Improving the quality of prestack inversionby prestack data conditioning

Bo Zhang1, Deshuang Chang2, Tengfei Lin1, and Kurt J. Marfurt1

Abstract

Prestack seismic inversion techniques provide valuable information of rock properties, lithology, and fluidcontent for reservoir characterization. The confidence of inverted results increases with increasing incidentangle of seismic gathers. The most accurate result of simultaneous prestack inversion of P-wave seismic datais P-impedance. S-impedance estimation becomes reliable with incident angles approaching 30°, whereas den-sity evaluation becomes reliable with incident angles approaching 45°. As the offset increases, we often encoun-ter “hockey sticks” and severe stretch at large offsets. Hockey sticks and stretch not only lower the seismicresolution but also hinder long offset prestack seismic inversion analysis. The inverted results are also affectedby the random noises present in the prestack gathers. We developed a three-step workflow to perform dataconditioning prior to simultaneous prestack inversion. First, we mitigated the hockey sticks by using an auto-matic nonhyperbolic velocity analysis. Then, we minimized the stretch at the far offset by using an antistretchworkflow. Last, we improved the signal-to-noise ratio by applying prestack structure-oriented filtering. Weevaluated our workflow by applying it to a prestack seismic volume acquired over the Fort Worth Basin, Texas,USA. The results inverted from the conditioned prestack gathers have higher resolution and better correlationcoefficients with well logs when compared to those inverted from conventional time-migrated gathers.

IntroductionSimultaneous prestack inversion (Hampson et al.,

2005) provides estimation of acoustic impedance (Zp),shear impedance (Zs), and density. Zhang et al. (2013b)obtain the P-wave velocity, S-wave velocity, and densityfrom prestack seismic data analysis. Those kinds of es-timations represent the intrinsic rock properties andare commonly used for predicting fluid, lithology,and geomechanical properties. Improving the data qual-ity of the prestack seismic gathers is key to obtainingreliable impedance and density estimations. The mainfactors that affects the data quality in the prestack gath-ers include (1) “hockey sticks” in the long offset seismicsurveys, (2) normal moveout (NMO)/migration stretch,and (3) random noise.

Hockey sticks arise in the long offset of prestackgathers when we do not account for the effects ofanisotropy (Alkhalifah, 1997; Fomel and Stovas, 2010)and heterogeneity (Taner and Koehler, 1969; de Baze-laire, 1988) in seismic processing. To mitigate thehockey stick at large offset, we need to perform nonhy-perbolic velocity analysis using a proper traveltimeequation. The conventional nonhyperbolic velocityanalysis (CNVA) first estimates the NMO velocity

Vnmo on offset-limited gathers using a hyperbolic NMOcorrection, then it picks effective anellipticity ηeff usingthe full-offset gathers. CNVA produces estimated modelof Vnmo and ηeff on a coarse grid of supergathers. Themodel at other common midpoint (CMP) gathers are in-terpolated from those at manually picked grids. How-ever, there is no guarantee that the interpolatedvelocity model is correct for all CMPs. Another disad-vantage of CNVA is that small-aperture Vnmo analysismay be inaccurate. Picking errors in Vnmo introduceserrors into the subsequent analysis of ηeff . Unfortu-nately, simultaneously manual picking of Vnmo andηeff at every CMP location is time consuming and tedi-ous. In this paper, we use an automatic nonhyperbolicvelocity analysis (Zhang et al., 2014) to mitigate thehockey stick in the long offset.

Migration and NMO corrections are conducted sam-ple by sample, which results in the well-known de-crease in frequency content and amplitude distortionthrough stretch at far offset. To avoid the effects of seri-ous stretch associated with large offsets, we usuallymute the farther offsets based on a user-defined stretchcriterion. Muting of large offset not only lowersthe stacking power, it also reduces the accuracy and

1The University of Oklahoma, ConocoPhillips School of Geology and Geophysics, Norman, Oklahoma, USA. E-mail: bo.zhang-1@ou.edu;kmarfurt@ou.edu; tengfei.lin@ou.edu.

2Fromerly BGP Inc., China National PetroleumCompany, Zhuozhou, Hebei, China; presently The University of Oklahoma, ConocoPhillips Schoolof Geology and Geophysics, Norman, Oklahoma, USA. E-mail: cds881@sina.com.

Manuscript received by the Editor 23 June 2014; published online 5 December 2014. This paper appears in Interpretation, Vol. 3, No. 1 (February2015); p. T5–T12, 7 FIGS.

http://dx.doi.org/10.1190/INT-2014-0124.1. © 2014 Society of Exploration Geophysicists and American Association of Petroleum Geologists. All rights reserved.

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Technical paper

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vertical resolution of prestack inversion for shearimpedance and density. Roy et al. (2005) propose ana-lytic correction for wavelets stretch due to imaging.Downton and Ursenbach (2006) propose AVO inversionby considering the stretch at large offset. Zhang et al.(2013a) develop a wavelet-based algorithm namedmatching pursuit NMO (MPNMO) to minimize thestretch at large offset. Their algorithm first applies re-verse NMO, which “resqueezes” the migration stretch ofthe time-migrated gathers, and then conducts a wavelet-based NMO correction on the reverse NMO gathers. Weapply their algorithm to minimize the stretch after hav-ing computed Vnmo and ηeff using automatic nonhyper-bolic velocity analysis.

The seismic signal is almost always contaminatedwith noise. To mitigate this undesired component ofseismic data, we assume that proper filters have alreadyrejected the coherent noise (such as multiples) and thatthe remaining “noise” is random prior to applying ourdata conditioning workflow. If we assume that the noiseand reflected signals are uncorrelated, then we can de-compose the prestack gathers into signal and noiseparts by principal component analysis (PCA) (Keyand Smithson, 1990) along the structural dip.

In this paper, we present a three-step workflow toperform prestack seismic data conditioning prior toprestack inversion. First, we mitigate the hockey sticksby using an automatic nonhyperbolic algorithm. Wethen minimize the stretch at large offset using an anti-stretch procedure. Finally, we improve the signal-to-noise ratio (S/N) by applying prestack-oriented filtering.The workflow is validated on a seismic data volume ac-quired over the Fort Worth Basin (FWB), Texas, USA.

Strategies to improve the data quality at far offsetTo use the critical information contained in the long-

offset data for prestack inversion, we need to (1) flattenthe reflections at the large offset using a nonhyperbolictraveltime equation, (2) minimize the stretch typicallyassociated with large offset, and (3) improve the S/Nby prestack structure-oriented filtering (PSOF).

Mitigating the hockey stick using automaticnonhyperbolic velocity analysis

To mitigate the hockey stick associated with thelarge offset and anisotropy, we apply an automatic non-hyperbolic velocity analysis algorithm (Zhang et al.,2014). Zhang et al. (2014) use a nonhyperbolic travel-time equation (Alkhalifah, 1997) to automatically findan interval model m such that the NMO velocity Vnmoand effective anellipticity ηeff derived from that modelgive the maximal stacking power. The model m of thealgorithm consists of the interval NMO velocity vnmoand instantaneous (interval) anisotropy ηint parameters.The workflow uses a genetic differential evolutionary(DE) algorithm to find the best model that can mitigatethe hockey stick at large offset. Our input data consistof prestack time-migrated CMP gathers, the initial mi-gration velocity, and interpreted horizons. The outputs

are flattened gathers, a model of interval velocity andanellipticity that best flatten the gathers. The prestacktime-migrated gathers are subjected to a reverse NMOusing the migration velocity. The horizons are manuallyinterpreted on an offset-limited stack of the migratedgathers and are used to parameterize the intervalmodel. The algorithm starts by building an initial inter-val velocity model from the migration velocity and set-ting the initial anellipticity model to zero, then itgenerates a suite of alternative models. Next, the modelundergoes DE mutation and crossover to generate a setof new trial interval models. The algorithm estimatesthe objective function for each model. Better modelssurvive into the next generation. We repeat generatingand evaluating the new models until all the reflectionevents are flattened or convergence slows down.

Minimizing the stretch at far offsetThe conventional NMO correction, which processes

the data sample-by-sample, results in the well-knowndecrease in frequency content and amplitude distortionthrough stretch. The NMO-uncorrected traces dðtÞ canbe regarded as the convolution of the seismic waveletwith the reflectivity series and added noise as

dðtÞ ¼ rðtÞ �wðtÞ þ nðtÞ; (1)

where rðtÞ is the reflectivity series, wðtÞ is the wavelet,and nðtÞ is the noise. This classic theory suggests thatNMO correction can be implemented on a wavelet-by-wavelet basis, with the moveout applied to thereflection events rðtÞ rather than to the data samplesdðtÞ. Zhang et al. (2013a) achieve this goal by usingan algorithm named MPNMO. Our input data consist ofprestack time migrated seismic gathers dðt; xnÞ afterperforming reverse NMO using the migration velocityfunction. The output is the nonstretch NMO-correctedgathers.

Improving S/NBy assuming that (1) coherent noise have been fil-

tered using proper filters, (2) noise and reflected signalsare uncorrelated with zero mean, and (3) noise is uncor-related from trace to trace and sample to sample, Keyand Smithson (1990) conclude that the first few eigen-values and eigenvectors of the covariance matrix of pre-stack seismic gathers represent the coherent reflectionsignals. Based on this assumption, we apply a PSOFbased on PCA to the seismic gathers to improve theS/N. The workflow begins by calculating the reflectors’dip in a running window on all traces of the stackedvolume (Marfurt, 2006). Then, we estimate the correla-tion coefficients for the stack volume along the localreflection dip (Gersztenkorn and Marfurt, 1999). Next,we extract the reflection signal whose correlation coef-ficients are greater than a user-defined threshold throughthe first eigenvalue and eigenvector of seismic covari-ance matrix. The signals whose correlation coefficients

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are less than the threshold do not undergo any process-ing, thereby preserving potential discontinuities.

Prestack seismic data conditioning workflowFigure 1 summarizes the proposed workflow for im-

proving the data quality contained the large offset. Ourinput data consist of prestack time-migrated gathersand the initial migration velocity Vnmo 0. The initial ef-fective anellipticity ηeff is set to zero. We obtain theinitial migration velocity by performing hyperbolicvelocity analysis on coarse grid supergathers. Theworkflow begins by performing reverse NMO on thetime-migrated gathers using the initial migration veloc-ity. Then, we obtain the optimal velocity and anelliptic-ity model using our automatic algorithm. Next, we applyMPNMO to the time-migrated gathers using new veloc-ity and anellipticity model resulting in flattened non-stretched prestack gathers. Last, we apply PSOF tofurther improve the S/N. In this manner, stacking powerand vertical resolution are improved first by aligning thedata and second by avoiding stretch.

ApplicationTo evaluate the data quality processed by our work-

flow, we first apply it to prestack time-migrated gathersacquired in the FWB. We then compare the prestack in-verted results computed from conventional migratedafter muting and new conditioned gathers. The FWB isa foreland basin and covers approximately 54;000 mi2

in north-central Texas (da Silva, 2013). The target isthe Mississippian Barnett Shale, which is one of thelargest unconventional reservoir in the world andspreads approximately 28,000 square miles across theFWB. In our survey, the core or main production areain the Barnett Shale Formation lies between 1.2 and1.4 s. The maximum offset is approximately 4267.2 m(14,000 ft), whereas the target Barnett Shale lies at ap-proximately a 7000-ft depth, implying a maximum inci-dence angle of approximately 45°.

Figure 2a shows a representative time-migrated CMPgather using a two-term hyperbolic traveltime equation.Note the hockey stick and stretch indicated by whitearrows at the far offset. To avoid the effect of seriousstretch, we usually mute those serious stretched dataaccording to a user-defined criterion. Figure 2b showsthe muted gather in which the wavelet is not allowed tostretch more than 130%. By combining the NMO veloc-ity Vnmo and effective anellipticity ηeff , nonhyperbolicvelocity analysis can mitigate the hockey stick butnot the stretch at the far offset (Figure 2c). Figure 2dshows the flattened nonstretch gather. Note thatMPNMOminimizes the stretch that occurs at the far-off-set data when compared to the original time-migratedgathers. Figure 2e and 2f shows the same gather afterapplying PSOF and the rejected random noise, respec-tively.

P-impedance is the most reliable result from pre-stack inversion. S-impedance estimation becomes reli-able when the incidence angle reaches 30°, whereas

density becomes reliable when the angle approachesto 45°. By applying the proposed workflow, more far-offset data (Figure 2e) are available for the subsequentprocessing and inversion. We apply simultaneous pre-stack inversion to the conventional (Figure 2b) andnew conditioned (Figure 2e) gathers. We first extractthree angle-range (0°–12°, 12°–24°, and 24°–36°)-depen-dent statistical wavelets for the conventional-migrated(Figure 3a) and the conditioned (Figure 3b) data afterthe seismic-well tie. The red, blue, and green lines showthe extracted small- (0°–12°), intermediate- (12°–24°),and large-angle wavelets (24°–36°), respectively. Notethat the large-angle wavelet extracted from the time mi-gration is distorted to some extent. To better comparethe improvements, we show the amplitude spectrum ofthe extracted wavelets from the time-migrated and con-ditioned gathers in Figure 3c and 3d. Due to the increas-ing stretch with increasing incidence angle in the time-migrated gathers, the spectral bandwidth (the blue andgreen lines in Figure 3c) of the intermediate- and large-angle wavelets are distorted and narrower than thatof the small-angle wavelet (the red line in Figure 3c).However, the proposed conditioning workflow pre-serves the spectral bandwidth of the intermediate-and large-angle (the blue and green lines in Figure 3d).Another factor responsible for the narrower bandwidthof large-angle wavelet is that we applied low-pass anti-aliasing filters to the far-offset data internal to thetime migration algorithms (Biondi, 2001). Figures 4–6

Figure 1. Flowchart showing the three data condition-ing steps to improve the data quality of prestack gathers:(1) automatic nonhyperbolic velocity analysis, (2) applyingantistretch processing on the time-migrated gathers, and(3) prestack structure-oriented filtering.

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compare the inverted P-impedance, S-impedance, anddensity from the conventional and long offset preservedgathers. The well track in those figures is indicated bythe gray arrow. It was used for quality controlling theinversion results. We observe an overall improvementby including the long offsets, especially for the invertedS-impedance. For example, the formations indicated bythe white arrow in the new inverted results from con-ditioned data are more laterally continuous comparedto those from of conventional data. The zones indicatedby dark arrows in the new data have higher resolutioncompared to those of conventional data. These im-provement are due to our ability to preserve the fre-quency content for wavelet in the mid and far offsets,

in particular. To better see the improvement, we qualitycontrol our inverted results from (Figure 7a) time-migrated and (Figure 7b) conditioned gathers with welllogs at the target zone. The left, middle, and right tracksshow the P-impedance, S-impedance, and density pan-els, respectively. The black, blue, and red curves indi-cate the initial model, the original well logs, and theinverted results. The blue curves in Figure 7a and 7bare from the well logs, and the red curves are fromthe inverted results. Note that we have obvious im-provements in the zone indicated by the red arrows.The new inverted results show a better correlation withthe original well logs. The improvement of density is notas good as those of the P- and S- impedances. This is

Figure 2. Representative gather showing theprocessing steps shown in Figure 1. (a) Thetime-migrated gather from the conventionalprocessing. (b) The same gather after apply-ing 130% stretch mute. (c) The correctedgather using rms velocity and effective anel-lipticity obtained from automatic nonhyper-bolic velocity analysis. (d) The antistretchprocessing result applied to (a) using thenew rms velocity and effective anellipticity.(e) The S/N improved gathers applied to(d) using the PSOF. (f) The rejected randomnoise.

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Figure 3. Three angle-range-dependent statistical extracted wavelets from (a) the time-migrated and (b) the conditioned anglegathers. (c) The corresponding amplitude spectra of wavelet shown in Figure 3a. (b) The corresponding amplitude spectra ofwavelets shown in Figure 3b. The red, blue, and green curves indicate the small (0°–12°), intermediate (12°–24°), and large-angle(24°–36°) wavelets and spectra. Note the wavelets extracted from conditioned gathers have high-frequency components comparedwith those of time-migrated gathers.

Figure 4. Comparison of inverted P-imped-ance from (a) conventional and (b) precondi-tioned gathers. The white arrows indicate theformations in which the new inverted result ismore laterally continuous compared to that ofconventional data. The black arrows indicatethe zone in which we have higher resolution.The gray arrow indicates the well track filledwith the P-impedance log.

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Figure 5. Comparison of inverted S-imped-ance from (a) conventional and (b) precondi-tioned gathers. The white arrows indicate theformations in which the new inverted result ismore laterally continuous compared to that ofconventional data. The black arrows indicatethe zone in which we have higher resolution.The gray arrow indicates the well track filledwith S-impedance log.

Figure 6. Comparison of inverted densityfrom (a) conventional and (b) preconditionedgathers. The white arrows indicate the forma-tions in which the new inverted result is morelaterally continuous compared to that of con-ventional data. The black arrows indicate thezone in which we have higher resolution. Thegray arrows indicate the well track filled withdensity log.

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because the maximum incidence angle of our gather isapproximately 36° and it is beyond the inversion algo-rithm’s capability to generate a reliable result.

ConclusionImproving the data quality of prestack gathers, espe-

cially the information contained in the large offsets, is

critical to obtaining a reliable prestack inverted results.The main tasks include (1) mitigating the hockey stickusing high-resolution automatic nonhyperbolic velocityanalysis, (2) minimizing the stretch introduced by con-ventional NMO correction/migration, and (3) improvingthe S/N by applying proper filters. By combining all ofthe processing, the proposed workflow maintains thefrequency content of wavelets and rejects unwantedrandom noise through the small intermediate and largeangles. Thus, the more information is available for sub-sequent inversion, the more accurate are the invertedresults. The prestack inverted results based on thenew conditioned gathers not only show higher resolu-tion but also exhibit a better match to the original welllogs due to critical information contained in the faroffset.

AcknowledgmentsThe authors would like to thank Devon Energy for

providing the data and CGG for providing the licensesfor Hampson-Russell for use in research and education.We thank the sponsors of the Attribute-Assisted SeismicProcessing and Interpretation (AASPI) Consortium fortheir guidance and financial support. Our gratitude alsogoes to editor Yonghe Sun, associate editor John O’Brien,and three anonymous reviewers.

ReferencesAlkhalifah, T., 1997, Seismic data processing in vertically

inhomogeneous TI media: Geophysics, 62, 662–675,doi: 10.1190/1.1444175.

Biondi, B. L., 2001, Kirchhoff imaging beyond aliasing:Geophysics, 66, 654–666, doi: 10.1190/1.1444956.

da Silva, M., 2013, Production correlation to 3D seismicattributes in the Barnett Shale, Texas: M.S. thesis,The University of Oklahoma.

de Bazelaire, E., 1988, Normal moveout revisited: Inhomo-geneous media and curved interfaces: Geophysics, 53,143–157, doi: 10.1190/1.1442449.

Downton, J. E., and C. Ursenbach, 2006, Linearized ampli-tude variation with offset (AVO) inversion with super-critical angles: Geophysics, 71, no. 5, E49–E55, doi:10.1190/1.2227617.

Fomel, S., and A. Stovas, 2010, Generalized nonhyperbolicmoveout approximation: Geophysics, 75, no. 2, U9–U18, doi: 10.1190/1.3334323.

Gersztenkorn, A., and K. J. Marfurt, 1999, Eigenstructure-based coherence computations as an aid to 3-D struc-tural and stratigraphic mapping: Geophysics, 64,1468–1479.

Hampson, D. P., B. H. Russell, and B. Bankhead, 2005,Simultaneous inversion of pre-stack seismic data: 75thAnnual International Meeting, SEG, Expanded Ab-stracts, 1633–1636.

Key, S., and S. B. Smithson, 1990, New approach to seismic-reflection event detection and velocity determination:Geophysics, 55, 1057–1069, doi: 10.1190/1.1442918.

Figure 7. Quality control of the inverted results using origi-nal well logs. The left, middle, and right panels show the P-impedance, S-impedance, and density logs. The black, blue,green, and red curves show the original logs, initial model,and inverted results from conventional and preconditionedgathers. Red arrows indicate the zone in which we have ob-vious improvement.

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Marfurt, K. J., 2006, Robust estimates of 3D reflectordip: Geophysics, 71, no. 4, P29–P40, doi: 10.1190/1.2213049.

Roy, B., P. Anno, R. Baumel, and J. Durrani, 2005, Analyticcorrection for wavelet stretch due to imaging: 75th An-nual International Meeting, SEG, Expanded Abstracts,234–237.

Taner, M. T., and F. Koehler, 1969, Velocity spectra: Digitalcomputer derivation and application of velocity func-tions: Geophysics, 34, 859–881, doi: 10.1190/1.1440058.

Zhang, B., K. Zhang, S. Guo, and K. J. Marfurt, 2013a, Non-stretching NMO correction of prestack time-migratedgathers using a matching-pursuit algorithm: Geophys-ics, 78, no. 1, U9–U18, doi: 10.1190/geo2011-0509.1.

Zhang, B., T. Zhao, J. Qi, and K. J. Marfurt, 2014, Horizon-based semi-automated nonhyperbolic velocity analysis:Geophysics, 79, no. 6, U15–U23, doi: 10.1190/geo2014-0112.1.

Zhang, R., M. Sen, and S. Srinivasan, 2013b, A prestackbasis pursuit seismic inversion: Geophysics, 78, no. 1,R1–R11, doi: 10.1190/geo2011-0502.1.

Bo Zhang received a B.S. (2002) fromthe China University of Petroleum(Huadong) and an M.S. in geophysics(2006) from the Institute of Geologyand Geophysics, Chinese Academy ofSciences. In 2009, Zhang joined the in-dustry-supported consortium (AASPI)at the University of Oklahoma as aPh.D. student in geophysics. In 2014,

he joined Michigan Technological University as a visitingassistant professor. His current research activity includes

broadband seismic data processing, development and cal-ibration of new seismic attributes, pattern recognition ofgeologic features on 3D seismic data, and shale resourceplay characterization.

Kurt. J. Marfurt began his geophysi-cal career teaching geophysics andcontributing to an industry-supportedconsortium on migration, inversion,and scattering (project MIDAS) atColumbia University’s Henry KrumbSchool of Mines in New York City.In 1981, he joined Amoco’s Tulsa Re-search Center and spent the next 18

years leading research efforts in modeling, migration, sig-nal analysis, basin analysis, seismic attribute analysis,reflection tomography, seismic inversion, and multi-component data analysis. In 1999, he joined the Universityof Houston as a professor in the Department of Geosci-ences and as director of the Allied Geophysics Laborato-ries. He is currently a member of the Geophysical Societiesof Tulsa and Houston, SEG, EAGE, AAPG, AGU, and SIAM,and he serves as an assistant editor for GEOPHYSICS. His cur-rent research activity includes prestack imaging, velocityanalysis and inversion of converted waves, computer-as-sisted pattern recognition of geologic features on 3D seis-mic data, and interpreter-driven seismic processing. Hisresearch interests are in seismic signal analysis, 3D seismicattributes, seismic velocity analysis, subsurface imaging,and multicomponent data analysis.

Biographies and photographs of the other authors arenot available.

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