Automatic seismic to well tying. See the video for the maple leaf to signal conversion here: https://www.youtube.com/watch?v=lmWDgTrsgw4

1. 74th EAGE Conference & Exhibition
incorporating SPE EUROPEC 2012
Automated seismic-to-well ties?
Roberto H. Herrera and Mirko van der Baan
University of Alberta, Edmonton, Canada
rhherrer@ualberta.ca

2. Outline
• Introduction
• Similarity in time series
• The manual seismic-to-well tie
• What is Dynamic Time Warping
– How DTW works?
– The automated approach
• Real examples
– Manual vs Automatic
• Conclusions

3. Seismic-to-well similarity
• Objective:
– Can you automate the seismic-to-well tie?
• Possible applications:
– Seismic-to-well tie, log-to-log correlation,
alignment of baseline + monitor in 4D
• Main problem
– Bulk shift, stretching and squeezing is an
interpretation item.
–How to implement semi-automatically?

4. Similarity vs Correlation

5. How similar are they?

6. How similar are they?
500 1000 1500 2000
-1
0
1
2
Shapes to Signals
500 1000 1500 2000
-1
0
1
2
500 1000 1500 2000
-1
0
1
2
500 1000 1500 2000
-1
0
1
2
Samples
-2000 -1000 0 1000 2000
0
0.5
1
Cross-Correlation
-2000 -1000 0 1000 2000
-0.2
0
0.2
0.4
0.6
0.8
-2000 -1000 0 1000 2000
-0.5
0
0.5
-2000 -1000 0 1000 2000
-0.2
0
0.2
0.4
0.6
0.8
Lag Samples

7. How similar are they?
1000 2000 3000 4000
-1
0
1
2
Shape to Signals
500 1000 1500 2000
-1
0
1
2
200 400 600 800 1000
-1
0
1
2
Time [Samples]
-4000 -2000 0 2000 4000
-0.5
0
0.5
1
Cross-Correlations
-2000 0 2000
-0.2
0
0.2
0.4
0.6
0.8
-2000 0 2000
-0.5
0
0.5
Time lags [Samples]

8. Common similarity measures
Cross-correlation
1
2 2 1/2
1 1
[ ( ) ][ ( ) ]
( )
( [ ( ) ] [ ( ) ] )
n
S T
i
ST n n
S T
i i
S i T i
S i T i
 
 
 


 
  

 

 
• Denominator: energy normalization term.
•  is the time lag where the best match occurs.
xcorr = Time alignment problems 
An alternative to xcorr (L_2-norm) between the two time series
2
1
( , ) ( ( ) ( ))
n
euclid
i
D S T S i T i

 
Euclidean distance

9. Euclidean Distance & xcorr
i
i
time
Euclidean distance:
aligns the i-th point on one time
series with the i-th point on the other
 poor similarity score.
Correlation of well logs has always
been a labor-intense interactive
task. It is a pattern recognition
problem better solved by the
human eye than a computer.
Zoraster et al., 2004
We are trying to simulate
the procedure with the way
humans perform the
comparison.Elena Tsiporkova:
http://www.psb.ugent.be/.../DTWAlgorithm.ppt

10. Manual seismic-to-well tie
The forward model
Sonic log
P-wave
Vp
Well logs
Bulk
density
ρ
Acoustic
Impedance
I
1
1
i i
i
i i
I I
R
I I





Reflectivity
r
Computed
Statistical
Wavelet
Wavelet
w
Convolution output
Synthetic
s

11. Experiments
Xline 42

12. Seismic-to-well tie
Correlation Coefficient = 0.59
800 ms
1100 ms

13. 600 ms
1100 ms
Correlation Coefficient = 0.40
Seismic-to-well tie

14. Seismic-to-well tie
Correlation Coefficient = 0.148 and could be 0.45 with 25 ms of time shift
600 ms
900 ms

15. How done manually
• Apply bulk shift and minimum amount of
stretching + squeezing to correlate major
reflectors
• QC – look at resulting interval velocity changes

16. Dynamic Time Warping?
i
i+2
i
i i
timetime
Euclidean distance:
aligns the i-th point on one time
series with the i-th point on the other
 poor similarity score.
DTW: A non-linear (elastic) alignment:
produces a more intuitive similarity
measure.
It matches similar shapes even if they
are out of phase on the time axis.
A pattern matching technique that is
“visually perceptive and intuitive”
Elena Tsiporkova:
http://www.psb.ugent.be/cbd/papers/gentxwarper/DTWAlgorithm.ppt

17. Dynamic Time Warping?
Euclidean Distance
Sequences are aligned “one to one”
DTW
Nonlinear alignments are possible
Dr. Eamonn Keogh http://www.cs.ucr.edu/~eamonn/tutorials.html

18. How is DTW Calculated?
[Ratanamahatana, E. Keogh, 2005]
Every possible warping between two time series, is a path through
the matrix. We want the best one…
S
T  1
( , ) min
K
kk
DTW S T w K
 
T
Warping path w
S
This recursive function gives us the
minimum cost path
(i,j) = d(si,tj) + min{ (i-1,j-1), (i-1,j ), (i,j-1) }
[Berndt, Clifford, 1994]

19. How is DTW Calculated?
Synthetic
Trace
warping path
j = i – w
j = i + w
s1 s2 s3
t1
s4 s5 s6 s7
t2
t3
t4
t5
t6
t7
S_warped = s1 s2 s2 s3 s3
t1 t2 t3 t3 t4T_warped =
s4
t5
s5
t5
s6
t5
s7
t6
s7
t7

20. Dynamic Time Warping
Example

21. Dynamic Time Warping

22. Manual Stretching/Squeezing
Initial
Synthetic
raw- P-wave
Selecting
Correlation
Window
Final
correction
CorrCoef
Improved
CorrCoef = -0.342 Max Corr: 0.250 at -9 ms
CorrCoef = -0.520 Max Corr: 0.8 at -9 ms
CorrCoef = 0.8
BLUE: seismic trace
RED : synthetic

23. Experiments: well 01-08
Seismic
Trace
Synthetic
0 50 100 150 200 250 300 350 400
-8
-6
-4
-2
0
2
4
Samples
ScaledAmplitude
BLUE: seismic trace
RED : synthetic

24. Experiments: well 01-08
SeismicTrace
Synthetic
BLUE: seismic trace
RED : synthetic
Distance
17
42
66
91
116
140
165
189
-2 0 2
430
420
410
400
390
380
370
360
350
340
330
320
310
300
290
280
270
260
250
240
230
220
210
200
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
Samples
Amp
50 100 150 200 250 300 350 400
-2
0
2
Samples
Amp
Warping path

25. Experiments: well 01-08
Seismic
Trace
Synthetic
0 50 100 150 200 250 300 350 400
-8
-6
-4
-2
0
2
4
Samples
ScaledAmplitude
BLUE: seismic trace
RED : synthetic

26. Bounded - DTW
Synthetic
Trace
warping path
j = i – w
j = i + w
s1 s2 s3
t1
s4 s5 s6 s7
t2
t3
t4
t5
t6
t7
S_warped = s1 s2 s2 s3 s3
t1 t2 t3 t3 t4T_warped =
s4
t5
s5
t5
s6
t5
s7
t6
s7
t7

27. SeismicTrace
Synthetic
Distance
0
20
39
59
79
98
118
138
-2 0 2
430
420
410
400
390
380
370
360
350
340
330
320
310
300
290
280
270
260
250
240
230
220
210
200
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
Samples
Amp
50 100 150 200 250 300 350 400
-2
0
2
4
Samples
Amp
Experiments: well 01-08
SeismicTrace
Synthetic
Warping path
BLUE: seismic trace
RED : synthetic

28. Experiments: well 01-08
50 100 150 200 250 300 350 400
-1
-0.5
0
0.5
1
Original signals. Synthetic (red) and Seismic Trace (blue)
NormalizedAmplitude
Samples
100 200 300 400 500 600
-3
-2
-1
0
1
2
3
4
Warped signals. Synthetic (red) and Seismic Trace (blue)
NormalizedAmplitude
Samples
BLUE: seismic trace
RED : synthetic

29. Experiments: well 01-08
Manual
Warping
(HRS)
Automatic
Warping
(DTW)
BLUE: seismic trace
RED : synthetic
Manual: time warping only in
the selected window.
CorrCoef = 0.92
CorrCoef = 0.80

30. Warping path: well 16-08SeismicTrace
Synthetic
BLUE: seismic trace
RED : synthetic
Distance
1
20
39
57
76
95
114
132
-2 0 2
430
420
410
400
390
380
370
360
350
340
330
320
310
300
290
280
270
260
250
240
230
220
210
200
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0Samples
Amp
50 100 150 200 250 300 350 400
-2
0
2
4
Samples
Amp

31. Automatic stretch/squeeze:
well 16-08
50 100 150 200 250 300 350 400
-1
-0.5
0
0.5
1
Original signals. Synthetic (red) and Seismic Trace (blue)
NormalizedAmplitude
Samples
100 200 300 400 500 600
-3
-2
-1
0
1
2
3
4
Warped signals. Synthetic (red) and Seismic Trace (blue)
NormalizedAmplitude
Samples
BLUE: seismic trace
RED : synthetic

32. Experiments: well 16-08
Manual
Warping
(HRS)
Automatic
Warping
(DTW)
BLUE: seismic trace
RED : synthetic
Manual: time warping only in
the selected window.
CorrCoef = 0.89
CorrCoef = 0.744

33. Discussion
• Pros and cons
– Independent of the selected window.
– Able to follow non linearities
– Only intended as a guide – not all stretching-
squeezing is realistic
– QC – examine changes in resulting interval
velocity curve

34. Conclusions
• DTW: optimal solution for matching similar events.
• DTW: complementary tool for seismic-to-well tie.
• Many other applications of DTW are possible for seismic data.
– log-to-log correlations, alignment of baseline and monitor
surveys in 4D seismics, PP and PS wavefield registration for
3C data.

35. BLISS sponsors
BLind Identification of Seismic Signals (BLISS)
is supported by
Hampson-Russell for software licensing

36. Takeaway
EuclideanDist = 52
DWT_dist = 41
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