quality factor inversion from prestack cmp data using epif matching jing zhao, jinghuai gao...

Xi’an Jiaotong UniversityXi’an Jiaotong UniversityXi’an Jiaotong University

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Quality Factor Inversion from Prestack CMP data using EPIF Matching

Jing Zhao, Jinghuai Gao

Institute of Wave and Information, Xi’an Jiaotong University


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introduction◊ why to estimate Q?● Lithology identification

●Inversing Q filtering to Improve the resolution of seismic imaging

● Predicting the fluid properties


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◊ The developed methods

►Time domain methods►Frequency domain methods

—the logarithm spectral ratio (LSR,1981)—centroid frequency shift (CFS,1993)—peak frequency shift (PFS,2002)—Modeling method (MF,1980)

—the IF matching (IFM) method(1995) ►Time-Frequency domain methods►Inversion methods

introduction


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◊ Why is pre-stack CMP data?

Pre-stack seismic data doesn’t process by NMO correction and the frequency information is not destroyed , so the Q estimation is available.

We further developed Mathneey and Nowack’s work, and propose a method for estimating Q from pre-stack data based on envelope peak instantaneous frequency matching analysis.

introduction


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The EPIF matching method— Instantaneous frequency (IF) matching at a wavelet

envelope peak

◊ The principleIn a media of horizontally layered anelastic with a frequency-independent Q, we can determine the wavefield of a source wavelet traveling through a distance by:

(1) ( , ) ( ) (0, ) exp( ) 2 ( )

i z zS z G z S

c c Q

z

wavefield of the source signature

the factor which is independent of frequency and attenuation

Phase velocity

Traveldistance


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the source wavelet can be approximated by

(2)

The EPIF is defined as:

(3)

◊ The principle■Pick up the EPIF (observation signals )

The EPIF matching method

21 4 2(0, ) ( ) exp[ ( ) ( ) / 2]s t A i t t

modulating frequency

energy decay factor

0

0

( ) ( , )( )

( , )p

f t A f dff

A f df

amplitude spectrum


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◊ The principleThe EPIF matching method

records

010002000300040005000600070008000900010000-1

-0.8

-0.6

-0.4

-0.2 0

0.2

0.4

0.6

0.8 1

IFIA IF

010002000300040005000600070008000900010000-1

-0.8

-0.6

-0.4

-0.2 0

0.2

0.4

0.6

0.8 1

010002000300040005000600070008000900010000-1

-0.8

-0.6

-0.4

-0.2 0

0.2

0.4

0.6

0.8 1

010002000300040005000600070008000900010000-1

-0.8

-0.6

-0.4

-0.2 0

0.2

0.4

0.6

0.8 1

010002000300040005000600070008000900010000-1

-0.8

-0.6

-0.4

-0.2 0

0.2

0.4

0.6

0.8 1

+

+

+

+

+

= EPIF

= EPIF

= EPIF

= EPIF

= EPIF

cosine roll-off window


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◊ The principle■Calculate the velocity


…

1avv

3avv2avv

offsetd

0t

t

…

1avv

3avv2avv

offsetd

0t

t

In the mini-spread and little offsets case, according to the geometrical relationship shown in figure 1, the average velocity is expressed as follows:

2 2 20

22

2 20

(2 ) ( ) ( )

(2 )

offset av av

offsetav

d t v t v

dv

t t

Fig. 1 Seismic wave propagation scheme

(4)


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For zero-offset trace, the interval velocities can be approximately determined by the average velocities:

(5)

◊ The principle■Calculate the velocity


0 0

0 0

( ) ( ) ( 1) ( 1)( )

( ) ( 1)av avt j v j t j v j

v jt j t j


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For the first event, the amplitude attenuation factor is: (6)

For the multilayer model, the amplitude attenuation factor is:

(7)

◊ The principle■Amplitude attenuation factor (Calculate the attenuated reference signals )


( ) exp( )ˆH f ft Q

1

1

( ) exp[ ( )]ˆ

Nj N

j j

ft ftH f

Q Q

error accumulation effect

attenuation esti-mated above the Nth layer

attenuation to be estimated


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◊ The principle■Optimization Algorithm


the objective function is defined as:

2

1

min ( | | ) (8)tracenumber

Tj obs j attref

Qj

E e e f f

the EPIF of observation signal of the jth trace

the EPIF of the attenuated reference signal of the same trace


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ˆ (0)Q ，Q̂

ˆ

2

1

2

1

- ( ) | [ ( 1) ( )]

[ | ( 1) | ( 1)] (9)

[ | ( ) | ( )]Q

tracenumber

j obs j attrefj

tracenumber

j obs j attrefj

k f k f k

f k f k

dEf k f k df

For an arbitrarily given initial is adjusted by the following formula for each time series variable:

◊ The principle■Optimization Algorithm


Namely the error of the (k+1)th step is modified along the negative gradient direction of the kth step error modification.


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◊ The steps of implement.Define events of pre-stack CMP data according to the correlation.

.Cut off the reference wavelet in each reflection interface, and then calculate the parameters of the wavelets, average velocities and interval velocities.

.Cut off the wavelet along all offsets of each event, and then calculate IA and IF.

.Pick the EPIF from IA and IF sections.

.Each event cycles. Matching the EPIF of the obser-vation signals of all offsets with that of the attenuated reference signals to calculate Q.



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◊ Find the event positions ■Why?

When the method is tested on the real dataset, the reflectivities information picked from post-stack data or log information are not coincident with the event positions of the pre-stack CMP data.

■How?

Using the correlation between adjacent traces of the pre-stack CMP data combining with priori layers information.



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-10 -8 -6 -4 -2 0 2 4 6 8 10

0

200

400

600

800

1000

1200

1400

1600

time/ms

-8 -6 -4 -2 0 2 4 6 8 10

0

200

400

600

800

1000

1200

1400

1600

time/ms

Having correlation

Having no correlationHaving no correlation

■How to find the event positions?


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Objective function is defined as:

(10)

■How to find the event positions?The EPIF matching method

2 2

( )

( ) ( )c op p p p pq q

p q N p

w w

the number of chosen traces

event position provided by priori layer information

the weight of correlation

coefficient

event position determined by reference trace

the event position of chosen traces of near offsets except the reference trace


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The steps of implement :①Chose several neighboring traces. Calculate IA and I

F of these traces, then pick the EPIF whose positions may be considered to be the event positions. ②Choose the reference trace. Calculate the correlation

of the EPIF positions between the reference trace and other choosing traces. ③ If the correlation coefficient is greater than the given threshold, the weight sets nonzero; otherwise, nulling.


pqw


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The steps of implement :④If the nonzero number of certain position is greater t

han another given threshold, the position is considered to be the reference event position. ⑤Calculate the correlation of the event positions recei

ved at the forth step and that provided by priori reflectivities knowledge. Similarly, if correlation coefficient is greater than the given threshold, the weight sets nonzero; and the weight sets zero on the contrary. Then the position with nonzero is considered to be the event position.


cpw

cpw


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◊ Test on the synthetic dataThe EPIF matching method

0 5 10 15 20 25 30 35 40 45 50

0

200

400

600

800

1000

1200

1400

1600

Common Midpoint Gather

offset(m)

time(

ms)

0

200

600

400

Depth

Layer 1

Layer 2

Layer 3

source geophone v=2. 0km/ sQ=150

v=2. 2km/ sQ=200

v=2. 4km/ sQ=100

mi dpoi nt0

200

600

400

Depth

Layer 1

Layer 2

Layer 3


v=2. 2km/ sQ=200

v=2. 4km/ sQ=100

mi dpoi nt

( a ) ( b )

(a) The parameters and observation system of the three-layer model (b) the synthetic seismogram


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50 100 150 200 250

100

200

300

400

500

600

700

800

900

1000

Q

Tim

e

Estimated QTrue Q

The estimated Q curve using EPIF matching analysis


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0 5 10 15 20 25 30 35 40 45 50

0

200

400

600

800

1000

1200

1400

1600

共中心点道集

offset(m)

time(

ms)

0

200

600

400

800

1000

Dept

hLayer 1

Layer 2

Layer 5

Layer 3

Layer 4


v=2. 2km/ sQ=200

v=2. 4km/ sQ=100

v=2. 6km/ sQ=150

v=2. 8km/ sQ=250

mi dpoi nt0

200

600

400

800

1000

Dept

hLayer 1

Layer 2

Layer 5

Layer 3

Layer 4


v=2. 2km/ sQ=200

v=2. 4km/ sQ=100

v=2. 6km/ sQ=150

v=2. 8km/ sQ=250

mi dpoi nt

a )

b )


(a) The parameters and observation system of the five-layer model (b) the synthetic seismogram


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0 50 100 150 200 250

0

200

400

600

800

1000

1200

1400

1600

Q

Tim

e

Estimated QTrue Q

The estimated Q curve using EPIF matching analysis


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Discussion and ConclusionsIf we don’t know the source wavelet parameters exactly, is the traveltime difference with the reference signal. The error is increasing from 7% of the first layer to the 15% of the third layer, so the error accumulation effects greatly. If we know the source wavelet parameters exactly, is the two-way traveltime of the received signal in the jth layer. This proves that the accuracy of the Q estimating depends on the accuracy of the wavelet parameters estimating and the traveltime picking.

jt

jt


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Discussion and Conclusions

In this paper, we propose a method for Q inversion from pre-stack CMP records using envelope peak instantaneous frequency matching analysis. A test using synthetic pre-stack CMP data shows that the method is more stable, more accurate while getting proper parameters, since the error of each step while iterating is the average effect of every offset. . This method has great potential for seismic attenuation estimation and gas reservoir characterization.


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Future work

Tomography to analyse complicated construction of the earth.


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Acknowledgments

We thank National Natural Science Foundation of China (40730424, 40674064), National 863 Program (2006A09A102-11) and National Science & Technology Major Project (2008ZX05023-005-005, 2008ZX05044 2-6-1) for their support.


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Quality Factor Inversion from Prestack CMP data using EPIF Matching

Jing Zhao, Jinghuai Gao

Institute of Wave and Information, Xi’an Jiaotong University

quality factor inversion from prestack cmp data using epif matching jing zhao, jinghuai gao...

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