drift time estimation by dynamic time warping...drift time estimation by dtw • drift time •...

Drift time estimation by dynamic time warping

Tianci Cui and Gary F. Margrave

1

Outline

• Drift time

• Well‐based 1D seismogram models

• Matching stationary and nonstationary seismograms

• Dynamic time warping

• Inclusion of internal multiples

• Conclusions and future work

2

Drift time estimation by DTW

• Drift time






3

Drift time: well logs

4

Drift time: fake Q log

: Well logging frequency : Seismic frequency

Kjartanssen (1979)

5

Drift time: frequency‐dependent velocity

: Well logging frequency : Seismic frequency

Kjartanssen (1979)

6

Drift time

7


• Drift time






8

Stationary seismogram: s(t)

=

minimum‐phasedominant frequency: 30 Hz

9

Nonstationary seismogram: sq(t)Synthetic zero‐offset VSP model with Q effects

(Margrave and Daley, 2014)

10

Nonstationary seismogram: sq(t)Synthetic zero‐offset VSP model with Q effects

(Margrave and Daley, 2014)Surface receiver

11

1 D seismogram models

Q effects: 1 Diminishing amplitude2 Widening wavelets3 Delaying events Drift time

12

1 D seismogram models

13


• Drift time






14

Matching without drift time correctionTime‐variant balancing and

time‐variant constant‐phase rotation

15

Matching with theoretical drift time correction

: drift time: stationary seismogram after drift time correction

Drift time correction

16

Matching perfection: time‐variant balancing and time‐variant constant‐phase rotation


17

Matching perfection: time‐variant balancing and time‐variant constant‐phase rotation


Drift time correction is necessary to match the stationaryto nonstationary seismograms.

Calculation of drift time in industrial practice needs oneof these:

• Knowledge of Q or

• A check‐shot survey or

• Manually stretching and squeezing the syntheticseismogram

18


• Drift time






19

Dynamic Time Warping

Dynamic time warping (Hale, 2012):• Estimates the time shift between two seismograms• Based on constrained optimization algorithm• Realized by dynamic programming• Similar to time‐variant crosscorrelation but more

sensitive to the rapid‐varying time shift

We use dynamic time warping (DTW) to estimate thedrift time between the stationary and nonstationaryseismograms caused by anelastic attenuation

20

DTW: drift time estimation

21


22


,

23


,

24


, ,

25


, ,

: sample number, : time sample rate: drift time, : drift lag

theoretical drift lag

26

DTW: drift time estimationtheoretical drift lag

• The alignment error is nearly zero along the theoretical drift lag.

• Choose a path traveling from to , sum alignmenterrors along this path. The estimated drift lag sequence is thepath of the minimal cumulative alignment error.

27

DTW: drift time estimationtheoretical drift lag

infinite

Constraint: | |≤1

28

Dynamic Programming

4 7 1

3 5 8

6 2 9

Alignment error array

1

0

‐1

1 2 3n

m

27 possible paths

29

Dynamic Programming: accumulation

4 7 1

3 5 8

6 2 9


1

0

‐1

1 2 3n

m

Cumulative alignment error array

1

0

‐1

m

n1 2 3

27 possible paths

30


Constraint: | |≤1

4 7 1

3 5 8

6 2 9

4

3

6


1

0

‐1

1 2 3n

m


1

0

‐1

m

n1 2 3

27 possible paths

?

31


Constraint: | |≤1

4 7 1

3 5 8

6 2 9

4

3

6


1

0

‐1

1 2 3n

m


1

0

‐1

m

n1 2 3

27 possible paths

?

32


Constraint: | |≤1

4 7 1

3 5 8

6 2 9

4

3

6


1

0

‐1

1 2 3n

m


1

0

‐1

m

n1 2 3

27 possible paths

?

33


Constraint: | |≤1

4 7 1

3 5 8

6 2 9

4 10

3

6


1

0

‐1

1 2 3n

m


1

0

‐1

m

n1 2 3

27 possible paths

34


Constraint: | |≤1

4 7 1

3 5 8

6 2 9

4 10

3

6


1

0

‐1

1 2 3n

m


1

0

‐1

m

n1 2 3

27 possible paths

?

35


Constraint: | |≤1

4 7 1

3 5 8

6 2 9

4 10

3

6


1

0

‐1

1 2 3n

m


1

0

‐1

m

n1 2 3

27 possible paths

?

36


Constraint: | |≤1

4 7 1

3 5 8

6 2 9

4 10

3 8

6


1

0

‐1

1 2 3n

m


1

0

‐1

m

n1 2 3

27 possible paths

37


Constraint: | |≤1

4 7 1

3 5 8

6 2 9

4 10

3 8

6 5


1

0

‐1

1 2 3n

m


1

0

‐1

m

n1 2 3

27 possible paths

38


Constraint: | |≤1

4 7 1

3 5 8

6 2 9

4 10 9

3 8 13

6 5 14


1

0

‐1

1 2 3n

m


1

0

‐1

m

n1 2 3

27 possible paths 3 possible paths

39

Dynamic Programming: backtracking

Constraint: | |≤1

4 7 1

3 5 8

6 2 9

4 10 9

3 8 13

6 5 14


1

0

‐1

1 2 3n

m


1

0

‐1

m

n1 2 3


40

Dynamic Programming: backtracking

Constraint: | |≤1

4 7 1

3 5 8

6 2 9

4 10 9

3 8 13

6 5 14


1

0

‐1

1 2 3n

m


1

0

‐1

m

n1 2 3


Estimated drift lag:

41

Dynamic Programming

4 10 9

3 8 13

6 5 14

1

0

‐1

1 2 3n

m


1

0

‐1

m

n1 2 3

, ,


4 10

3 8

6 5

,

Dynamic: optimal solution varies at different stageWarping path: drift lag

42

DTW: drift time estimationestimated drift lag

infinite

Constraint: | |≤1Further Constraint: ∑ ≤1

The drift lag sequence is constrained to change in blocks of samples

( )

43

DTW: drift time estimationestimated drift lag

infinite

Constraint: | |≤1Further Constraint: ∑ ≤1

The drift lag sequence is constrained to change in blocks of samples

( )

44

DTW: drift time estimation∗

: estimated drift lag: estimated drift time

45

DTW: matching seismograms

46


• Drift time






47

Inclusion of internal multiplessq(t)

sqi(t)

48

Inclusion of internal multiples: sqi(t)

=(Richards and Menke, 1983)

49

Inclusion of internal multiples

50

Conclusions

• DTW succeeds in estimating drift time automaticallywithout knowledge of Q or a check‐shot survey.

• Application of drift time correction results in a muchsimpler residual phase.

• DTW estimates drift time associated with apparent Qincluding both intrinsic and stratigraphic effects.

51

Future work

• Conduct stationary and nonstationary deconvolution onthe seismic trace and tie the deconvolved seismic traceto well log reflectivity by DTW

• Estimate Q value from the drift time estimated by DTW

52

Acknowledgements

• CREWES sponsors

• NSERC: grant CRDPJ 379744‐08

• CREWES staff and students

53

Choosing values

54

Choosing values

55

Applications of DTW

• Tying synthetic to recorded seismograms

• Registration of P– and S–wave images

• Residual normal moveout correction

• Alignment of images computed for differentsource‐receiver offsets or propagation angles.

56

drift time estimation by dynamic time warping...drift time estimation by dtw • drift time •...

Documents