Automatic approaches for seismic to well tying

Roberto H. Herrera1, Sergey Fomel2, and Mirko van der Baan1

Abstract

Tying the synthetic trace to the actual seismic trace at the well location is a labor-intensive task that relies onthe interpreter’s experience and the similarity metric used. The traditional seismic to well tie suffers from sub-jectivity by visually matching major events and using global crosscorrelation to measure the quality of that tying.We compared two automatic techniques that will decrease the subjectivity in the entire process. First, we evalu-ated the dynamic time warping method, and then, we used the local similarity attribute based on regularizedshaping filters. These two methods produced a guided stretching and squeezing process to find the best matchbetween the two signals. We explored the proposed methods using real well log examples and compared to themanual method, showing promising results with both semiautomatic approaches.

IntroductionReliable well-seismic tying is a crucial step in seismic

interpretation to correlate subsurface geology to ob-served seismic data. Even though the method involvesa well-known workflow (Hall, 2013), it turns out to be ahardly repeatable experiment. The ease and quality ofthe tying procedure depend on the availability of high-quality logs, the estimation of a suitable wavelet, andthe interpreter’s experience. Excellent recipes by Whiteand Simm (2003) and two short essays by Newrick(2012) describe good practices in the tying procedure.An initial statistical wavelet is estimated from the seis-mic data and convolved with the reflectivity calculatedfrom the well logs (sonic log and bulk density log) togenerate the first synthetic trace. Then, the interpreterfinds the best match between the generated syntheticand the actual seismic trace. Following these steps doesnot guarantee the “correct” tie (Anderson and Newrick,2008) because the entire process is prone to pitfalls dueto subjectivities in interpretation and procedures.

The above-cited papers are good practices to followto reach the best outcomes with the available tools. Inthis paper, we concern ourselves with the specific stepsof optimal matching and quantifying the quality of thatmatch. Hence, we assume that all the basic principleshave been followed (White and Simm, 2003; Andersonand Newrick, 2008) and that we have a synthetic traceand a seismic trace to find the optimum match betweenboth signals.

The first issue comes from the fact that the quality ofthe tie between the synthetic and the seismic trace isbased on the correlation coefficient, which is limited

to linear features. The time-variant nature of the seismicwavelet adds nonlinearities to the trace that cannot beeasily followed by a linear metric, such as the correla-tion coefficient further represented in equation 1. Wecompare two nonlinear approaches to match these timeseries. Our procedures substitute the manual stretchingand squeezing step by an optimization algorithm, whichis still supervised by the interpreter. This improves therepeatability of the tying, while the critical and oftenabused stretch and squeeze (Newrick, 2012) is stillunder control. The first alternative to perform the auto-mated tying is based on dynamic time warping (DTW)(Herrera and Van der Baan, 2012a, 2014), and the sec-ond approach faces the nonlinearity correction usingthe local similarity attribute (LSIM) (Fomel, 2007a).Both techniques share the quality-control step bymonitoring the relative velocity change produced bythe tying.

Nonlinear correlation of seismic time series has beenpreviously explored in the context of well-to-well cor-relation (Lineman et al., 1987; Zoraster et al., 2004), inwhich well logs from different wells are correlated toinfer common earth features. The crosscorrelationwas unable to follow local distortions such as stretchingor shrinking of stratigraphic intervals, typical of logscollected even from closely spaced wells. Essentially,these methods aim to correlate common features invarious logs (Anderson and Gaby, 1983). An early ap-proach to DTW is presented by Martinson et al.(1982) and Martinson and Hopper (1992). They developa mapping function able to track stretching and squeez-ing in time series based on a correlation technique to

1University of Alberta, Department of Physics, Edmonton, Alberta, Canada. E-mail: rhherrer@ualberta.ca; mirko.vanderbaan@ualberta.ca.2The University of Texas at Austin, Bureau of Economic Geology, Austin, Texas, USA. E-mail: sergey.fomel@beg.utexas.edu.Manuscript received by the Editor 27 August 2013; published online 20 March 2014. This paper appears in Interpretation, Vol. 2, No. 2 (May

2014); p. SD101–SD109, 6 FIGS.http://dx.doi.org/10.1190/INT-2013-0130.1. © 2014 Society of Exploration Geophysicists and American Association of Petroleum Geologists. All rights reserved.

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Special section: Well ties to seismic data

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establish a point-for-point correlation between traces.Liner and Clapp (2004) propose a global optimizationmethod to create pairwise alignments between seismictraces. More recently, Hale (2013) uses DTW in seismicimage processing, which aligns seismic images withdifferences not limited to time shifts.

The first of our approaches follows the constrainedoptimization of Sakoe and Chiba (1978) with DTW, andit is not pairwise, but it allows for one-to-many connec-tions in both directions between two traces (Herreraand Van der Baan, 2014). The second alternative, LSIM,measures signal characteristics not instantaneously ateach data point, but in a local neighborhood aroundthe point. Thus, the correlation between two traces isconsidered as a local attribute controlled by the sizeof the neighborhood (Fomel, 2007a).

We start with a brief introduction to DTW and its im-plementation and follow with an introduction to theLSIM derived from global correlation. We then describethe quality-control tool based on relative velocitychange. Finally, we illustrate the performance of bothmethods in a real well-seismic tie and compare the re-sults with the manual method.

TheoryDTW

The correlation coefficient is often used to measurethe quality of the well-seismic tie (Hampson-Russell,1999). Having two (time-dependent) sequences at andbt, both of length n, the correlation coefficient is

cðτÞ ¼P

nt¼1 atbt−τffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn

t¼1 a2tPn

t¼1 b2t

q ; (1)

where the denominator supplies the energy normaliza-tion term and the numerator is the dot product of twotime series. The optimal time lag τ is generally set at themaximum correlation coefficient. Values of c span fromone for perfect correlation, zero for uncorrelated sig-nals, and −1 for perfect correlation of signals with re-verse polarity (Fomel, 2007a).

This measure works well if a constant time shift τcharacterizes both signals. When this time alignmentis constant, the problem is reduced to the correctionof the time lag by crosscorrelation. But this measurefails to find the best matching in nonstationary cases(Herrera and Van der Baan, 2014).

Most geophysical applications have nonstationarytime alignment problems (Anderson and Gaby, 1983).An alternative to crosscorrelation is to find the Euclid-ean distance (L2-norm) between the two time series(Keogh and Kasetty, 2003):

Deuclidða; bÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXni¼1

ðai − biÞ2s

; (2)

where Deuclidða; bÞ is the one-to-one distance betweenthe synthetic trace a and the seismic trace b. The index

i is the discrete time representation, i.e., samples ofeach signal.

The Euclidean distance (L2-norm) in equation 2 isthe most widely used distance measure. It is trivial toimplement but also is very sensitive to small distortionsin the time axis (Berndt and Clifford, 1994; Keogh andKasetty, 2003). Taking the advantages of the Euclideandistance and adapting it for nonstationary matching,Berndt and Clifford (1994) propose DTW.

The DTW distance can accommodate stretching andsqueezing in the time series by linear programming. Ituses the Euclidean distance as the initial metric but al-lows for the one-to-many alignment. The warping dis-tance is represented as the minimum path in a gridrepresentation of both sequences; see Herrera andVan der Baan (2014) for a graphical representation ofthe warping matrix with an example.

In the warping matrix, the squared distance in theelements (ith, jth) is calculated by

δðai; bjÞ ¼ ðai − bjÞ2: (3)

The optimal path that minimizes the total warping cost(Berndt and Clifford, 1994) is

DTWða; bÞ ¼ minW

Xpk¼1

δðwkÞ; (4)

where each wk corresponds to a point ði; jÞk and eachgrid point (i; j) corresponds to an alignment or connec-tion between ai and bj .

The dynamic programming approach uses the fol-lowing recurrence to find the warping path (Berndtand Clifford, 1994):

γði; jÞ ¼ δðai; bjÞþmin½γði − 1; jÞ; γði − 1; j − 1Þ; γði; j − 1Þ�; (5)

where δðai; bjÞ is the distance defined in equation 3 andthe cumulative distance γði; jÞ is the sum of the distancebetween the current elements and the minimum cumu-lative distance of the three neighboring cells.

This mapping process produces stretched versionsof the original signals with length k. Only if the two sig-nals are fully aligned from the start do we have i ¼j ¼ k.

For the final warping process, we compute a new ar-gument i, by extracting the indices of the intersection ofthe two sets fikg and fjkg:

i ¼ ikðjpÞ; jp ⊆ position of fjkg in fikg ⋂ fjkg: (6)

With the new argument i, we can now get the warpedsignal ai by selecting the ith samples from ai. This signalis the best approximation of bj following the optimumwarping path (ai ≈ bj).

In time-domain signals, this monotonic transforma-tion of the initial time interval into itself with differentaxis distribution is called curve registration (Ramsay

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and Silverman, 2005). The argument i accelerates ordecelerates the synthetic signal along the time axis tomatch the seismic trace, such that well tops can bematched to corresponding reflections.

To prevent the occurrence of nonphysical alignmentsbetween both signals, we use a global distance constraintr to limit themaximum allowed amount of stretching andsqueezing (Sakoe and Chiba, 1978). Elements of thewarping matrix are restricted by the warping windowjik − jkj < r where r is the window width. The con-strained DTW prevents unrealistic velocity changesdue to stretching and squeezing of the synthetic trace.Proper specification of the allowed warping windowguarantees meaningful results in the tying process. Alarge value of r allows more stretching, which is some-times undesirable, but also provides better matching. Itschoice allows for a trade-off between algorithmic perfor-mance and physical meaning. This initial value of thewindow width should be based on experience and bymonitoring the quality of the resultant tie.

LSIMThe LSIM starts with the observation that the

squared correlation coefficient given in equation 1can be split as the product of two factors c2 ¼ pq(Fomel and Jin, 2009), with the first factor:

p ¼P

tatbtPtb2t

(7)

being the solution of a least-squares minimization prob-lem minp

Pt ðat − pbtÞ2. The first factor p normalizes

the dot product ðhat; btiÞ with the energy of the seismictrace b. The second factor q does the same but normal-izes with the energy of the synthetic trace a:

q ¼P

tatbtPta2t

; (8)

and the least-squares minimization problem is the solu-tion that minimizes the difference minq

Pt ðbt − qatÞ2

between the seismic trace and the synthetic trace.This is a two-way minimization problem, and we can

provide p and qwith local properties, such that pt and qtbecome the solution of a regularized least-squares prob-lem (Fomel and Jin, 2009):

minpi

�Xt

ðat − ptbtÞ2 þ R½pt��; (9)

and

minqt

�Xt

ðbt − qtatÞ2 þ R½qt��; (10)

where R is a regularization operator designed to en-force a desired behavior such as smoothness, estimatedfrom shaping regularization (Fomel, 2007b).

The application of local similarity to the well-seismictying problem consists of squeezing and stretching thesynthetic trace with respect to the seismic trace whilecomputing the LSIM. By picking the strongest similaritytrend from the attribute panel, we identify the corre-sponding shift to correct the synthetic trace (Fomeland Jin, 2009). These time shifts form a vector that issimilar to the warping path used in DTW.

The procedure is then to create a warping functionwðtÞ from the local similarity scan by means of a short-est-path ray tracer (Fomel, 2007a). At this point, thewarping function is just a new time scale i, like theone estimated with DTW; i.e., wðtÞ ¼ i ≈ t.

Quality control: The relative velocity changeBoth methods create a warping function wðtÞ that

maps the synthetic trace onto the seismic traces bythe following transformation: aðwðtÞÞ ≈ bðtÞ.

The base two-way traveltime is

t ¼ 2Z

H0

0

dzv0ðzÞ

; (11)

where voðzÞ is the base velocity as a function of depth zand H0 is the base depth, where base stands for refer-ence values. The warping path is related to the newvelocity v1ðzÞ by (Fomel and Jin, 2009)

wðtÞ ¼ 2Z

H1

0

dzv1ðzÞ

¼Z

tþΔt

0

v0ðτÞv1ðτÞ

dτ; (12)

where H1 is the depth in the well logs, voðtÞ, and v1ðtÞare the old and updated sonic velocities as a function oftime, and Δt is the time shift caused by the stretching orsqueezing Δt ¼ 2∫ H1

H0

dzv1ðzÞ.

The relative velocity change can be estimated by sim-ple differentiation of equation 12:

dwdt

≈v0ðtÞv1ðtÞ

: (13)

The warping function produced by the local similar-ity method has been smoothed by the shaping filters(Fomel, 2007b). In DTW, an additional interpolationstep is used to smooth out the discrete warping pathbefore computing the derivative.

In a perfect correlation, the estimated velocity ratioshould be close to one; i.e., the relative velocity changesdue to the nonlinear transformation produce good cor-relation and no velocity variations. These variations arequantified by the relative stretch measure sðtÞ ¼ wðtÞ∕t.Deviations of sðtÞ from one indicate possible misalign-ment and therefore velocity changes.

ExperimentsWe apply both approaches, DTW and LSIM, to obtain

well-seismic ties between observed seismic data andsynthetic traces created from well logs. The data setused in our experiment consists of a 3D poststack

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time-migrated seismic profile, with 13 wells and theircorresponding logs. This data set is provided as bench-mark seismic data within a commercial package(Hampson-Russell, 1999). Figure 1 shows a seismic sec-tion with one well at CDP 39. The well-seismic tie forthis well is shown in the inset figure. We scanned theseismic section to find the best matching location, fol-lowing White and Simm (2003), which isat CDP 41. The generated synthetictrace (red) and the corresponding seis-mic trace (blue) have been exportedfor postprocessing. The sampling rateis 500 Hz (2 ms), and both signals havethe same length; i.e., the seismic tracehas been shortened to the well loglength. Also, both signals have beenstandardized in amplitude. The initialsynthetic is created as the convolutionof the computed reflectivity from welllogs with a zero phase statistical wave-let. This zero phase wavelet is calculatedfrom the seismic amplitude spectrum(Hampson-Russell, 1999).

Figure 2a shows how the synthetic(upper trace) and seismic traces (lowertrace) match after constrained DTWwith a warping window r ¼ 10. Theoriginal (Figure 2a) and stretched ver-sions (Figure 2b) are shown. The DTWtechnique allows for one-to-many sam-ple connections in both directions. Notethat the original signals have 423 sam-ples and their stretched versions have527 samples. This new length comes

from mapping the initial time (length n) onto the warp-ing path (length k). The gray lines connecting individualtime samples are useful for quality control becausethey indicate time shifts between traces (forward orbackward slanting lines) and changes in the relativevelocity profiles (diverging or converging neighbor-ing lines).

Figure 1. Seismic section with study well annotated at CDP 39. The inset shows the synthetic seismogram with the initial manualcorrelation of 0.77 in the time window 800–1144 ms.

50 100 150 200 250 300 350 400−1

−0.5

0

0.5

1Original signals. Seismic trace (upper) and synthetic (bottom).

Nor

mal

ized

am

plitu

deSamples

50 100 150 200 250 300 350 400 450 500

−2

0

2

4Stretched signals

Nor

mal

ized

am

plitu

de

Samples

SeismicSynthetic

a)

b)

Figure 2. Illustration of the warping process using DTW. In panel (a), the seis-mic trace (upper signal) is connected to the synthetic trace (bottom signal)through gray lines representing connected time samples. Note the one-to-manyconnections in both directions; that is, the connecting lines have either positiveor negative slopes. The stretched versions of both signals shown in panel (b) arehighly correlated, but the number of samples is increased compared to the origi-nal signals.

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Visual inspection reveals that automatic matchingleads to physically acceptable results for points 260–420 in the original series (Figure 2 top), but likely ex-cessive stretching and squeezing have occurred inthe first 200 points and around point 250.

To avoid unrealistic connections, the original ob-served data and the synthetic are subjected to the con-strained DTW approach. We use a global constraintbased on the Sakoe-Chiba band (Sakoe and Chiba,1978), which constrains the alignmentprocess to a limited window. This re-duces the freedom of the warping pathto align events within a limited distance.The estimated warping path is shown inFigure 3, where we used r ¼ 10 samplesto limit the maximum amount of permit-ted point-to-point shifting. With a sam-pling rate of 2 ms, two peaks can thenstill be aligned even if they are 20 msapart. The relative velocity change isthen estimated by computing the deriva-tive of the smoothed warping path inFigure 3.

The LSIM performs an automaticsqueezing and stretching of the syn-thetic trace with respect to the seismictrace while computing the local correla-tion. This process leads to a local-simi-larity scan shown in Figure 4. The redcolor indicates high similarity, and fromthese pick values, we estimate the rela-tive stretch measure sðtÞ, represented asa black curve in Figure 4. This curve isalready the derivative of the warpingpath; thus, from equation 13 we cancompute the velocity ratio.

Figure 5a shows the relative stretch(dw∕dt) for both methods. The LSIM method (in blackbold) shows few variations, while the DTW result(dashed line) shows reliable stability in the bottom halfof the display, i.e., little change between the syntheticand the seismic trace. These variations are reflected inthe velocity changes shown Figure 5b. The originalsonic log (thick gray) is almost overlapped by the LSIMresult (black line), with little difference only at the ini-tial samples. DTW (dashed line), as expected, producesmore changes in the velocity curve in the areas wheremore stretching and squeezing was performed. It isknown that DTW will find the best match betweentwo events and improve the final correlation, but atthe cost of more velocity variations (Herrera and Vander Baan, 2014). Careful control of the warping windowshould be taken to avoid unrealistic changes, such asthe fluctuations in the shallower part, which could beamplified for wider warping windows.

In the final comparison, we perform a manual tie,following recommended practices in well-seismic tying(White and Simm, 2003; Anderson and Newrick, 2008).We first select a high-quality region of interest for the

synthetic and seismic trace where the correlation win-dow is placed. This region of interest comprises themain stratigraphic features and is situated where bothsignals are similar. In this case, the correlation windowis between 800 and 1144 ms; only a constant time shift isneeded in this region to reach the best match. Figure 6ashows that the correlation of the manual well-seismictie is 0.77 inside this window. The shallower portionof the manual tie shows little similarity and would

Figure 3. Constrained DTW. The warping path represented by the center line islimited by the warping window r ¼ 10 samples. Vertical and horizontal signalsare the seismic and synthetic traces, respectively.

Relative stretch

Sam

ples

Stretch/squeeze scan

0.9 0.95 1 1.05 1.1

50

100

150

200

250

300

350

400

Figure 4. Relative stretch LSIM. Local similarity scan fordetecting the warping function. Red indicates strong similar-ity. The black curve shows an automatically detected trend.

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require significant stretching and squeezing to obtainan acceptable fit; the global correlation including thisarea is 0.24. Because excessive stretching and squeez-ing are never recommended, we exclude this portionfrom the well tie, and we consider any automatedmatching in this portion as suspect for this reasonas well.

DTW corrected the simple time shifts observed in theanalysis window for the manual tie. It produces the bestpossible match in the shallower part with mostly rea-sonable velocity changes (less than 10%) except pos-sibly between 550 and 850 m. Inspection of therelative stretch variations as well as the updated localvelocities will reveal if and where the automated tyingprocedure has produced unrealistic stretching andsqueezing. Such areas can then be discarded, or thewarping window can be limited further. For the LSIMmethod, the local velocity variations are more stable.The correlation shows an actual improvement, consid-ering that the correlation in the entire trace can improvefrom 0.24 to 0.68 with little velocity change.

DiscussionWell-seismic ties are challenging due to the high

number of subjective decisions and pattern recognitiontasks involved. Proper selection of the analysis window,identification of major corresponding reflections in syn-thetic and seismic traces and connecting them by theappropriate amount of stretching and squeezing, and

accurate wavelet estimation are among these challeng-ing tasks (Herrera and Van der Baan, 2014). We stronglyadvise interpreters always to verify their results usingthe quality-control measures described in this article.In particular, unrealistic local velocity changes or rela-tive slowness perturbations are highly suspect, even ifthe final traces look perfectly matched.

In DTW, the warping window parameter should becarefully adjusted to satisfy the trade-off between goodmatching and reasonable alignment of events. This issimilar to controlling the amount of stretching andsqueezing in the manual method. This critical parameterkeeps the velocity curve limited to realistic values,which is similar to controlling the amount of stretchingand squeezing in the manual method. The controllingparameter in LSIM is the amount of regularization ofthe smoothing shaping filter along with the smoothingradius. In practice, start the method with strongsmoothing and decrease it when the results stop chang-ing and before they become unstable (Fomel andJin, 2009).

The LSIM method produced a better correlation withfew changes in the velocity pattern. The constrainedDTW method performed in good agreement with themanual method inside the correlation window, whichvalidates this approach. The matching outside this win-dow represents the best possible tie, but it is the veloc-ity variation that helps to identify when these changesare acceptable or not.

0.5 1 1.5

400

600

800

1000

1200

1400

1600

Relative stretch

Ver

tical

dep

th fr

om s

urfa

ce (

m)

DTWLSIM

2000 4000 6000

VP (m/s)

VPDTWLSIM

a) b)

Figure 5. Quality control. Relative stretch curves for LSIM(bold line) and DTW with r ¼ 10 (dashed line) are shownin (a). The local velocity change for LSIM (black line) andDTW (dashed line) together with the original sonic log (lightgray) are shown in (b). The LSIM velocity shows few varia-tions, whereas the DTW velocity has local variations due tothe warping process.

Manual methodCorrelation coefficient = 0.77

DTWCorrelation coefficient = 0.85

LSIMCorrelation coefficient = 0.68

1144800Time (ms)

500300

a)

b)

c)

Figure 6. Comparison of the automated approaches andmanual well-seismic ties. The manual tie with correlation of0.77 in the window 800–1144 ms is shown in (a), where thebold vertical lines indicate the correlation window. TheDTW output with a warping window r ¼ 10 is shown in(b); with this approach and using the full trace length, the cor-relation is 0.85. The LSIM output using the entire trace lengthas shown in (c) achieves a correlation of 0.68. In all displays,the upper signal is the seismic trace, the bottom signal isthe synthetic trace, and black arrows indicate correlativereflections.

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The methods vary in the matching criteria and ex-traction of the warping paths. DTW has one-to-many(point by point) sample matching, which causes issues.DTW finds the locally optimal path from point to point,but the LSIM method is allowed to jump across sequen-ces (it is locally nonoptimal). This causes more localstretching/squeezing in DTW.

Our general recommendations extend previousworks to the automatic approach (White and Simm,2003; Anderson and Newrick, 2008):

1) First, an appropriate wavelet is to be estimated.2) Then, choose the correct wavelet polarity.3) Next, apply a global bulk shift, for instance, via a

simple correlation; this precludes having large warp-ing windows in DTW and produces faster conver-gence in LSIM.

4) For DTW, slowly increase the length of the warpingwindow until the quality-control procedure indi-cates unrealistic stretching and squeezing results.

5) In LSIM, adjust the regularization parameter to gen-erate a smooth relative stretch curve controlling thedeviation from unity.

Wavelet estimation is a crucial step because it cangreatly affect the ease and quality of manual and semi-automated well tying. The wavelet power spectrum isgenerally best estimated using spectral averaging (Her-rera and Van der Baan, 2012b); however, this leads to azero-phase wavelet, which is likely nonoptimal. For theappropriate wavelet phase, we recommend the use ofkurtosis-based methods for constant-phase wavelets(Van der Baan, 2008) or short-time homomorphic wave-let estimation (Herrera and Van der Baan, 2012b) forfrequency-dependent wavelet phases. These methodsuse statistical means to obtain the wavelet estimates di-rectly from the data and have been shown to be reliableeven for relatively low signal-to-noise ratios (Edgar andVan der Baan, 2011; Herrera and Van der Baan, 2012b).

Regarding the selection of wavelet polarity, our rec-ommendation is to compute a crosscorrelation betweenthe synthetic and observed trace first to check if there isa significant difference in the absolute value betweenthe most positive and most negative correlation coeffi-cients. If not, we suggest running the algorithm with thenormal and reverse polarity and compare both outputstaking into account the effects on the velocity changes.The best tie connects reflectors with the same polarityand produces meaningful velocity changes (Herreraand Van der Baan, 2014).

Both automatic approaches compared here forwell-seismic tying are good candidates for otherapplications in seismic data. These include log-to-logcorrelations and alignment of baseline and monitorsurveys in 4D seismic data (Fomel and Jin, 2009;Hale, 2013). PP- and PS-wavefield registration for 3Cdata (Gaiser, 1996) is another field to explore withDTW because LSIM has already shown good results(Fomel, 2007a).

ConclusionsThe twomethods compared in the paper aim to guide

the interpreter by supporting standard methodologiesof well-seismic tying, but we strongly advocate inter-preters to be wary of fully automated and nonsuper-vised applications of these methods. Velocity changesand visual quality control of the end result remainhighly advisable. Although fitting all the reflections isa mathematical goal because real seismic and well in-formation can contain spurious data, it is still left tothe interpreter’s judgment as to which reflections canbe reliably correlated to well data. For example, low-amplitude, discontinuous reflections on the seismicmay contain significant noise that masks weak events,and consequently whether these reflections have agood or poor well tie is moot. Similarly, logging toolsmay make erroneous measurements; consequently, acalculated synthetic reflection may have no counterpartin the real seismic section.

The main advantage of using automatic approachesis their objective repeatability and reproducibility of thetying process. Both automated methods create superiormatches over the manual method and with just a fewtuning parameters. The integration of the automaticwell-seismic tie with the traditional method reduces in-terpreter bias and other subjective factors. The robust-ness of the tying process is improved in this guidedframework. The interpreter should expect to see theseautomatic approaches integrated into the processingsoftware in the near future.

AcknowledgmentsR. H. Herrera and M. Van der Baan thank Hampson-

Russell for software licensing and the sponsors of theBlind Identification of Seismic Signals (BLISS) projectfor their financial support. S. Fomel thanks the Bureauof Economic Geology, The University of Texas at Aus-tin, for authorizing the publication of his results. Wealso thank the three reviewers: J. Sumner for the pos-itive comments, R. Newrick for the in-depth revisionand challenging questions, and D. Herron for the de-tailed review and helpful comments that helped shapethis article. Suggestions from the associate editor, R.Wegner, made a significant improvement in the conclu-sions of this paper.

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Fomel, S., 2007b, Shaping regularization in geophysical-estimation problems: Geophysics, 72, no. 2, R29–R36,doi: 10.1190/1.2433716.

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Roberto H. Herrera received a B.S.and M.S. in electronics and telecom-munications and a Ph.D. in signalprocessing from UCLV, Cuba. Since2010 he has been working on the BlindSeparation of Seismic Signals (BLISS)project and the Microseismic IndustryConsortium at the University of Al-berta, Canada. His research interests

include statistical signal processing, exploratory dataanalysis, time-frequency transforms and pattern recogni-tion. He serves as reviewer for GEOPHYSICS, GeophysicalJournal International, and Journal of Applied Geophys-ics. He is a member of CSEG, AGU, EAGE, and IEEE.

Sergey Fomel received a Ph.D.(2001) in geophysics from StanfordUniversity and worked previously atthe Institute of Geophysics in Russia,Schlumberger Geco-Prakla, and theLawrence Berkeley National Labora-tory. He is a professor at the JacksonSchool of Geosciences, the Universityof Texas at Austin, with a joint ap-

pointment between the Bureau of Economic Geologyand the Department of Geological Sciences. He has re-ceived a number of professional awards, including the J.Clarence Karcher Award from SEG in 2001 and the ConradSchlumberger Award from EAGE in 2011. He devotes partof his time to developing "Madagascar," an open-sourcesoftware package for geophysical data analysis.

Mirko van der Baan received adegree (1996) from the Universityof Utrecht, the Netherlands, and aPh.D. (honors) (1999) from the Jo-seph Fourier University in Grenoble,France, and an HDR (Habilitation)from University Denis Diderot, Paris,France. He then joined the Universityof Leeds, UK, where he became the

reader of exploration seismology. He is a professor atthe University of Alberta in the Department of Physics, spe-cializing in exploration seismology. He is the principal

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investigator of the joint-industry projects on Blind Identi-fication of Seismic Signals, focusing on advanced statisti-cal signal processing and technology/knowledge transferto the hydrocarbon industry; and the Microseismic Indus-try Consortium, a collaborative venture with the Universityof Calgary, dedicated to research in microseismicity. He is

also a co-founder of the Centre of Integrated PetroleumEngineering and Geosciences, a joint initiative of severaldepartments at the University of Leeds, UK, to fosterand promote multidisciplinary petroleum-related researchand teaching. He is a member of the editorial board ofGEOPHYSICS and SEG’s research committee.

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