Designing Optimum Zero-Phase Wavelets

R. S. Kallweit and L. C. WoodAmoco Houston DivisionDGTS January 12, 1977

This PowerPoint version of the material, was compiled by Greg Partyka (October 2006) G. Partyka (Oct 06)

Wavelet Shape and Sidelobe Interference

• Wavelets designed with a vertical or near-vertical high end slope exhibit high frequency sidelobes that can cause significant distortions in reflection amplitudes and associated event character.

• An alternate wavelet is proposed called the Texas Double in recognition of the primary characteristic being a 2-octave slope on the high frequency side.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Texas Double Wavelets

• Time Domain Characteristics:– negligible high frequency sidelobe tuning effects.– maximum peak-to-sidelobe amplitude ratios.

• Frequency Domain Characteristics:– vertical or near-vertical low-end slope.– 2-octave linear slope on the high-end. Amplitudes are measured

using a linear rather than decibel scale.– end frequencies correspond to the highest and lowest recoverable

signal frequency components of the recorded data.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of High Frequency Side-Lobes

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

High frequency sidelobes can be attenuated to an insignificant levelvia a 2-octave or greater high side slope.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of High Frequency Side-Lobes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

High frequency sidelobes can be attenuated to an insignificant levelvia a 2-octave or greater high side slope.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of High Frequency Side-Lobes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

3 octave slope

High frequency sidelobes can be attenuated to an insignificant levelvia a 2-octave or greater high side slope.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of High Frequency Side-Lobes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

2 octave slope

High frequency sidelobes can be attenuated to an insignificant levelvia a 2-octave or greater high side slope.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of High Frequency Side-Lobes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

1 octave slope

High frequency sidelobes can be attenuated to an insignificant levelvia a 2-octave or greater high side slope.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of High Frequency Side-Lobes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

High frequency sidelobes can be attenuated to an insignificant levelvia a 2-octave or greater high side slope.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of Low Frequency Side-Lobes

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

Low frequency sidelobes are a function of the wavelet’s bandpass.They cannot be reduced beyond what is shown here.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of Low Frequency Side-Lobes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

Low frequency sidelobes are a function of the wavelet’s bandpass.They cannot be reduced beyond what is shown here.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of Low Frequency Side-Lobes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

4.0 octaves

Low frequency sidelobes are a function of the wavelet’s bandpass.They cannot be reduced beyond what is shown here.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of Low Frequency Side-Lobes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

3.0 octaves

Low frequency sidelobes are a function of the wavelet’s bandpass.They cannot be reduced beyond what is shown here.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of Low Frequency Side-Lobes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

2.4 octaves

Low frequency sidelobes are a function of the wavelet’s bandpass.They cannot be reduced beyond what is shown here.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Development of Low Frequency Side-Lobes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

2.0 octaves

Low frequency sidelobes are a function of the wavelet’s bandpass.They cannot be reduced beyond what is shown here.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

High Frequency Held Constant (Klauder Wavelets)

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

High Frequency Held Constant (Klauder Wavelets)

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

4.0 octaves

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

High Frequency Held Constant (Klauder Wavelets)

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

3.0 octaves

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

High Frequency Held Constant (Klauder Wavelets)

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

2.4 octaves

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

High Frequency Held Constant (Klauder Wavelets)

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

2.0 octaves

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

High Frequency Held Constant (Klauder Wavelets)

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

1.4 octaves

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the Low Frequency Slope

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the Low Frequency Slope

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

3 octaves

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the Low Frequency Slope

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

2 octave slope

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the Low Frequency Slope

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

3 octave slope

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the High and Low Frequency Slopes

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the High and Low Frequency Slopes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

3 octave sinc

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the High and Low Frequency Slopes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the High and Low Frequency Slopes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Decreasing the High and Low Frequency Slopes

frequency

100

am

plit

ud

e

20 30 40 50 60

REFLECTIVITY IMPEDANCE0

100

Tra

vel T

ime

(m

s)

200

300

50

150

250

0

100

200

300

50

150

250

Temporal Thickness (ms)

0 5040302010

Temporal Thickness (ms)

50403020100

Texas Double

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Texas Double in Practice

• One may implement the Texas Double on real data by first running an amplitude whitening program followed by a 2-octave slope Ormsby filter.

• The Texas Double design criteria should not be a goal of data acquisition.

• It is of utmost importance that the signal-to-noise ratio of the high-frequency components be as large as possible, and therefore filtering process such as the Texas Double should occur in data processing and not in data acquisition.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Example Amplitude Response of Dynamite Data

0.4

0.6

0.8

1.0a

mp

litu

de

Frequency (Hz)

0

0.2

04020 60 70 9010

Raw

Whitened

Texas Double

30 50 80 100

The Texas Double in effect does not attenuate the high frequency components of the recorded data,but rather amplifies them less than the conventional whitened output obtained using program DAFD.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Proposed Standard Equi-Resolution Comparison

• One of the difficulties involved in trying to compare traces containing different zero-phase wavelets designed over identical bandpasses is the question of what to compare and measure each trace against.

• It is rather unsatisfactory to compare the traces against one another since there are too many unknowns.

• A standard comparison is needed.• The standard trace proposed is one where the convolving wavelet

has the same temporal resolution as the sinc wavelet over a given bandpass but has no sidelobes whatsoever.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Temporal Resolution – Low-Pass Sinc vs Low-Pass Texas Double

0

10

20

30

pe

ak-

to-t

rou

gh

se

pa

ratio

n (

ms)

0 10 20 30

spike separation (ms)

0–0-62-64 HzSinc

TR

0

10

20

30

pe

ak-

to-t

rou

gh

se

pa

ratio

n (

ms)

0 10 20 30

spike separation (ms)

TR

Conclusion: Over a given low-pass, temporal resolution of the Texas Double wavelet equals 80% of the temporal resolution of the sinc wavelet.

TR = 1 / 1.5f4

0–0-20-80 HzTexas Double

TR = 1 / 1.2f4

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Equivalent Temporal Resolution: Ormsby to Low-Pass Sinc

fs

frequency

ampl

itude

f4

f3

0.5

0.6

0.7

f s/f

4

0.8

0.9

1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

f3 / f4

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Is it worth giving up the 20% loss in Temporal Resolution?

• Can the benefits associated with attenuating high-frequency sidelobes outweigh the 20% loss in temporal resolution?

• The following well-log based comparisons, suggest that they can.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Well-Log Comparison

raw 00-00-20-80

00-00-62-64

08-09-62-64

08-09-16-64

08-09-20-80

Ra

w I

np

ut

L

ay

eri

ng

or

Re

fle

cti

vit

y

De

sir

ed

Sta

nd

ard

N

o S

ide

lob

es

(re

so

luti

on

of

a 6

4 H

z s

inc

)

Hig

h F

req

ue

nc

y T

un

ing

Eff

ec

ts O

nly

H

igh

Fre

qu

en

cy

Sid

elo

be

s(r

es

olu

tio

n o

f a

64

Hz

sin

c)

Ne

gli

gib

le E

ffe

ct

L

ow

Fre

qu

en

cy

Sid

elo

be

s(r

es

olu

tio

n o

f a

64

Hz

sin

c)

Sin

c W

av

ele

t

Hig

h a

nd

Lo

w F

req

ue

nc

y S

ide

lob

es

(re

so

luti

on

of

a 6

4 H

z s

inc

)

Te

xa

s D

ou

ble

L

ow

Fre

qu

en

cy

Sid

elo

be

s(8

0%

re

so

luti

on

of

of

a 6

4 H

z s

inc

)

• Any observed differences are due to sidelobe tuning or temporal resolution.

• To determine differences associated with sidelobes as opposed to those associated with temporal resolution, compare each trace to the 8-9-20-80 track.

• 2-octave and 3-octave bandpass wavelets:

• have identical terminal frequencies.

• have the same high frequency sidelobes and temporal resolution.

• allow low frequency sidelobes to be compared.

• Traces containing different wavelets but with the same temporal resolution can be compared in order to observe differences due to sidelobe tuning effects.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Well-Log Comparison - 3 Octaves

raw rc00-00-20-80

00-00-62-64

08-09-62-64

08-09-16-64

08-09-20-80

raw layering

00-00-20-80

00-00-62-64

08-09-62-64

08-09-16-64

08-09-20-80Layering Reflectivity

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Well-Log Comparison - 2 Octaves

raw rc00-00-20-80

00-00-62-64

16-17-62-64

16-17-18-64

16-17-20-80

raw layering

00-00-20-80

00-00-62-64

16-17-62-64

16-17-18-64

16-17-20-80Layering Reflectivity

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Well-Log Comparison - 3 Octaves

raw rc00-00-20-80

00-00-62-64

08-09-62-64

08-09-16-64

08-09-20-80

raw layering

00-00-20-80

00-00-62-64

08-09-62-64

08-09-16-64

08-09-20-80Layering Reflectivity

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Well-Log Comparison - 2 Octaves

raw rc00-00-20-80

00-00-62-64

16-17-62-64

16-17-18-64

16-17-20-80

raw layering

00-00-20-80

00-00-62-64

16-17-62-64

16-17-18-64

16-17-20-80Layering Reflectivity

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Well-Log Comparison - 3 Octaves

raw rc00-00-20-80

00-00-62-64

08-09-62-64

08-09-16-64

08-09-20-80

raw layering

00-00-20-80

00-00-62-64

08-09-62-64

08-09-16-64

08-09-20-80Layering Reflectivity

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Well-Log Comparison - 2 Octaves

raw rc00-00-20-80

00-00-62-64

16-17-62-64

16-17-18-64

16-17-20-80

raw layering

00-00-20-80

00-00-62-64

16-17-62-64

16-17-18-64

16-17-20-80Layering Reflectivity

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Well-Log Examples

• The following figures illustrate the sensitivity of the side-lobe tuning effects of the sinc and Texas Double wavelets to small changes in high frequency components.

• The layered log and corresponding reflectivity were filtered holding the low side constant for each filter and varying the high side in 1 Hz increments.

• Since the filters change in a linear and gradual manner, we would hope that the traces would do likewise. Unfortunately, significant trace-to-trace variations are apparent.

• Two sets of Texas Double filters are also applied, and compared with the sinc wavelet results. One Texas Double set exhibits the same temporal resolution as the bandpass sinc set. The other Texas Double set mirrors the f1 and f4 filter positions of the sinc wavelets.

• The Texas Double design reduces tuning effects to a negligible level, and trace-to-trace variations are gradual and consistent.

Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977 G. Partyka (Oct 06)

Well-Log Example - Layering

Sinc Wavelets – high frequency side varies 40 to 100 Hz; low frequency held constant

Raw Layering

6-10-096-100

6-10-066-070

6-10-036-040

Raw Layering

6-10-096-100

6-10-066-070

6-10-036-040

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

G. Partyka (Oct 06)

Well-Log Example - Layering

10 Hz High-Cut Slope Wavelets – high frequency side varies 40 to 100 Hz; low frequency held constant

Raw Layering

6-10-090-100

6-10-060-070

6-10-030-040

Raw Layering

6-10-090-100

6-10-060-070

6-10-030-040

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

G. Partyka (Oct 06)

Well-Log Example - Layering

Texas Double Wavelets – high frequency side varies 52 to 112 Hz; low frequency held constant

Raw Layering

6-10-028-112

6-10-021-082

6-10-013-052

Raw Layering

6-10-028-112

6-10-021-082

6-10-013-052

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

G. Partyka (Oct 06)

Well-Log Example - Layering

Texas Double Wavelets – high frequency side varies 40 to 100 Hz; low frequency held constant

Raw Layering

6-10-025-100

6-10-020-070

6-10-011-040

Raw Layering

6-10-025-100

6-10-020-070

6-10-011-040

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

G. Partyka (Oct 06)

Well-Log Example - Reflectivity

Sinc Wavelets – high frequency side varies 40 to 100 Hz; low frequency held constant

Raw RC

6-10-096-100

6-10-066-070

6-10-036-040

Raw RC

6-10-096-100

6-10-066-070

6-10-036-040

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

G. Partyka (Oct 06)

Well-Log Example - Reflectivity

10 Hz High-Cut Slope Wavelets – high frequency side varies 40 to 100 Hz; low frequency held constant

6-10-090-100

6-10-060-070

6-10-030-040

6-10-090-100

6-10-060-070

6-10-030-040

Raw RC

Raw RC

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

G. Partyka (Oct 06)

Well-Log Example - Reflectivity

Texas Double Wavelets – high frequency side varies 52 to 112 Hz; low frequency held constant

6-10-028-112

6-10-021-082

6-10-013-052

6-10-028-112

6-10-021-082

6-10-013-052

Raw RC

Raw RC

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

G. Partyka (Oct 06)

Well-Log Example - Reflectivity

Texas Double Wavelets – high frequency side varies 40 to 100 Hz; low frequency held constant

6-10-025-100

6-10-020-070

6-10-011-040

6-10-025-100

6-10-020-070

6-10-011-040

Raw RC

Raw RC

After Designing Optimum Zero-Phase Wavelets, R. S. Kallweit and L. C. Wood, Amoco Houston Division DGTS, January 12, 1977

G. Partyka (Oct 06)