74 th eage conference & exhibition incorporating spe europec 2012 automated seismic-to-well...

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

[email protected]

mailto:[email protected]

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

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?

Similarity vs Correlation

How similar are they?


500 1000 1500 2000-1012

Shapes to Signals

500 1000 1500 2000

-1012

500 1000 1500 2000

-1012

500 1000 1500 2000

-1012

Samples

-2000 -1000 0 1000 2000

0

0.5

1Cross-Correlation

-2000 -1000 0 1000 2000-0.2

00.20.40.60.8

-2000 -1000 0 1000 2000-0.5

0

0.5

-2000 -1000 0 1000 2000-0.2

00.20.40.60.8

Lag Samples


1000 2000 3000 4000-1012

Shape to Signals

500 1000 1500 2000-1012

200 400 600 800 1000-1012

Time [Samples]

-4000 -2000 0 2000 4000

-0.5

0

0.5

1Cross-Correlations

-2000 0 2000-0.2

00.20.40.60.8

-2000 0 2000

-0.5

0

0.5

Time lags [Samples]

Common similarity measuresCross-correlation

1

2 2 1/2

1 1

[ ( ) ][ ( ) ]( )

( [ ( ) ] [ ( ) ] )

n

S Ti

ST n n

S Ti 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

euclidi

D S T S i T i

Euclidean distance

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

http://www.psb.ugent.be/cbd/papers/gentxwarper/DTWAlgorithm.ppt


The forward model

Sonic logP-waveVp

Well logs

Bulk densityρ

AcousticImpedanceI

1

1

i ii

i i

I IR

I I

Reflectivityr

Computed

StatisticalWavelet

Waveletw

Convolution output

Synthetics

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 – look at resulting interval velocity changes

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


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

http://www.cs.ucr.edu/~eamonn/tutorials.html

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…

ST 1

( , ) minK

kkDTW 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]

How is DTW Calculated?

Synthetic

Trace

warping path

j = i – w

j = i + w

s1 s2 s3t1

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

Dynamic Time WarpingExample

Dynamic Time Warping

Manual Stretching/Squeezing

InitialSyntheticraw- P-wave

SelectingCorrelationWindow

Final correctionCorrCoefImproved

CorrCoef = -0.342 Max Corr: 0.250 at -9 ms

CorrCoef = -0.520 Max Corr: 0.8 at -9 ms

CorrCoef = 0.8BLUE: seismic traceRED : synthetic

Experiments: well 01-08

Seismic Trace

Synthetic

0 50 100 150 200 250 300 350 400-8

-6

-4

-2

0

2

4

Samples

Sca

led

Am

plitu

de

BLUE: seismic traceRED : synthetic

Experiments: well 01-08S

eis

mic

Tra

ce

SyntheticBLUE: seismic traceRED : synthetic

Dis

tance

17

42

66

91

116

140

165

189

-2 0 2

430420410400390380370360350340330320310300290280270260250240230220210200190180170160150140130120110100

908070605040302010

0

Sam

ples

Amp

50 100 150 200 250 300 350 400

-202

Samples

Am

p

Warping path


Seismic Trace

Synthetic

0 50 100 150 200 250 300 350 400-8

-6

-4

-2

0

2

4

Samples

Sca

led

Am

plitu

de


Bounded - DTW

Synthetic

Trace

warping path

j = i – w

j = i + w

s1 s2 s3t1

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

Se

ism

ic T

race

Synthetic

Dista

nce

0

20

39

59

79

98

118

138

-2 0 243042041040039038037036035034033032031030029028027026025024023022021020019018017016015014013012011010090 80 70 60 50 40 30 20 10 0

Sa

mp

les

Amp

50 100 150 200 250 300 350 400-2

0

2

4

Samples

Am

p

Experiments: well 01-08S

eis

mic

Tra

ce

Synthetic

Warping path



50 100 150 200 250 300 350 400-1

-0.5

0

0.5

1Original signals. Synthetic (red) and Seismic Trace (blue)

No

rma

lize

d A

mp

litu

de

Samples

100 200 300 400 500 600

-3

-2

-1

0

1

2

3

4

Warped signals. Synthetic (red) and Seismic Trace (blue)

No

rma

lize

d A

mp

litu

de

Samples


Experiments: well 01-08ManualWarping(HRS)

AutomaticWarping(DTW)


Manual: time warping only in the selected window.

CorrCoef = 0.92

CorrCoef = 0.80

Warping path: well 16-08S

eis

mic

Tra

ce

SyntheticBLUE: seismic traceRED : synthetic

Dis

tan

ce

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

0

Sa

mp

les

Amp

50 100 150 200 250 300 350 400

-2

0

2

4

Samples

Am

p

Automatic stretch/squeeze: well 16-08

50 100 150 200 250 300 350 400-1

-0.5

0

0.5

1Original signals. Synthetic (red) and Seismic Trace (blue)

No

rma

lize

d A

mp

litu

de

Samples

100 200 300 400 500 600-3

-2

-1

0

1

2

3

4

Warped signals. Synthetic (red) and Seismic Trace (blue)

No

rma

lize

d A

mp

litu

de

Samples


Experiments: well 16-08 ManualWarping(HRS)

AutomaticWarping(DTW)


Manual: time warping only in the selected window.

CorrCoef = 0.89

CorrCoef = 0.744

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

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.

BLISS sponsors

BLind Identification of Seismic Signals (BLISS) is supported by

Hampson-Russell for software licensing

Takeaway

EuclideanDist = 52

DWT_dist = 41

THANK YOU

74 th eage conference & exhibition incorporating spe europec 2012 automated seismic-to-well...

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