Interpretation. Noise suppression of time migrated gathers using structure oriented filtering

Transcription

1 Noise suppression of tie igrated gathers using structure oriented filtering Journal: Manuscript ID: Draft Manuscript Type: 0-0 Seisic data conditioning Date Subitted by the Author: n/a oplete List of Authors: Zhang, Bo; The University of Alabaa, The Departent of Geological Sciences Lin, Tengfei; University of Oklahoa, School of Geology and Geophysics Guo, Shiguang; University of Oklahoa, School of Geology and Geophysics Davogustto ataldo, Oswaldo; Shell Exploration and Production opany, US Onshore Regional Marfurt, Kurt; University of Oklahoa, ollege of Earth and Energy; Keywords: filtering, gathers, inversion, K-L transfor, noise Subject Areas: Reservoir characterization/surveillance, Aplitudes, attributes, and subsurface properties

2 Page of Noise suppression of tie igrated gathers using prestack structure oriented filtering Bo Zhang, Tengfei Lin, Shiguang Guo, Oswaldo E. Davogustto, and Kurt J. Marfurt, The University of Alabaa, Departent of Geological Sciences, The University of Oklahoa, onocophillips School of Geology and Geophysics, bzhang@ua.edu, tengfei.lin@ou.edu beiergo@ou.edu, dellpi@e.co, and karfurt@ou.edu orresponding author: Kurt J. Marfurt The University of Oklahoa, onocophillips School of Geology and Geophysics Sarkeys Energy enter 00 East Boyd Street Noran, OK karfurt@ou.edu

3 Page of ABSTRAT Prestack seisic analysis provides inforation on rock properties, lithology, fluid content, and the orientation and intensity of anisotropy. However such analysis deands high-quality seisic data. Unfortunately there are always noise present in seisic data even after careful processing. Noise in the prestack gathers ay not only containate the seisic iage thereby lowering the quality of seisic interpretation, but ay also bias the seisic prestack inversion for rock properties such as acoustic and shear ipedance estiation. oon post-igration data conditioning includes running window edian and Radon filters applied to the flattened coon reflection point gathers. In this paper we cobine filters across offset and aziuth with edge-preserving filters along structure to construct a true D filter that preserves aplitude, thereby preconditioning the data for subsequent quantitative analysis. We illustrate our workflow by applying it to a prestack seisic volue acquired over the Fort Worth Basin (FWB), TX. The inverted results fro noise suppressed prestack gathers have noticeable iproveent when copared to those inverted fro conventional tie igrated gathers. LIST OF KEYWORDS Prestack inversion, Noise, Filtering

4 Page of INTRODUTION During the past decade, poststack structure-oriented, edge-preserving filtering has led to iproved data continuity, providing sharper fault edges, and the iproved perforance of autoated picking. Such poststack igrated seisic data can provide excellent iage of the subsurface structure and stratigraphy. More quantitative interpretation products such as siultaneous prestack inversion provide estiation of acoustic ipedance (Z P ), shear ipedance (Z S ), and density, while prestack aplitude vs. aziuth analysis (AVAz) provide easures of the orientation and strength of subsurface anisotropy. The quality of estiated properties is highly depend on the data quality of prestack seisic data. Since stacking it itself a filter, it is obvious that noise that containates poststack data is equal or stronger on prestack seisic gathers. The undesired prestack seisic phenoena need to be diinished or reoved prior to reservoir characterization (Singleton, 00). Although there has been considerable work on residual velocity analysis and tried statics, ost publications on reducing crosscutting noise on seisic gathers has been liited to processing across offset, one gather at a tie. Structure oriented filtering is one of ost popular processes to iprove the quality of poststack seisic iage. Bilateral filters were initially used for soothing photographic iages while preserving edges (Toasi and Manduchi, ). However, bilateral filters cannot directly be applied to seisic iages, since seisic edges differ significantly fro those in photographic iages (Hale, 0). Weickert () enhanced the continuity of coherent reflections while preserving lateral discontinuities such as chaotic structures and faults using an anisotropic diffusion filter. Luo et al. (00) eployed a ultiwindow Kuwahara filter to achieve the sae

5 Page of purpose, where they coputed the ean and variance in a suite of overlapping windows containing the sae analysis point. The output was then set to the ean of the window having the sallest variance. Fehers and Höcker (00) coputed structural dip and chaos (a coherence like easure) using the gradient structure tensor. If the chaos was below a threshold, the data were sooth anisotropically along structure, while if the chaos was large, such as about a fault, the data were left unchanged. AlBinHassan et al. (00) generalized Luo et al. s (00) algorith to used general D one-sided and centered soothing operators. Marfurt (00) built on the Kuwahara concept by using coherence rather than variance to choose the ost coherent window, followed by increasing the statistical leverage against noise by applying a D Karhunen Loeve (principal coponent) filter to the data along structural dip. Whitcobe et al. (00) and Helore (00) introduced frequency dependent, structurally conforable filters. Wang et al. (00) also noticed that the local reflector dip depends on the frequency band of the seisic data, and suppressed seisic noise using a suite of band passed structure-oriented filters. Liu et al. (00) reduced rando noise while protect structural inforation by cobining structural prediction with either ean filtering or lower-upper-edian (LUM) filtering, using plane-wave destructors to estiate reflector dip. orrao et al. (0) also used a structureoriented LUM filters, and showed how it provided greater control over noise rejection over ore coon ean and edian filters. Hale (0) applied bilateral filters to perfor edgepreserving soothing for seisic iages by replacing the doain kernel of bilateral filter with a soothing filter. Like Fehers and Höcker (00), their anisotropic soothing filter is based on the gradient structure tensor.

6 Page of The traditional way of reoving rando noise with a Gaussian distribution is to stack the data (Hendrickson, ). However prestack analysis require prestack seisic gathers or liited stacked gathers. Prestack noise suppression is an iportant but inadequately-solved proble in seisic processing. It is iportant for iproving aplitude variation with offset (AVO) and aziuthal (AVAZ) analysis. astagna and Backus () showed that noise in the prestack gathers could bias or corrupt the reflectivity variation with offset. abois () stated that background trend observed fro AVO crossplots can be indicator of rock properties or a noise trend. Hendrickson () noticed that AVO crossplot fro Auger Field and rando noise share siilar features which indicate that the observed background AVO trend can be just noise. abois (000) further found that noise in the P-wave seisic data ay changes the fors of wavelets variation with offset and bias the estiation of rock properties. Si et al (000) found that rando noise can be a principle coponent of noise on AVO crossplots. Buland and Ore (00) found that both AVO inversion and the wavelet estiation depend on the noise covariance. Koza and astagna (00) concluded that rando noise ay rotate the trend of AVO crossplots and obscure the petrophysics properties. They tried to reove the noise by applying a Radon filter. Hennenfent and Herrann (00) presented a ethod to stabilize the three ter AVO inversing by denoising the prestack gathers using curvelet and wavelet transfors. Li and ouzens (00) designed a tie-frequency adaptive noise suppression to isolate and attenuate localized high aplitude noise in prestack seisic data. In this paper, we present a workflow to perfor structure-oriented filtering on prestack seisic data prior to siultaneous prestack inversion. We begin by describing the ethodology,

7 Page of whereby we filter not only along offset (and when present, aziuth), but also in the inline and crossline direction along structural dip. We evaluate the effect of principal coponent filtering on prestack inversion by applying it to a high fold seisic data volue acquired over the Fort Worth Basin, TX. Finally, we show the value of applying a nonlinear LUM filter to a legacy data set acquired over a Mississippi Lie play, where the filter fors part of a preconditioned least-squares igration workflow. METHODOLOGY Attenuation of noise and enhanceent of structural continuity can significantly iprove the quality of seisic interpretation and stabilize the rock properties estiation by prestack analysis. As the nae iplies, the key steps for structure-oriented filtering are the accurate estiation of reflector dip followed by the application of a filter. In our application, we use a variation of the dip-scan estiation of reflector dip described by Marfurt (00). Other accurate eans of estiating reflector dip include the gradient structure tensor (as used by Fehers and Hoeker, 00), consistent dip by crosscorrelating in a circuitous anner (Aarre et al., 0), and plane wave destructor ethods that are siilar to a lateral predictive deconvolution (Liu et al., 00). In ters of filtering, the ore coon ethods include ) ean filtering, ) edian filtering, ) a-tried ean filtering, )lower-upper-edian (LUM) filtering and ) principal coponent (or Karhunen Loeve) filtering. For the first four ethods, the filters are based on a single length-j saple vector (actually a plane) oriented along a plane following reflector dip (Figure a). The ean filter is siply

8 Page of d ean = J J j= d j, where is the tie index and is the filtered output. The next three filters require first sorting the data saples fro low to high values: {, d, K, d,, d d } u = sort d,, j, K J,, J,, { u, K, u,, u u } u = u,,, j, K J,, J,. The edian filter is then d = u, () edian ( J+) / while the α-tried ean filter is ( J α, () J α ) d tri = u j, J α ( J ) j= + α ( J ) and the LUM filter is d * u + α ( J ), u < u + α ( J ) * + α ( J ), α ( ), = u α ( ), u > u α ( ) 0 0. J J J J J J * u otherwise * ( u, u, u ) LUM = edian α where for both the α-tried ean and LUM filters 0 α 0.. () The principal coponent or KL filter has greater statistics that are coputed fro ultiple saple vectors (again, planes for our application) above and below the analysis point (Figure ). First we for the covariance atrix ( d ω )( d ω ) + K i, j, = K+ k= K i, + k i, j, + k j, () () ()

9 Page of where ω j, = d j, + k () K+ + K k= K is the local vertical ean within the analysis window of the j th trace, K is the half vertical window size along tie axis. Given a suite of J traces (J= in our exaple), the covariance atrix is defined as,,,,, J,,,,,, J, =. () J,, J,, J, J, The J by J covariance atrix is decoposed into J eigenvectors,, and J eigenvalues,, where by construction represents ost of the lateral aplitude variation across the saple vectors, best represents that part of the aplitude variation not represented by the eigenvector(s) before it, and so on. In general, seisic data aligned along a structurally-oriented window are quite coherent, such that first one or two eigenvectors represent the seisic reflection signal and the reaining eigenvectors represent less coherent noise. By construction, the eigenvectors have unit length. To copute the aplitude of the pattern represented by the n th eigenvector at tie saple index, we copute n J a, = v, d, () j= j n j and then reconstruct the signal (i.e. we KL filter the data) at the analysis point, p:

10 Page of d KL = N n= a v n, p, n. (0) Principal coponent structure-oriented filtering can be quite effective in suppressing crosscutting igration operator aliasing and certain coponents of acquisition footprint on poststack data (Davogustto et al., 0). Of the five filters presented, KL filtering best preserves signal aplitude when the noise is low aplitude with approxiately Gaussian statistics. However, since the first eigenvectors represent the ost energy in the data, KL filters behave poorly when the input data has high aplitude spikes, in which case they represent the noise. Figure shows a plan view of the ultiwindow Kuwahara filter. The original analysis window in Figure a represents a saple vector of length J=. In our ipleentation, we copute coherence in the windows shown in Figure b, each of which contain the red analysis point, p. Finally, one of the five filters described above is applied to the data falling within the window having the highest coherence, with filtered output being assigned to (perhaps uncentered) analysis point. Key and Sithson (0) applied KL filters to prestack gathers and found that ift ) coherent (i.e. non-gaussian) noise such as ultiples and ground roll have been previously filtered, ) noise and reflected signals are uncorrelated and have zero ean, and ) noise is uncorrelated fro trace to trace and saple to saple in the gather, that the first eigenvalue and eigenvector of covariance atrix of prestack seisic gathers corresponding to the reflection signals. Based on this assuption, we apply a prestack structure oriented filter (PSOF), which is based on the principal analysis (PA), to the seisic gathers to iprove the SNR.

11 Page 0 of Figures illustrate the steps for pre-stack structure-oriented filtering along local structure using a centered analysis window. We sort the prestack gathers into different coon offset volue and soothing the data along local structure. In this exaple there are crosslines by inlines and offsets resulting in a length saple vector, (=,,,) for each interpolated horizon slice at tie index. These saple vectors are cross-correlated and averaged fro k=-k to k=+k tie saples using equation resulting in a by covariance atrix. Siilarly we only preserve the value of analysis point (the blue point in Figure b) after the eigenap. Figure suarizes the proposed workflow of prestack oriented filtering by considering the geology discontinuities. The workflow begins by stacking the original seisic gathers. We next estiate the reflectors orientation in a running window on all traces of the stacked volue (Marfurt, 00). We then calculate the correlation coefficients for the stack volue along the local reflection dip and aziuth (Gersztenkorn and Marfurt, ). To archive the edge preserving filtering, we only perfor PA filtering to those gathers whose correlation coefficients are greater than a user defined threshold through the first eigenvalue and eigenvector of seisic covariance atrix. The gathers whose correlation coefficients are less than the threshold are not undergoing any processing. In this anner we iprove the SNR and avoid searing aplitude inforation across the geology discontinuities such as faults and channels. APPLIATION Modern high-fold data

12 Page of To evaluate the effectiveness of our workflow, we first apply it to prestack tie-igrated gathers acquired in the Fort Worth Basin (FWB), USA. We then copare the prestack inversion results based on unconditioned and conditioned gathers. The FWB is a foreland basin and covers approxiately 000 i (000 k ) in north-central Texas (da Silva, 0). The target is the Mississippian Barnett Shale which is one of the largest unconventional reservoir in the world and spreads approxiately 000 i (0 k ) across the FWB. In our survey, the Barnett Shale foration lies between.s and.s which is the core area of the ain production area in the FWB. The axiu offset is around 000 ft while the target Barnett Shale lies at approxiately 000 ft depth. Figure a shows a representative tie igrated MP gather after apply nonstretch processing (Zhang et al. 0). White arrows indicate the zone we have obvious spikes noise. Figure b and Figure c show the sae gather after apply PSOF and the rejected noise, respectively. Note that the reflection events indicated by white arrows are clearer in the filtered gather. Figures a shows a stacked tie slice through the target zone generated fro unconditioned gathers (Figure a). Figures b and c show the sae stacked tie slice after apply PSOF and the rejected stacked noise. We do not observe uch difference between Figures a and b. This is due to the fact that the energy of rejected noise is very sall copare to that of reaining seisic signal. Note that stacking can reoves ost of the rando noise in the prestack gathers (Hendrickson, ), Figures c and c together indicate that PSOF reoves both rando noise and artifacts introduced by acquisition or processing. Figures a show seisic-well tie between stacked volues and a well located in our study survey. The procedure

13 Page of was done by correlating the stacked traces nearby the borehole with the synthetic seisogra generated fro well logs. The correlation coefficient of conditioned seisic data (Figure a) is 0. while the coefficient of unconditioned data (Figure b) and 0.. We next extract the angle dependent statistical wavelets for both the unconditioned (Figure a) and the conditioned (Figure b) data after the seisic-well tie. The red, blue, and green lines show the extracted sall (0 o - o ), interediate ( o - o ), and large angle wavelets ( o - o ), respectively. We observe a slightly iproveent of large angle wavelets. To better copare the iproveents, we show the aplitude spectru of extracted wavelets for unconditioned and conditioned gathers in Figure c and d. Note that the spectru of large angle wavelet are extorted soe content in both cases. The factor responsible for the narrower bandwidth of large angle wavelets is that we applied a low band pass filter for antialiasing to the far offset data during the tie igration processing (Biondi, 00). However we still notice a slightly spectru iproveent for the wavelets estiated fro conditioned gathers. The prestack inversion was conducted 0s above the top of Marble Fall liestone and 0s below the Viola liestone. Figures,, and 0 copare the inverted P-ipedance, S-ipedance, and density fro the unconditioned and conditioned gathers. The vertical black curve in those figures are the well tract that used for quality control of inverted results. We observe an overall iproveent by rejecting the noise of prestack gathers. For exaple the forations indicated by the white arrow are ore laterally continuous in the new inverted sections when copared to those of unconditioned data. The zone indicated by black arrows have higher resolution in the new inverted section when copared to that of conventional data. The fault indicated by the gray arrows are also easier to interpret in the

14 Page of new inverted sections. Note the iproveent of density is not as good as those of P- and S- ipedance. This is due to that the axiu incidence angle of our gather is approxiately o and it is beyond capability to generate a reliable result. To better quantify the iproveent, we quality control our inverted results fro (Figure a) unconditioned and (Figure b) conditioned gathers with well logs at the target zone. The left, iddle, and right tracks show the P-ipedance, S-ipedance, and density panels. The black, blue, and red curves are initial odel, the original well logs, and inverted results. Note the new inverted results indicated by the red arrows have noticeable better correlation with original well logs and initial odels, resulting in a lower inversion errors. ONLUSIONS The proposed workflow not only reoves rando noise but also suppresses coherent acquisition, processing, and igration artifacts that crosscuts the reflectors of interest. We preserve the edge inforation by only applying the algorith to the prestack gathers whose coherency is larger than a user defined threshold. Rejecting the noise in the prestack gathers results in ) an iproved stacked iage, ) a better seisic-well tie, ) higher resolution and lateral continuities of inverted result, and ) lower error between inverted elastic paraeters and original well logs. AKNOWLEDGEMENTS The authors would like to thank Devon Energy in providing the data and GG provides the license for Hapson-Russell. We also thank the sponsors of Attribute-Assisted Seisic Processing and onsortiu (AASPI) for their guidance and financial support.

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16 Page of REFERENES Aarre, V., D. Astratti, T. N. A. al-dayyni, S. L. Mahoud, A. B. S. lark, M. J. Stellas, J. W.Stringer, B. Toelle, O. V. Vejbaek, and G. White, 0, Seisic detection of subtle faults and fractures, Schluberger Oilfied Review,, no., -. AlBinHassan, N. M., Y. Luo, and M. N. Al-Faraj, 00, -D edge-preserving soothing and applications: Geophysics,, P-P. Biondi, 00, Kirchhoff iaging beyong aliasing: Geophysics,, -. Buland, A., and H. Ore, 00, Bayesian wavelet estiation fro seisic and well data: Geophysics,, Buland, A., and H. Ore, 00, Bayesian linearized AVO inversion: Geophysics,, -. abois G., 000, an P-wave AVO be quantitative?: The Leading Edge,, -. abois, G.,. AVO attributes and noise-pitfalls of crossplotting: 0th Annual International Meeting, SEG, Expanded Abstracts, -. astagna, J., and M. Backus,, Offset-dependent reflectivity: Theory and practice of AVO analysis: SEG. orrao, A., M. Fervari, and M. Galbiati, 0, Hewett Plattendoloite: Reservoir haracterization by Resolution Enhanced Seisic data: GSSEPM st Annual Bob. F. Perkins Research onference on Seisic attributes New views on seisic iaging: Their use in exploration and production, -. da Silva, M., 0, Production correlation to D seisic attributes in the Barnett Shale, Texas: M.S. thesis, The University of Oklahoa.

17 Page of Davogustto, E. O., Reoving footprint fro legacy seisic data volues: M.S. thesis, The University of Oklahoa. Fehers, G..,.F.W. Höcker, 00, Fast structural interpretations with structure-oriented filtering: Geophysics,, -. Gersztenkorn and Marfurt,, Eigenstructure-based coherence coputations as an aid to -D structural and stratigraphic apping,, -. Hale, D., 0, Structure-oriented bilateral filtering of seisic iages: st Annual International Meeting, SEG, Expanded Abstracts, -00. Helore, S., 00, Dealing with the noise Iproving seisic whitening and seisic inversion workflows using frequency split structurally oriented filters: th Annual International Meeting of the SEG, Expanded Abstracts, -. Hendrickson, J.S.,. Stacked: Geophysical Prospecting,, -0. Hennenfent, G., and F. Herrann, 00, Three-ter aplitude-versus-offset (avo) inversion revisited by curvelet and wavelet transfors: th Annual International Meeting, SEG, Expanded Abstracts, -. Key, S., and S. B. Sithson, 0, New approach to seisic-reflection event detection and velocity deterination: Geophysics,, 0-0. Koza, S. and astagna, J., 00, The effects of noise on AVO crossplots: rd Annual International Meeting, SEG, Expanded Abstract, -. Li, X. and R. ouzens, 00, Attacking localized high aplitude noise in seisic data - A ethod for AVO copliant noise attenuation: SEG recorder.

18 Page of Liu, Y., S. Foel, and G. Liu, 00, Nonlinear structure-enhancing filtering using plane-wave prediction: Geophysical Prospecting,,. Luo, Y., S. Al-Dossary, and M. Alfaraj, 00, Edge-preserving soothing and applications: The Leading Edge,, -. Marfurt, K. J., 00, Robust estiates of D reflector dip: Geophysics,, P-P0. Si, R., White, R., and Uden, R., 000, The anatoy of AVO crossplots: The Leading Edge, 0-. Singleton, S., 00, The effects of seisic data conditioning on pre-stack siultaneous ipedance inversion: th Annual International Meeting, SEG, Expanded Abstracts, 0-0. Toasi,., and R. Manduchi,, Bilateral filtering for gray and color iages: Proceedings of the th International onference on oputer Vision, IEEE oputer Society,. Wang, J., Y. hen, D. Xu, and Y Qiao, 00, Structure-oriented edge-preserving soothing based on accurate estiation of orientation and edges: Applied Geophysics,, - Weickert, J.,, oherence-enhancing diffusion filtering: International Journal of oputer Vision,, -. Whitcobe, D. N., L. Hodgson, H. Hoeber, and Z. Yu, 00, Frequency dependent, structurally conforable filtering: th Annual International Meeting, SEG, Expanded Abstracts, -. Zhang, B., K. Zhang, S. Guo and K. J. Marfurt, 0, Nonstretching NMO correction of prestack tie-igrated gathers using a atching-pursuit algorith: Geophysics,, U-U.

19 Page of LIST OF FIGURE APTIONS Figure. (a) artoon showing structure oriented filtering applied to a poststack data volue along structural dip using a centered analysis window about the red analysis point. In this exaple there are crosslines by lines resulting in a length saple vector for each interpolated dipping horizon slice at tie k. These saple vectors are cross-correlated and averaged fro k=-k to k=+k (K=) tie saples using equation resulting in a by covariance atrix. (b) The first N length eigenvectors represent x aps that best represents the lateral variation of aplitude within the analysis window. These aps are crosscorrelated with the saple vector at tie to copute a suite of N principal coponents. One or ore of these coponents are then sued to for the filtered data given by equation. Figure. (a) An circular analysis window seen fro above containing J= seisic traces centered about the red analysis point. (b) overlapping Kuwahara windows, all of which contain the sae red analysis point. In this workflow, coherence is coputed within each window. The filter is then applied to the data window having the highest coherence, with the output being assigned to the (perhaps uncentered) red analysis point. (After Davogustto et al., 0). Figure. artoon showing structure oriented filtering applied to prestack coon offset igrated gathers. The windows are oriented along structure and centered about the red analysis point. In this exaple there are DPs by lines and offsets resulting in a length saple vector for each interpolated horizon slice at tie k. These saple vectors are cross-correlated and averaged fro k=-k to k=+k (K=) tie saples using equation resulting in a by

20 Page of covariance atrix. (b) As in Figure, the first length eigenvectors represent three x aps, one for each of the three offsets. These aps are crosscorrelated with the saple vector at tie k to copute a suite of N principal coponents. One or ore of these coponents are then sued to for the filtered data. Figure. A siplified workflow of prestack oriented filtering. The igrated data are stacked, which in turn provide an average estiate of structural dip and coherence. For each analysis point, one or ore data points are extracted fro either side along structural dip in the adjacent inline direction, crossline direction, offset direction, and if present, aziuth direction to for a saple vector such as shown in Figure. If the coherence fall below a lower threshold, a discontinuity is assued to be present and no filtering is applied. If the coherence is above an upper threshold, the data are filtered using either a KL (principal coponent), LUM, or α- tried ean filter. In our actual ipleentation we add a Kuwahara window construct (Marfurt, 00) such that the filtering occurs in the ost coherent (non-centered) window containing that analysis point. Figure. Representative gather showing the conditioning workflow shown in Figure. (a) The tie igrated gather after applying the nonstretch processing. (b) The sae gather after applying prestack structure-oriented KL filtering. (c) The rejected noise. White arrows indicate noticeable iproveents. Figure. The stacked tie slice through the target zone showing the conditioning workflow shown in Figure. The tie slice (a) before and (b) after applying prestack structure-oriented KL filtering. (c) The rejected noise. Note that while stacking reoves ost of the rando noise,

21 Page 0 of Figure c and (c) together indicate that the proposed workflow reoves both rando noise and artifacts introduced by acquisition and processing. Figure. Seisic-well ties between (a) unconditioned and (b) conditioned stacked volue and a well located in our study area. The procedure was done by correlating the stacked traces nearby the borehole with the synthetic seisogra generated fro well logs. We obtain the correlation coefficient of 0. for conditioned data and 0. for the unconditioned data. Figure. Statistically extracted wavelets and corresponding aplitude spectra fro (a), (c) the tie igrated and (b), (d) conditioned angle gathers. The red, blue, and green curves correpsond to sall, interediate, and large angle wavelets. Note the spectru of large angle wavelet is distorted to soe extent; this reduction is due to the application of an antialiasing filter in the Kirchhoff prestack igration algorith. Nevertheless, we still notice a slight iproveents of wavelets after apply PSOF. Figure. oparison of inverted P-ipedance fro (a) unconditioned and (b) conditioned gathers. White arrows indicate forations where we have ore lateral continuity copared to the conventional data. The black arrows indicate the zones where we have higher resolution. Figure. oparison of inverted S-ipedance for (a) unconditioned and (b) conditioned gathers. The white arrows indicate the forations where we have ore lateral continuity copared to that of conventional data. The black arrows indicate the zones where we have higher resolution.

22 Page of Figure 0. oparison of inverted density for (a) unconditioned and (b) conditioned gathers. We did not observe any obvious iproveent, this is due to that a reliable density estiation requires the axiu incident angle of o which is beyond that of our input data. Figure. Validation of the inverted results with the original well logs. The left, iddle, and right panels show the P-ipedance, S-ipedance, and density logs. The black, blue, green, and red curves show the original logs, initial odel, and inverted results fro conventional and new processing gathers. The red arrow indicates an obvious iproveent zone.

23 Tie Page of Figure a. a) p Inline Data slice d k Trace (,,, ) x covariance atrix..,,,,,,....,,..,

24 Page of b) Figure b. For x covariance atrix..,,,,,, opute KL-filtered data at analysis point p, N< N KL a v.. d, p n p..,,.., n, p, n opute first N x eigenaps v n Obtain α n by cross correlating x eigenap v n with x data slice d k a, n d v n j d j, v j, n

25 Page of Figure a. a) rossline (x) Inline (x)

26 Page of Figure b. rossline (x) b) Inline (x)

27 Tie Page of Figure a Offset - Inline p Offset Offset + Trace (,, Data slice d k ) x covariance atrix..,,,,,,....,,..,

28 Page of Figure b. For x covariance atrix..,,,,,,. opute first N xx eigenaps v n. N KL d p nv,, pn n Offset q- Offset q Offset q+ p,,, opute KL-filtered data at analysis point p, N<.... Offset q- Offset q Offset q+ Obtain α n by cross correlating xx eigenap v n with xx data slice d a, n d v n j d j, v j, n

29 Page of Figure. Keep original saple Migrated seisic gathers Yes Is there a significant discontinuity at analysis point p? No Build saple vectors for offset at analysis index k along local reflector orientation Filter using PA, LUM, or α-tried ean Yes More traces or saples? No Stacking Structure oriented filtered gathers Stacked Volue opute structural dip Reflector dip opute coherence oherence

30 t 0 (s) Page of Figure a. a) Offset - x() Ap 0 - -

31 t 0 (s) Page of Figure b. b) Offset - x() Ap 0 - -

32 t 0 (s) Page of Figure c. c) Offset - x() Ap 0 -

33 crossline Page of Figure a. Inline 0.0 Kiloeters

34 crossline Page of Figure b. Inline 0.0 Kiloeters

35 crossline Page of Figure c. Inline 0.0 Kiloeters + 0 -

36 t 0 (s) Page of Figure a Density (g/c ). P-wave (/s) Marble Falls Upper Barnett LM Upper Barnett SH Forestburg Lower Barnett

37 t 0 (s) Page of Figure b Density (g/c ) P-wave (/s) Marble Falls Upper Barnett LM Upper Barnett SH Forestburg Lower Barnett

38 Page of Figure a. a) Sall Interediate Large

39 Page of Figure b. b) Sall Interediate Large

40 Page of Figure c. c) Sall Interediate Large

41 Page 0 of Figure d. d) Sall Interediate Large

42 t 0 (s) Page of a)... Figure a. DP Nuber P-ipedance High Low 0 0. Kiloeters

43 t 0 (s) Page of b)... Figure b. DP Nuber P-ipedance High Low 0 0. Kiloeters

44 t 0 (s) Page of a)... Figure a. DP Nuber S-ipedance High Low 0 0. Kiloeters

45 t 0 (s) Page of b)... Figure b. DP Nuber S-ipedance High Low 0 0. Kiloeters

46 t 0 (s) Page of a)... Figure 0a. DP Nuber Density High Low 0 0. Kiloeters

47 t 0 (s) Page of b)... Figure 0b. DP Nuber Density High Low 0 0. Kiloeters

48 t 0 (s) Page of Figure a. a)... Z P Z S ρ Low High Low HighLow High Marble Falls Marble Falls Upper Barnett LM Upper Barnett Shale Forestburg Lower Barnett Shale

49 t 0 (s) Page of Figure b. b)... Z P Z S ρ Low High Low HighLow High Marble Falls Upper Barnett LM Upper Barnett Shale Forestburg Lower Barnett Shale