cwp seminar jianmin lin 061025

Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Time Coded Impulsive Seismic Technique

Jianmin Lin, Feng Su, Yong Chen

[email protected]

October 25, 2006

Jianmin Lin Time Coded Impulsive Seismic Technique

Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Table of contents

1 Motivation

2 Method

3 Analysis

4 Synthetic Experiment

5 Conclusion


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Motivation of this study

Conventional method:

R(t) = P(t) ∗ h(t) + n(t) (1)

Contradiction: Resolution ↔ Signal to Noise Ratio (SNR)

Improve the resolution in reflection seismology.

Improve the SNR in the seismic record.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Method - Time Coded Impulsive Seismic Technique

The principle of this method (TCIST) may be loosely described asfollows, instead of using a big energy source, a large number of smallenergy are released in a sophisticated manner according to a timecoded scheme. Finally the result wavelet achieved by decodingprocess has nearly the same shape as single wavelet sharing the samemain frequencies, but its amplitude will be enlarged by n.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Basic Principle

TCIST method:The small sources is excited at instants determined by the time codedscheme whose mathematical expression is

y(t) =

i=n∑

i=1

δ(t − ti), (2)

Single pulse p(t) is released at each time ti in coded sequence y(t)to create coded pulses Sc(t) as follows,

Sc(t) = y(t) ∗ p(t) (3)

which will be transmitted with the coded sequence y(t) as a newseismic signal.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Basic Principle

Corresponding to Sc(t), the coded seismic record Rc(t) can beexpressed as follows,

Rc(t) = Sc(t) ∗ h(t) + n(t)

= y(t) ∗ p(t) ∗ h(t) + n(t). (4)

The decode process can be expressed as:

Rd(t) = Rc(t) ⊗ y(t)

= y(t) ∗ p(t) ∗ h(t) ⊗ y(t) + n(t) ⊗ y(t)

= ACF{y(t)} ∗ p(t) ∗ h(t) + n(t) ⊗ y(t), (5)

where ⊗ represents cross-correlation operation and ACF{} theauto-correlation function.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Better Resolution

conventional R(t) = P(t) ∗ h(t) + n(t)TCIST Rd (t) = ACF{y(t)} ∗ p(t) ∗ h(t) + n(t) ⊗ y(t)

If {ACF{y(t)} = kδ(t), k >> 1}⇒ ACF{y(t)} ∗ p(t) will be an amplified p(t) without any waveformdistortion.

⇒ Rd (t) contains the seismic events with same waveform hencesame main frequency but much bigger amplitude, compared to thatfrom the single p(t).

⇒ TCIST has better resolution than conventional total energyreleased as a big source.

Key:ACF{y(t)} = kδ(t), k >> 1


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Improved SNR

Time domain:

Rd(t) = ACF{y(t)} ∗ p(t) ∗ h(t) + n(t) ⊗ y(t) (6)

Frequency domain:

|Pd (jω)| = |Y (jω)|2 × |P(jω)| × |H(jω)|+|N(jω)| × |Y (jω)| (7)

If {ACF{y(t)} = kδ(t), k >> 1}, every frequency of signal isamplified with power spectrum |Y (jω)|2, but the ambient noise isamplified with square-root of the power spectrum.⇒A SNR improvement by square-root of the power spectrum.Since the total energy of the power spectrum is proportional to n, sowe can improve the SNR by

√n in TCISTmethod.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Ricker Wavelet

−0.05 0 0.05−0.5

0

0.5

1

fm

=150Hz

Time (s)

A

Ricker Wavelet

0 200 400 600 800 1000−300

−250

−200

−150

−100

−50

0

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

Ricker Wavelet

Figure: Ricker Wavelet with peak frequency equal to 150Hz and itspower spectrum density


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Number of Excitations n

0 200 400 600 800 1000 1200 1400 16000

10

20

30

40

Number of ExcitationsS

NR

Impr

ovem

ent

0 200 400 600 800 1000 1200 1400 16000

0.05

0.1

0.15

0.2

0.25

Number of Excitations

SN

R Im

prov

emen

t Inc

rem

ent

Figure: The square-root relationship between the SNR improvementand total number of impulsive excitations in TCIST method.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Random Coded Scheme

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

Time (s)

Pseudo−random Coded Sequence

0 2 4 6 8 100

100

200

300

400

500

Time (s)

Pul

se R

ate

(Hz)

Pulse Rate

0 200 400 600 800 1000−75

−70

−65

−60

−55

−50

−45

−40

−35

−30

−25

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

Pseudo−random Coded Sequence

Figure: Random coded sequence with 300 impulsive excitationsrandomly distributed in 10s and its power spectrum density


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Random Coded Scheme

−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

A

Auto−correlation Function of Pseudo−random Coded Sequence

0 200 400 600 800 1000−100

−90

−80

−70

−60

−50

−40

−30

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

Auto−correlation function of Pseudo−random Coded Sequence

Figure: Auto-correlation function of random coded sequence and itspower spectrum density


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Random Coded Scheme

0 2 4 6 8 10−1.5

−1

−0.5

0

0.5

1

1.5

2

Time (s)

A

Pseudo−random Coded Signals

0 200 400 600 800 1000−300

−250

−200

−150

−100

−50

0

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

PSD Compare

Single Signal p(t)Coded Signals p(t)*y(t)

Figure: Random coded signals and its power spectrum density


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Random Coded Scheme

−0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08−150

−100

−50

0

50

100

150

200

250

300

Time (s)

A

Decoded Signal ACF{y(t)}*P(t) ( Pseudo−random Coded Scheme )

0 200 400 600 800 1000−60

−50

−40

−30

−20

−10

0

10

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

Decoded Signal (Pseudo−random Coded Scheme)

Figure: Decoded signal of random coded scheme and its powerspectrum density


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Linear Coded Scheme

0 1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1

Time (s)

Linear Coded Sequence

0 1 2 3 4 5 6 7 80

20

40

60

Time (s)

Pul

se R

ate

(Hz)

Pulse Rate

0 200 400 600 800 1000−90

−80

−70

−60

−50

−40

−30

−20

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

Linear Coded Sequence

Figure: Linear Coded Sequence (LCS) with impulsive rate increasinglinearly from 20Hz to 60Hz and its power spectrum density


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Linear Coded Scheme

−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

AAuto−correlation Function of LCS

0 200 400 600 800 1000−110

−100

−90

−80

−70

−60

−50

−40

−30

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

Auto−correlation function of Linear Coded Sequence

Figure: Auto-correlation function of LCS and its power spectrumdensity which is square of that of LCS in Fig.6 according toEquation(7).


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Linear Coded Scheme

0 1 2 3 4 5 6 7 8−0.5

0

0.5

1

Time (s)

A

Linear Coded Signals

0 200 400 600 800 1000−300

−250

−200

−150

−100

−50

0

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

PSD Compare


Figure: Linear Coded Signals Sc(t) and its power spectrum density.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Linear Coded Scheme

−0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08−150

−100

−50

0

50

100

150

200

250

300

Time (s)

A

Decoded Signal ACF{y(t)}*P(t) ( Linear Coded Scheme )

0 200 400 600 800 1000−70

−60

−50

−40

−30

−20

−10

0

10

20

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

Decoded Signal (Linear Coded Scheme)

Figure: Decoded signal of linear coded scheme and its powerspectrum density.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

More Sophisticated Coded Schemes

To develop the TCISTmethod further, more sophisticated codedscheme has been tried borrowing ideas from the Vibrator technique.Assume monotonical sweep or coded sequence (though discrete)could be represented as follow,

s(t) = Im

{

exp

[

i2π

∫ t

0

fi (t)dt

]}

= Im{exp[iΦ(t)]} (8)

Its spectrum could be expressed with following integral,

S(fa) =

∫

T

0

exp

{

i2π

[∫

t

0

fi (t)dt − fat

]}

dt

=

∫

T

0

exp

{

i2π

[∫

t

0

(fi (t) − fa)dt

]}

dt, (9)

where fa is the frequency one wants to analysis on.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Principle of Stationary Phase

An integral tends to be nil when its integrand oscillates rapidly aboutzero value. However, if its integrand contains some part withstationary phase where the integrand keeps nearly constant, theintegral will monotonically accumulate the contribution of thisinterval to the overall value of the integral. How much it contributesdepends on the duration of this interval which in turn is directlycontrolled by the rate of change of the sweep.⇒S(fa) depends on the length of the duration when the difference(fi (t) − fa) vanishes, thus controlled by the rate of the change offi (t). ( So linear coded sequence has flat spectrum.)


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Principle of Stationary Phase

For a nonlinear coded scheme, the frequencies whose rate of changeis the lowest will contribute the most to the spectrum, while, theamplitude spectrum of the frequencies with fastest rate of change willbe depressed.

This property could be used to design seismic signals in the means offrequency modulation according to our needs.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Exponential Coded Scheme

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

Time (s)

Exponential Coded Sequence

0 0.5 1 1.5 2 2.5 3 3.5 40

20

40

60

80

100

fi(t)=100*(2−exp(0.25t))

Time (s)

Pul

se R

ate

(Hz)

Pulse Rate

0 200 400 600 800 1000−90

−80

−70

−60

−50

−40

−30

−20

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

Exponential Coded Sequence fi(t)=100*(2−exp(0.25t))

Figure: Exponential coded sequencefi (t) = 100 ∗ (2 − exp{0.25t})(10Hz <= fi <= 100Hz) with 196impulsive excitations and its power spectrum density.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion


−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

AAuto−correlation Function of ECS f

i(t)=100*(2−exp(0.25t))

0 200 400 600 800 1000−90

−80

−70

−60

−50

−40

−30

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

Auto−correlation function of ECS fi(t)=100*(2−exp(0.25t))

Figure: Auto-correlation function of exponential coded sequencefi (t) = 100 ∗ (2− exp{0.25t})(10Hz <= fi <= 100Hz) and its powerspectrum density.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion


0 0.5 1 1.5 2 2.5 3 3.5 4−0.5

0

0.5

1

Time (s)

A

Exponential Coded Signals fi(t)=100*(2−exp(0.25t))

0 200 400 600 800 1000−300

−250

−200

−150

−100

−50

0

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

PSD Compare


Figure: Exponential coded (fi (t) = 100 ∗ (2 − exp{0.25t})) signalsand its power spectrum density.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion


−0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08−150

−100

−50

0

50

100

150

200

Time (s)

A

Decoded Signal ACF{y(t)}*P(t) ( Exponential Coded Scheme fi(t)=100*(2−exp(0.25t)))

0 200 400 600 800 1000−300

−250

−200

−150

−100

−50

0

50

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

PSD Compare

Decoded Signal ( ECS fi(t)=100*(2−exp(0.25t)))

Original Signal

Figure: Decoded signal of exponential coded scheme(fi (t) = 100 ∗ (2 − exp{0.25t})) and its power spectrum density.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion


0 50 100 150−85

−80

−75

−70

−65

−60

−55

−50

−45

−40

−35

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

Auto−correlation function of ECS fi(t)=100*(2−exp(0.25t))

Figure: Power spectrum density of auto-correlation function of theexponential coded sequence (10Hz <= fi <= 100Hz), the biggerfrequencies near 100Hz are more emphasized than smaller frequenciesbecause the rate of change of the bigger frequency around 100Hz issmaller (Figure. 11).


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Conclusion

−0.05 −0.04 −0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04−150

−100

−50

0

50

100

150

200

250

300

Time (s)

A

Decoded Signal

ECS fi(t)=60*exp−0.2t

ECS fi(t)=100*(2−exp0.25t)

LCSRCSSingle Ricker wavelet * 150

0 200 400 600 800 1000−300

−250

−200

−150

−100

−50

0

50

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

dB/H

z)

Decoded Signal

ECS fi(t)=60*exp−0.2t

ECS fi(t)=100*(2−exp0.25t)

LCSRCSSingle Ricker wavelet

Figure: Different decoded signals, single Ricker wavelet’s amplitude isenlarged by 150 simply for display, and power spectrum density.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Conclusion

TCISTcould improve SNR with the order of√

n;

TCISTcould improve resolution;

Cross-correlation should be researched further to suppress.


Time Coded

Impulsive

Seismic

Technique

Jianmin Lin

Motivation

Method

Analysis

Synthetic

Experiment

Conclusion

Acknowledgements

Thanks!


cwp seminar jianmin lin 061025

Career

feng su

yong chen