74 th 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

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?

Common similarity measures Cross-correlation 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 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:

The forward model Sonic log P-wave Vp Well logs Bulk density ρ Acoustic Impedance I Reflectivity r Computed Statistical Wavelet w Convolution output Synthetic s

Experiments Xline 42

Seismic-to-well tie Correlation Coefficient = ms 1100 ms

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

Correlation Coefficient = 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 time 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:

Dynamic Time Warping? Euclidean Distance Sequences are aligned “one to one” DTW Nonlinear alignments are possible Dr. Eamonn Keogh

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 This recursive function gives us the minimum cost path  (i,j) = d(s i,t j ) + 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 s1s2s3 t1 s4 s5 s6s7 t2 t3 t4 t5 t6 t7 S_warped = s1s2 s3 t1t2t3 t4 T_warped = s4 t5 s5 t5 s6 t5 s7 t6 s7 t7

Dynamic Time Warping Example

Dynamic Time Warping

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

Experiments: well Seismic Trace Synthetic Samples Scaled Amplitude BLUE: seismic trace RED : synthetic

Experiments: well Seismic Trace Synthetic BLUE: seismic trace RED : synthetic Warping path

Experiments: well Seismic Trace Synthetic Samples Scaled Amplitude BLUE: seismic trace RED : synthetic

Bounded - DTW Synthetic Trace warping path j = i – w j = i + w s1s2s3 t1 s4 s5 s6s7 t2 t3 t4 t5 t6 t7 S_warped = s1s2 s3 t1t2t3 t4 T_warped = s4 t5 s5 t5 s6 t5 s7 t6 s7 t7

Experiments: well Seismic Trace Synthetic Warping path BLUE: seismic trace RED : synthetic

Experiments: well BLUE: seismic trace RED : synthetic

Experiments: well 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

Warping path: well Seismic Trace Synthetic BLUE: seismic trace RED : synthetic

Automatic stretch/squeeze: well BLUE: seismic trace RED : synthetic

Experiments: well 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

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