quality factor inversion from prestack cmp data using epif matching jing zhao, jinghuai gao...
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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. introduction. ◊ why to estimate Q? ● Lithology identification ●Inversing Q filtering to Improve the resolution of seismic imaging - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
The EPIF matching method
…
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
The EPIF matching method
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 )
The EPIF matching method
( ) 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 EPIF matching method
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
The EPIF matching method
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.
The EPIF matching method
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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.
The EPIF matching method
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The EPIF matching method
-10 -8 -6 -4 -2 0 2 4 6 8 10
0
200
400
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time/ms
-8 -6 -4 -2 0 2 4 6 8 10
0
200
400
600
800
1000
1200
1400
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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.
■How to find the event positions?The EPIF matching method
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.
■How to find the event positions?The EPIF matching method
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
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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
source geophone v=2. 0km/ sQ=150
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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◊ Test on the synthetic dataThe EPIF matching method
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
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1000
1200
1400
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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
source geophone v=2. 0km/ sQ=150
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
source geophone v=2. 0km/ sQ=150
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 )
◊ Test on the synthetic dataThe EPIF matching method
(a) The parameters and observation system of the five-layer model (b) the synthetic seismogram
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◊ Test on the synthetic dataThe EPIF matching method
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