the
Earth ‘Q’
Reflectivity Scattering
Attenuation
Inverse Geophone Filter
Filter
Phase
Amplitude
Filters that Deconvolution must
remove to recover the reflectivity
of the Earth
Klauder Wavelet
Vibrator Electronic and
Hydraulic Distortions
Baseplate Flexing
Differential Filter
Geophone Impulse
Response
Instrument Impulse
Response
Attenuation of the
Earth ‘Q’
Reflectivity Scattering
Attenuation
Inverse Instrument Filter (phase has
been removed by cross correlation)
Amplitude
spectrum in dBs
Filters that Deconvolution must
remove to recover the reflectivity
of the Earth
Klauder Wavelet
Vibrator Electronic and
Hydraulic Distortions
Baseplate Flexing
Differential Filter
Geophone Impulse
Response
Instrument Impulse
Response
Attenuation of the
Earth ‘Q’
Reflectivity Scattering
Attenuation
Q from VSP
Q - Spectral Ratios (blue) and Centroid
Frequency (red)
Q
Theoretical effect of a
constant Q of 50
Wavelet at 102
meters depth
Wavelet at 514.5
meters depth
102 meter wavelet
after applying a Q of
50 over a distance of
400 meters
Filters that Deconvolution must
remove to recover the reflectivity
of the Earth
Klauder Wavelet
Vibrator Electronic and
Hydraulic Distortions
Baseplate Flexing
Differential Filter
Geophone Impulse
Response
Instrument Impulse
Response
Attenuation of the
Earth ‘Q’
Reflectivity Scattering
Attenuation
Downgoing wavelets displayed
in depth versus time
Time
D
e
p
t
h
Downgoing
Multiple
Downgoing Wavelets
10 ms
+200 degrees
90 degrees
0 Hz
-200 degrees
200 Hz
• wavelets have been compensated for the
amplitude and phase effects of the geophone
Finding the best fit
Constant phase Wavelet
Correlation Coefficient versus Constant Phase
Blue is the best fit constant phase wavelet
Red is the actual wavelet
Green is the zero phase equivalent wavelet
Downgoing Wavelets
10 ms
Average
constant phase
is 49 degrees
+200 degrees
0 Hz
-200 degrees
200 Hz
90%
100%
• wavelets have been compensated for the
amplitude and phase effects of the geophone
Spectra for the Downgoing
Wavelets before and after
Deconvolutions
Amplitude (dB)
Geophone
at 394.5
meters
Wavelets after zero phase
deconvolution and geophone phase
removal (80 ms operator 0.1% PW)
Downgoing
multiple
10 ms
Precursor
+200 degrees
-200 degrees
0 Hz
Average
constant phase
is 46 degrees
200 Hz
Deconvolution operator
designed on wavelets
averaged over 400 meters
90%
100%
Low Frequency Adjustments
when computing the phase of
the T5 Deconvolution Operator
22 dB
Amplitude (dB)
48 dB/octave
Applied to reduce the effect of low frequency
estimation problems on the phase of the output
Wavelets after T5 deconvolution (4 Hz
frequency smoothing 0.01% PW) with
geophone phase and amplitude removal
10 ms
Average
constant phase
is -75 degrees
+200 degrees
-200 degrees
0 Hz
Deconvolution operator
designed on wavelets
averaged over 400 meters
90%
200 Hz
100%
Wavelets after T5 deconvolution (4 Hz
Frequency smoothing 0.01% PW), low
frequency filtering and Vibop
10 ms
Average
constant phase
is 41 degrees
+200 degrees
Deconvolution operator
designed on wavelets
averaged over 400 meters -200 degrees 200 Hz
0 Hz
90%
100%
Wavelets after T5 deconvolution (4
Hz frequency smoothing 0.01%
PW) and spectral replacement
10 ms
Average
constant phase
is 3 degrees
+200 degrees
0 Hz
-200 degrees
200 Hz
Deconvolution operator
designed on wavelets
averaged over 400 meters
90%
100%
Wavelets after T5 deconvolution (4
Hz frequency smoothing 0.01% PW)
and low frequency filtering
10 ms
Average
constant phase
is -27 degrees
+200 degrees
0 Hz
-200 degrees
200 Hz
Deconvolution operator
designed on wavelets
averaged over 400 meters
90%
100%
Conclusions I
• T5 deconvolution gave the most consistent
constant phase results.
• Adjusting the Klauder wavelet to minimum
phase resulted in wavelets that were less
constant phase or compressed (but they
appeared to be close to minimum phase).
• Spectral replacement of the low
frequencies resulted in the wavelets being
less consistent than using low frequency
filtering.
Conclusions II
• The amount of low frequency filtering
changed the slope of the low frequency
phase curve.
• Zero phase deconvolution of course did not
change the phase of the original data and
did not remove the down-going multiple.
• Removing the geophone impulse response
was not desirable.
Acknowledgements
•
•
•
•
•
•
Husky Energy
Geo-X (Xi-Shuo Wang and Mike Perz)
Schlumberger
Dr. Gary Margrave
Guillaume Cambois
AOSTRA and the CREWES sponsors