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74th EAGE Conference & Exhibition
incorporating SPE EUROPEC 2012
Automated seismic-to-well ties?
Roberto H. Herrera and Mi...
Outline
• Introduction
• Similarity in time series
• The manual seismic-to-well tie
• What is Dynamic Time Warping
– How D...
Seismic-to-well similarity
• Objective:
– Can you automate the seismic-to-well tie?
• Possible applications:
– Seismic-to-...
Similarity vs Correlation
How similar are they?
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
...
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
...
Common similarity measures
Cross-correlation
1
2 2 1/2
1 1
[ ( ) ][ ( ) ]
( )
( [ ( ) ] [ ( ) ] )
n
S T
i
ST n n
S T
i i
S...
Euclidean Distance & xcorr
i
i
time
Euclidean distance:
aligns the i-th point on one time
series with the i-th point on th...
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...
Experiments
Xline 42
Seismic-to-well tie
Correlation Coefficient = 0.59
800 ms
1100 ms
600 ms
1100 ms
Correlation Coefficient = 0.40
Seismic-to-well tie
Seismic-to-well tie
Correlation Coefficient = 0.148 and could be 0.45 with 25 ms of time shift
600 ms
900 ms
How done manually
• Apply bulk shift and minimum amount of
stretching + squeezing to correlate major
reflectors
• QC – loo...
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 poin...
Dynamic Time Warping?
Euclidean Distance
Sequences are aligned “one to one”
DTW
Nonlinear alignments are possible
Dr. Eamo...
How is DTW Calculated?
[Ratanamahatana, E. Keogh, 2005]
Every possible warping between two time series, is a path through
...
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...
Dynamic Time Warping
Example
Dynamic Time Warping
Manual Stretching/Squeezing
Initial
Synthetic
raw- P-wave
Selecting
Correlation
Window
Final
correction
CorrCoef
Improved
...
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...
Experiments: well 01-08
SeismicTrace
Synthetic
BLUE: seismic trace
RED : synthetic
Distance
17
42
66
91
116
140
165
189
-2...
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...
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 ...
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
29...
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...
Experiments: well 01-08
Manual
Warping
(HRS)
Automatic
Warping
(DTW)
BLUE: seismic trace
RED : synthetic
Manual: time warp...
Warping path: well 16-08SeismicTrace
Synthetic
BLUE: seismic trace
RED : synthetic
Distance
1
20
39
57
76
95
114
132
-2 0 ...
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...
Experiments: well 16-08
Manual
Warping
(HRS)
Automatic
Warping
(DTW)
BLUE: seismic trace
RED : synthetic
Manual: time warp...
Discussion
• Pros and cons
– Independent of the selected window.
– Able to follow non linearities
– Only intended as a gui...
Conclusions
• DTW: optimal solution for matching similar events.
• DTW: complementary tool for seismic-to-well tie.
• Many...
BLISS sponsors
BLind Identification of Seismic Signals (BLISS)
is supported by
Hampson-Russell for software licensing
Takeaway
EuclideanDist = 52
DWT_dist = 41
THANK YOU
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Automatic seismic to well tying. See the video for the maple leaf to signal conversion here: https://www.youtube.com/watch?v=lmWDgTrsgw4

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Automated seismic-to-well ties?

  1. 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. 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. 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. 4. Similarity vs Correlation
  5. 5. How similar are they?
  6. 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. 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. 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. 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. 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. 11. Experiments Xline 42
  12. 12. Seismic-to-well tie Correlation Coefficient = 0.59 800 ms 1100 ms
  13. 13. 600 ms 1100 ms Correlation Coefficient = 0.40 Seismic-to-well tie
  14. 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. 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. 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. 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. 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. 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. 20. Dynamic Time Warping Example
  21. 21. Dynamic Time Warping
  22. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 35. BLISS sponsors BLind Identification of Seismic Signals (BLISS) is supported by Hampson-Russell for software licensing
  36. 36. Takeaway EuclideanDist = 52 DWT_dist = 41 THANK YOU
  • beherca

    May. 7, 2018
  • ANSayedMohammmed

    Dec. 12, 2017
  • chenxiaoou

    Jul. 17, 2017
  • YuriyIvanov9

    Oct. 27, 2016
  • veritas839

    Jul. 29, 2014

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

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