Dip Correction of Spectral Components. Dip correction of spectral components: Application to time- vs. depth-migrated seismic.

Transcription

1 Dip Correction of Spectral Components Dip correction of spectral components: Application to time- vs. depth-migrated seismic data Tengfei Lin 1, Bo Zhang 2, Kurt Marfurt 1, Deshuang Chang 1,3, Shifan Zhan 3 and Zhonghong Wan 3 1 The University of Oklahoma, ConocoPhillips School of Geology and Geophysics, 2 The University of Alabama, Department of Geological Sciences, 3 BGP Inc., China National Petroleum Company, tengfei.lin@ou.edu, kmartfurt@ou.edu, bzhang33@ua.edu, cds881@sina.com, zhanshifan@cnpc.com.cn, wanzhonghong@cnpc.com.cn Corresponding author: Tengfei Lin The University of Oklahoma, ConocoPhillips School of Geology and Geophysics 71 Sarkeys Energy Center 1 East Boyd Street Norman, OK 7319 tengei.lin@ou.edu 1

2 Dip Correction of Spectral Components ABSTRACT Seismic spectral decomposition is a powerful analysis tool that has had significant success in delineating channels, fans, overbank deposits and other relatively thin architectural elements of clastic and carbonate depositional environments. Most publicaitons of spectral decompositon have been applied to time-migrated data rather than depth-migrated data. Interpreting spectral components and spectral attributes such as peak frequency on depth-migrated data requires a slightly different perspective. First, the results are computed in cycles/km (or alternatively as cycles/1 ft) rather than as cycles/s or Hertz, with the dominant wavenumber decreasing with increasing velocities at depth. Second, interpreters resort to depth migration when there are significant lateral velocity changes in the overburden and/or steep dips. All present-day implementations compute spectral components vertical trace by vertical trace rather than perpendicular to the bedding plane, giving rise to tuning and other anomalies at an apparent rather than at a true frequency or wavenumber. We illustrate the interpretational differences of spectral decomposition between time- and depth-migrated data through the use of a simple synthetic model and a modern 3D data volume. We show how one can approximately compensate for reflector dip by normalizing each spectral magnitude component by 1/cosθ, where θ is the volumetric dip magnitude commonly computed in seismic attribute analysis. LIST OF KEYWORDS Spectral decomposition, Dip compensation factor. 2

3 Dip Correction of Spectral Components INTRODUCTION Most publications on seismic attributes have used time-migrated data. Interpreting seismic attributes such as spectral components on depth-migrated data requires a slightly different perspective. First, the samples are in meters or feet rather than as milliseconds. Second, spectral components are computed in cycles/km (or alternatively as cycles/1 ft) rather than as cycles/s or Hertz, with the dominant wavenumber decreasing with increasing velocities at depth. Third, since depth-migration is often used to image most structurally complex geology, the spectral components will provide a measure of apparent vertical thickness rather than true thickness. Spectral decomposition is computed trace by trace which implicitly ignores any dipping structure. One of the most common uses of spectral decomposition is to map fluvial (e.g. Partyka et al., 1999; Peyton et al., 1998) and deep water (e.g. Bahorich et al., 22; Braccini and Adeyemi, 211) depositional systems. Key to interpreting these spectral components is the thin bed tuning model (e.g. Marfurt and Kirlin, 21). Widess (1973) and Kallweit and Wood (1982) used wedge models to quantify the response of thin-bed anomalies. For a constant impedance wedge embedded in a surrounding constant impedance matrix, the maximum constructive interference occurs when the wedge thickness equals the tuning thickness (one-half of the twoway travel-time period for the time-migrated data or one-quarter of the wavelength for the depthmigrated data). By applying this model to spectral components, Laughlin et al. (22) show that a thicker channel axis exhibits a stronger response at lower frequencies, while the thinner channel flanks exhibit a stronger response at higher frequencies. Although this is the most common use of spectral decomposition, spectral components are currently the method of choice in estimating attenuation (1/Q) (e.g. Taner and Treitel, 23), and are also used in pore-pressure prediction (e.g. Young and LoPicollo, 25), in mapping seismic unconformities (Smythe et al., 3

4 Dip Correction of Spectral Components 24; Davogustto et al., 213), as well as in some implementations of seismic chronostratigraphy (Qayyum et al., 215). The objective of this paper is simple to alert the interpreter that spectral components need to be corrected in the presence of steep dip. We begin by illustrating the effect of dip on spectral components through the use of some simple synthetics. We then show the subtle effects of dip on spectral components along the flanks of karst collapse in the Fort Worth Basin, TX. Finally, we highlight differences in spectral component displays on time- vs. depth-migrated using 3D survey from onshore China. We conclude with summary remarks of some common interpretation pitfalls. 4

5 Dip Correction of Spectral Components THEORY Spectral Components of Time- and Depth-Domain Data There are currently four algorithms commonly used to generate spectral components: shortwindow discrete Fourier transforms (SWDFT), continuous wavelet transforms, the S transform, and matching pursuit. Leppard et al. (21) find that matching pursuit provides greater vertical resolution and less vertical stratigraphic mixing than the other techniques. The fixed-window length least-squares spectral analysis technique described by Puryear et al. (28) provides similar spectral resolution to the (least-squares) matching pursuit algorithm. While all of our examples here will be generated using a matching pursuit algorithm described by Liu and Marfurt (27), the concept of apparent vs. true frequency is perhaps easiest to understand using the fixed length analysis window used in the SWDFT. For time data, the window will be in seconds, such that the spectral components are measured in cycles/s or Hz. For depth data, the window will be in kilometers, such that the spectral components are measured in cycles/km. Significant care must be made when loading the data into commercial software, where the SEGY standard stores the sample interval in microseconds. For everything to work correctly, a depth sample interval of 1 m will need to be stored as 1 microkilometers. If the units are not stored in this manner, the numerical values of the data may appear to be in fractions of cycles/m. Many commercial software packages will not operate for cycles/s (or cycles/km) that fall beyond a reasonable numerical range of Once the data are loaded, the range of values will be different. If the time domain data range between 8-12 Hz, depth domain data will range between 2-3 cycles/km at a velocity of 4 km/s, such that anomalies will be shifted to lower frequencies. 5

6 Dip Correction of Spectral Components Figures 1a and b show a vertical slice through an impedance and corresponding reflectivity model. Figure 1c shows a synthetic section created by convolving a Hz Ormsby wavelet with the reflectivity and adding 5% random noise. It is critical that one use spectrally flattened data prior to peak frequency tuning thickness estimation to remove the effect of the seismic wavelet. Figure 1d shows the peak frequency computed using a CWT decomposition algorithm. Note that the peak frequency increases with decreasing thickness of the wedge model. Dip Compensation Lin et al., (213) added dip compensation to spectral decomposition and noted that the apparent peak frequency and the corrected peak frequency are different by 1/cosθ in the presence of dip θ. If the dip angle is θ, and the real thickness is h r, then the apparent vertical thickness will be h a = h r / cos θ (Figure 2). The tuning frequency (and tuning wavenumber) will therefore decrease with increasing values of θ. The shift to lower apparent frequency is familiar to those who examine data before and after time migration, where dipping events on unmigrated stacked data with moderate apparent frequency migrate laterally to steeper events with lower apparent frequency (Chun and Jacewitz, 1981). Since spectral decomposition is calculated trace by trace in the vertical direction, the results will be accurate for flat horizons where θ=. However, for dipping horizons, spectral decomposition tuning effects will be in terms of the vertical apparent thickness which is always larger than the true thickness for dipping layers. According to tuning phenomenon and the schematic diagram in Figure 2, and (6a) 6, (6b)

7 Dip Correction of Spectral Components where h a is the apparent vertical thickness in vertical direction, h r is the real thickness of the thin layer, θ is the dip angle of the thin layer. V pa and V pr are the phase velocities of apparent vertical frequency and real frequency. If we ignore dispersion, we can consider V pa V pa. In contrast, one would not wish to make such an assumption for estimation of Q. The relationship between f a, the apparent tuning frequency in the vertical direction, and f r, the real tuning frequency of the thin layer is simply. (7) The model in Figure 3a was constructed with a 1 ft/s, constant 1 ft vertical thickness layer such as encountered in similar folds of more ductile lithologies, resulting in an apparent tuning frequency of 5 Hz. Correcting the apparent thickness by 1/cosθ gives the true laterally variable tuning frequency that ranges between 5 and 72 Hz indicated by the red line. The model in Figure 3b shows the true thickness to be a constant 1 ft, such as encountered in concentric folds of more brittle rocks, resulting in an apparent tuning frequency that ranges laterally between 35 and 5 Hz across the model. Compensation for dip results in a constant tuning frequency of 5 Hz. 7

8 Dip Correction of Spectral Components APPLICATION A salt withdrawal minibasin, Gulf of Mexico Salt withdrawal often generates minibasins with steep flanks. The peak frequency shown in Figure 4 thus falsely implies increasing thickness towards the minibasin edges. Correction of the apparent peak frequency (Figure 4a) by the dip magnitude (Figure 4b), corrects the image to be a more accurate thickness of the true peak frequency normal to the reflectors and hence a more accurate measure of tuning thickness (Figure 4c). Correction of the peak frequency is trivial. Correction of a given spectral component is also simple but requires interpolation of the irregularly sampled corrected spectral components to produce the desired regularly sampled output components. An East China Carbonate Oil Field The next example comes from an oilfield of east China. The oilfield contains multiple fault-controlled reservoirs, which can be seen on vertical slices through both the time-migrated (Figure 5a) and depth-migrated (Figure 5b) data. Superficially, the reservoir appears to be significantly deeper in the depth-migrated data than the in time-migrated data. This appearance, along with the increase in wavelength and decrease in apparent resolution is due to the increase of velocity with depth. Figure 5 shows vertical slices through seismic amplitude computed after (a) time-migration ( t=.2 s) and (b) depth-migration ( z=.1 km). Red arrows indicate faults, which are both stronger and more continuous in the depth-migrated data. The blue arrow in the depth-migrated data shows a clearly imaged fault plane, which is blurred in the time-migrated data. Orange arrows indicate migration artifacts. In this case, the depth-migrated data suffer from more artifacts than the time-migrated data. The green arrow in the depth-migrated data indicates a 8

9 Dip Correction of Spectral Components lower frequency response compared to the time-migrated data. The frequency range is 4 Hz for the time-migrated data, while the wavenumber range is about 2 cycles/km for depthmigrated data (Figure 6). The shift to frequencies falling below that used in acquisition and premigration low-cut filters is a common feature in migration of steep dips (Chun and Jacewitz, 1981). We find that the numerical value of the wavenumber for depth-migrated data is about half of the frequency for time-migrated data. Figures 6a and b display the peak frequency co-rendered with seismic amplitude on the time- and depth-migrated data. Both figures exhibit a similar peak frequency distribution, even though the values of peak frequency measured in cycles/km in the depth-migrated data are approximately half those measured in Hz in the time-migrated data. Low peak frequency anomalies are lithogically bound (consistent with increasing velocity with age) along the horizon, except for the zone seriously blurred by the migration artifacts indicated by orange arrows in Figure 5. The peak frequency tracks the horizons for the time-migrated data in Figure 6a. The combination of the increased velocity below the pink horizon, steeper depth dip than time dip, as well as some steeply dipping migration artifacts give rise to the low frequency zones. Figures 7a and b show the impact of dip compensation as defined by equation 7. As expected, the areas of flat dip show no changes while those with steep dip have a greater compensation factor, shifting the result to a higher (true) peak frequency. The dip compensation factors follow faults and horizons. Because of the greater noise in the depth-migrated data, some of the dip estimates are erratic, giving rise to the erratic dip compensation values shown in Figure 7b. Such errors can be ameliorated by first smoothing the reflector dip estimates. Figures 8a and b show the corrected (true) peak frequency of the time-migrated and depthmigrated data. In the shallower part of the section, the corrected peak frequency changes only 9

10 Dip Correction of Spectral Components slightly, since the dip is small. For the steeply dipping deeper section, the corrected peak frequency is significantly (~5%) higher than the original apparent peak frequency. The corrected peak frequency better correlates to the horizons than those in Figures 6a and b, especially for the depth-migrated data, suggesting that these deformed layers have nearly uniform rather than laterally varying thickness. CONCLUSIONS In the presence of strong lateral variations in velocity, time-migration fails to properly image the subsurface. Imaging errors include velocity pull-up and push-down and poorly imaged steeply dipping horizons and fault planes. Accurate prestack depth migration removes most of these artifacts but introduces problems of its own. In order to image steep dips, depth migration often generates steeply dipping migration aliasing artifacts. Such steeply dipping artifacts have a low frequency (vertical) spectrum that may overprint reflectors of interest. Fortunately, steeply dipping coherent noise that cuts across less steeply dipping reflectors can be suppressed using edge-preserving structure-oriented filtering. A second feature of depth-migrated data is the change in wavenumber with depth due to the velocity gradient which can be is much greater than the corresponding decrease in frequency of time-migrated data. Given these two caveats, the interpretation of spectral components computed from depth-migrated data are similar, and in principal, more accurate that those computed from time-migrated data. A major headache encountered by many interpreters is the need to load the seismic data in such a manner that the spectral range falls within that supported by their software, which can be achieved by defining the SEGY sample increment in units microkilometers or microkilofeet (e.g. with a 3 foot sample increment being stored as 3 microkilofeet). 1

11 Dip Correction of Spectral Components Depth migration is designed to handle lateral changes in the velocity overburden. Such changes are often if not usually associated with steep dips. In general, spectral components of seismic data are computed trace by trace and therefore provide vertical or apparent spectral components vs. true spectral components. Fortunately, since most interpreters who use spectral decomposition also compute and interpret volumetric dip estimates, θ, one can correct for dip by scaling the frequencies by 1/cosθ. Correction of the full spectrum requires resampling and interpolating the apparent spectrum at each voxel, which is algorithmically trivial, but difficult to do in commercial software package not designed to do so. Such compensation provides more accurate images of the lateral variation of layer thickness. We suspect, but have not shown, that the accuracy for Q-estimation and pore-pressure prediction based on spectral components will be similarly improved. ACKNOWLEDGEMENTS We thank the Bureau of Geophysical Prospecting of China National Petroleum Corporation for allowing us to use and publish data from their East China Oil Field. We also thank PGS Co. for providing OU a license to their offshore Gulf of Mexico data volume for use in education and research. The first three authors wish to thank the industry supporters of the AASPI consortium for their encouragement and financial support. The last three authors are thank BGP for permission to collaborate with OU on this effort. 11

12 Dip Correction of Spectral Components REFFERENCES Bahorich, M., A. Motsch, K. Laughlin, and G. Partyka, 22, Amplitude responses image reservoir: Hart s E&P, January, Braccini, E., and A. Adeyemi, 211, Integrating seismic attributes for geomodeling purposes: Nigeria deep water turbidite environment case study: GCSSEPM 31st Annual Bob. F. Perkins Research Conference on Seismic attributes New views on seismic imaging: Their use in exploration and production, Chun, J. H., and C. A. Jacewitz, 1981, Fundamentals of frequency domain migration: Geophysics, 46, Davogustto D., MC de Matos, C Cabarcas, T Dao and K. J. Marfurt, 213, Resolving subtle stratigraphic features using spectral ridges and phase residues: Interpretation, 1, Laughlin. K., P. Garossino and G. Partyka, 22, Spectral decomp applied to 3D: AAPG Explorer: 23, Leppard, C., A. Eckersley, and S. Purves, 21, Quantifying the temporal and spatial extent of depositional and structural elements in 3D seismic data using spectral decomposition and multi-attribute RGB, in L. J. Wood, T. T. Simo, and N. C. Rosen, 21, Seismic imaging of depositional and geomorphic systems: 3th Annual GCSSEPM Foundation Bob F. Perkins Research Conference, 1-1. Lin, T., 213, Spectral decomposition of time- vs. depth-migrated data: 83th Annual International Meeting, SEG, Expanded Abstracts, Liu, J. L., and K. J. Marfurt, 27, Multi-color display of spectral attributes: The Leading Edge, 26,

13 Dip Correction of Spectral Components Kallweit, R. S., and L. C. Wood, 1982, The limits of resolution of zero-phase wavelets: Geophysics, 47, Marfurt, K. J., and R. L. Kirlin, 21, Narrow-band spectral analysis and thin-bed tuning: Geophysics, 66, Partyka, G., J. Gridley, and J. A. Lopez, 1999, Interpretational applications of spectral decomposition in reservoir characterization: The Leading Edge, 18, Peyton, L., R. Bottjer, and G. Partyka, 1998, Interpretation of incised valleys using new 3D seismic techniques: A case history using spectral decomposition and coherency: The Leading Edge, 17, Puryear, C. I., S. Tai and J.P Castagna, 28, Comparison of frequency attributes from CWT and MPD spectral decompositions of a complex turbidities channel model: 78th Annual International Meeting, SEG, Expanded Abstracts, Qayyum, F., O. Catuneaunu, and C. E. Bouanga, 215, Sequence stratigraphy of a mixed siliciclastic-carbonate setting, Scotian Shelf, Canada: Interpretation, 3, SN21-SN37. Smythe, J., A. Gersztenkorn, B. Radovich, C.-F. Li, and C. Liner, 24, SPICE: Layered Gulf of Mexico shelf framework from spectral imaging: The Leading Edge, 23, Taner, M.T. and S. Treitel, 23, A robust method for Q estimation: 73rd Annual International Meeting of the SEG, Expanded Abstracts, Widess, M. B., 1973, How thin is a thin bed? : Geophysics, 38, Young, R. A., and R. D. LoPicollo, 25, A risk-reduction recipe using frequency-based pore pressure predictions from seismic: Gulf Coast Association of Geological Societies Transactions, 55,

14 Dip Correction of Spectral Components FIGURE CAPTIONS Figure 1. (a) The impedance (b) reflectivity (c) synthetic seismic profile computed using a Hz Ormsby wavelet, and (d) peak frequency co-rendered with the seismic amplitude of (c). The velocity of the wedge is 4 ft/s. The theoretical peak (tuning) frequency of the wedge is f=v/(4h), where h is the thickness. Figure 2. A schematic diagram showing differences in apparent thickness ha to the real thickness, hr with respect to dip magnitude, θ. Figure 3. (a) A constant apparent thickness thin bed model showing a layer with flat dip, strong negative dip and moderate positive dip (top); (b) The real (marked by red line) tuning frequency (the apparent tuning frequency is 5 Hz) of the layer. (c) A constant real thickness thin bed model showing a layer with flat dip, strong negative dip and moderate positive dip; (d) The real (marked by red line) tuning frequency (the real tuning frequency is 5 Hz) of the layer. Figure 4. Vertical and horizon slice through (a) peak frequency, (b) dip magnitude, θ, and (c) corrected peak frequency. White arrow in (a) shows a decrease in peak frequency indicating layer thickening towards the basin edges. After correction by 1/cosθ we see in (c) an increase in peak frequency indicating layer thinning towards the minibasin edges consistent with decreased accommodation space. (Data Courtesy of PGS). Figure 5. Vertical slices through (a) time-migrated data and (b) depth-migrated data. Figure 6. Apparent peak frequency blended with seismic amplitude of (a) time-migrated data and (b) depth-migrated data. Figure 7. Dip compensation (1/cosθ) blended with seismic amplitude of (a) time - and (b) depth - migrated data. 14

15 Dip Correction of Spectral Components Figure 8. Dip-corrected peak frequency blended with seismic amplitude of (a) time - and (b) depth - migrated data. 15

16 (a). Time (s) Thickness (ft) 2 Figure 1a.

17 (b). Time (s) Thickness (ft) 2 Figure 1a.

18 (c). Amp Pos Time (s).5 1. Neg 1.5 Thickness (ft) 2 Figure 1c.

19 (d). fpeak (Hz) 4 Time (s) Thickness (ft) 2 Figure 1c.

20 2. Seismic attributes analysis ha hr Figure 2.

21 Hz Depth (ft) (a) (a) ft Tuning Thickness Model (b) 8 8 ha= 1 ft, V = 1,ft/s 6 4 Real Peak frequency (Hz) Apparent Peak frequency (Hz) Figure 3a.

22 Hz Depth (ft) (b) (c) ft Tuning Thickness Model (d) 8 ha= 1 ft, V = 1,ft/s 8 6 Real Peak frequency (Hz) 4 Apparent Peak frequency (Hz) Figure 3b.

23 Time (s) (a).5 1 km Amp Pos f Opacity 75 Neg 25 1

24 Time (s) (b).5 1 km Amp Pos dip Opacity 3 Neg 1

25 Time (s) (c).5 1 km Amp Pos f Opacity 75 Neg 25 1

26 Time (s) (a) 2.5 Amp Pos 3. Neg km Figure 5a.

27 Depth (km) (b) Amp Pos Neg km Figure 5b.

28 Time (s) (a) 2.5 Amp Opacity Pos 3. Neg 1 fpeak km Figure 6a.

29 Depth (km) (b) Amp Opacity Pos Neg 1 fpeak km Figure 6b.

30 Time (s) (a) 2.5 Amp Opacity Pos 3. Neg 1 Dip factor km 1 Figure 7a.

31 Depth (km) (b) Amp Opacity Pos Neg Dip factor km 1 Figure 7b.

32 Time (s) (a) 2.5 Amp Opacity Pos 3. Neg 1 fpeak km Figure 8a.

33 Depth (km) (b) Amp Opacity Pos Neg 1 kpeak km Figure 8b.