Seismic attributes of time-vs. depth-migrated data using self-adaptive window

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1 Seismic attributes of time-vs. depth-migrated data using self-adaptive window Tengfei Lin*, Bo Zhang, The University of Oklahoma; Zhifa Zhan, Zhonghong Wan, BGP., CNPC; Fangyu Li, Huailai Zhou and Kurt Marfurt, the University of Oklahoma Summary Seismic attributes are routinely used to assist for seismic interpretation and reservoir characterization. The more commonly used geometric attributes include 1) reflector dipazimuth, 2) coherence, and 3) curvature. Most publications seismic attributes were used in time-migrated data. While interpreting seismic attributes such as coherence on depth migrated data requires a slightly different perspective. First, the samples are meters or feet rather than as milliseconds. Second, Fourier Transform is necessary during the estimation of seismic attributes. They are computed as cycles/km (or alternatively as cycles/1000 ft) rather than as cycles/s or Hertz, with the dominant wavenumber decreasing with increasing velocities at depth. Third, we conventionally use a constant user-defined window to calculate those attribute, while the constant window size is not capable to handle layers with different thickness at the same time, the complexity of structure in seismic data makes it invalid, especially for the depth migrated data. In this paper we proposed a workflow to estimate the seismic attributes using a self-adaptive window size by integrating the result from seismic spectrum analysis. We test our algorithm on both time and depth migrated data from an oilfield of East China. Introduction Seismic attributes have been applied to seismic data since their inception. Since the dominant wavelength increases with increasing velocity which in turn increases with depth, attributes such as coherence benefit by using a shorter vertical analysis windows in the shallow section and longer vertical analysis windows in the deeper section. Since most coherence implementations are design to use a fixed vertical analysis window, the interpreter simply runs the algorithm using an appropriate window for each zone to be analyzed. Both coherence and curvature are structurally driven algorithms, with coherence computed along structural dip and curvature computed from structural dip (e.g. Lin et al., 2013). Volumetric dip and azimuth volumes can be very valuable interpretation tools (e.g. Chopra and Marfurt, 2007). They are also the foundation for the structurally driven seismic attributes. Chopra and Marfurt (2007) mentioned in their book that Picou and Utzman (1962) introduced dip estimation into 2D seismic interpretation. Finn and Backus (1986) extended dip estimation to 3D as a piecewise continuous function of spatial position and seismic traveltime. Cerveny and Zahradnik (1975) introduced Hilbert transform and application into geophysics to calculate complex traces of seismic data. Luo et al. (1996) described method to estimate vector dip based on a 3D extension of this work. Marfurt et al., (1999) improved the estimation of 3D vector dip by smoothing with mean or median filters. In order to compensate for the blurring caused by such smoothing, Luo et al., (2002), applied multiple analysis window (Kuwahara et al., 1976) to generate an edge-preserving smoothing algorithm. Later, Marfurt (2006) modified this approach for volumetric dip calculations where he used 3D rather than 2D overlapping windows. One of the important application for volumetric dip is structurally driven coherence. Bahorich and Farmer (1995) published the first-generation 3-D seismic discontinuity - coherence, by calculating localized waveform similarity in both inline and crossline directions, to help distinguish faults and stratigraphic features in seismic interpretation. Marfurt et al., (1998) provided the second-generation, semblancebased coherency algorithm, which improved the vertical resolution. Gersztenkorn and Marfurt (1996, 1999) offered the third-generation, coherence based on calculating the eigenvalues and eigenvectors of the covariance matrix. Volumetric dip and coherence Geologically, we define a planar interface such as a formation top or internal bedding surface by means of apparent dips θx and θy, or more commonly, by the surface s true dip θ, and its strike, ψ (Figure 1). Page 1659

2 Figure 1. The definition of volumetric dip. (After Marfurt, 2006). First, the algorithm estimates coherence using semblance, the maximum coherence is calculated along the dip indicated by the red dashed line. The peak value of this curve estimates coherence, while the dip value of this peak estimates instantaneous dip. To improve the accuracy of the results, the multiple-analysis-window (Kuwahara et al., 1976) and self-adaptive window are applied. As for the coherence, we calculate the energy of the five input traces within an analysis window first, and then we get the average trace, and finally, we replace each trace by the average trace and calculate the energy of the five average traces. The semblance is the ratio of the energy of the coherent (averaged or smoothed) traces to the energy of the original (unsmoothed) traces. High resolution seismic attributes estimation using selfadaptive window We define the window height as the half-height of the analysis window, the window itself will always be centered along dip. Spectral analysis of the seismic data allows us to map the dominant frequency (wavenumber) of the seismic source wavelet as well as tuning frequency phenomena. If the dominant source wavelet frequency (wavenumber) is 50 Hz (10 circles/km), the dominant period is s (0.100 km), suggesting a half-window size of s (0.050 km) for attribute calculation. However, we know that the dominant frequency (wavenumber) changes laterally and vertically with thin bed tuning and attenuation effects, such that many areas of the survey will be analyzed using a suboptimum window. Lin et al., (2013) added dip compensation to spectral decomposition and noted that the apparent peak frequency (wavenumber) and the real peak frequency (wavenumber) are different by 1/cosθ in the presence of dip θ. Here, we are going to use apparent peak frequency (wavenumber) to get the window height. H gate = 1 2f peak the actual size may be a smaller or larger depending on the data quality. For our data we use a size that will be 1.05 times larger. The following single trace example illustrates the workflow. Figure 2. (a) The time migrated seismic trace; (b) frequency spectrum (circles/s or Hz) of (a) seismic trace; (c) the original (blue curve indicated by blue arrow) and smoothed (red curve indicated by red arrow) peak frequency curves; (d) the original (blue curve indicated by blue arrow) and smoothed (red curve pointed by red arrow) self-adaptive window size (ms). Figure 2 and Figure 3 show us the seismic trace, frequency (wavenumber) spectrum and peak frequency (peak wavenumber) curves as well as the corresponding self-adaptive window size of time migrated data and depth migrated data, respectively. The smoothing for peak frequency (wavenumber) is very necessary because the existence of the abnormal values pointed by blue arrow. The yellow arrows in Figure 2 and Figure 3 indicate the relevant self-adaptive window size (ms for time migrated data; m for depth migrated data). We can found that the self-adaptive size match the seismic trace (time migrated data and depth migrated data) very well. Figure 3. (a) The depth migrated seismic trace; (b) wavenumber spectrum (circles/km) of (a) seismic trace; (c) the original (blue curve indicated by blue arrow) and smoothed (red curve indicated by red arrow) peak wavenumber curves; (d) the original (blue curve indicated by blue arrow) and smoothed (red curve indicated by red arrow) self-adaptive window size (m). Page 1660

3 Application The data is from an oilfield of east China. There are lots of fault-controlled reservoirs, exhibiting strongly on the seismic profile shown on both the time migrated and depth migrated data in Figure 4. We found that the horizons are much deeper in depth migrated data than the ones in time migrated data. This is because the increase of velocity with time (depth). The sample increments are 0.002s and 0.01km for time and depth migrated data, separately. We found the data focus on the low frequency (wavelength). Figure 4 shows us the seismic profile of (a) time migrated data and (b) depth migrated data. The red arrows indicate the faults, which are much clearer in depth migrated data and the fault planes are more continuously. The orange arrows show us the migration artifacts, the depth migrated data are suffered more than the time migrated data. The green arrow in depth migrated data indicates a lower frequency compared to the time migrated data. For the blue arrow in depth migrated, it gives us a clearly fault plane, which is blurred in time migrated data. The frequency range is 0 40 Hz for time migrated data, while the wavenumber range is about 0 20 circles/km for depth migrated data (Figure 5). We can found that the wavenumber for depth migrated data is about half of the frequency for time migrated data. The white arrow in Figure 5 shows us the low peak frequency (wavenumber) which should be a little higher. This is because the existence of the migration artifacts. The black y describes the main faults of the data. Figure 4. Seismic profile of (a) time migrated data and (b) depth migrated data. The figure 6 indicates us the huge difference of coherence profiles using two different algorithm. The red arrow shows us the three main faults, they are clearer in the profile with self-adaptive window, for both the time and the depth migrated data, though the stair steps are still existed. The orange arrows point to two faults, the stair step phenomenon is obviously in time migrated data, while the faults are continuous in depth migrated data, and the noise are removed a lot for the coherence profile using self-adaptive window. The black arrows in Figure 8 (a) and (c) show us the vertical window artifacts generated by user-define constant window, while they disappear in Figure 8 (b) and (d) because the usage of the self-adaptive window. Figure 5. Vertical slices of peak frequency (wavenumber) of (a) time migrated data and (b) depth migrated data. Conclusions The attributes calculation using user-define window is more suitable to detect geology structures. The artifacts suffering from constant window size can be removed by the proposed algorithm Furthermore our technique has the ability to improve both the lateral and vertical resolution of seismic attributes, especially the vertical resolution both in time and depth domain. Page 1661

4 Acknowledgements We thank the sponsors of the OU Attribute-Assisted Processing and Interpretation Consortium for their financial support and BGP for permission to publish showing their data. We also thank The National Science Foundation of China (seismic multi-wave fields characteristics analysis of the thin interbedded reservoirs, Grant No ) EDITED REFFERENCE Figure 6. The coherence profiles of time migrated data with (a) user-define constant window and (b) self-adaptive window; and the coherence profiles of depth migrated data with (c) user-define constant window and (d) self-adaptive window. Page 1662

5 EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2014 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES Bahorich, M. S., and S. L. Farmer, 1995, 3D seismic discontinuity for faults and stratigraphic features: The coherence cube: The Leading Edge, 14, , Cerveny, V., and J. Zahradnik, 1975, Hilbert transform and its geophysical applications: The Czech Digital, Acta Universitatis Carolinae: Mathematica et Physica, 16, no. 1, Chopra, S., and K. J. Marfurt, 2007, Seismic attributes for prospect identification and reservoir characterization: SEG, Finn, C. J., 1986, Estimation of three dimensional dip and curvature from reflection seismic data: M. S. thesis, University of Texas. Gersztenkorm, A., and K. J. Marfurt, 1996, Eigenstructure based coherence computations : 66 th Annual International Meeting, SEG, Expanded Abstracts, Gersztenkorm, A., and K. J. Marfurt, 1999, Eigensturcture based coherence computations as an aid to 3D structural and stratigraphic mapping: Geophysics, 64, , Kuwahara, M., K. Hachimura, S. Eiho, and M. Kinoshita, 1976, Digital processing of biomedical images: Plenum Press, Lin, T. F., B. Zhang, and K. J. Marfurt, 2013, Spectral decomposition of time-versus depth-migrated data: Presented at the 83 rd Annual International Meeting, SEG. Luo, Y., S. Al Dossary, M. Marhoon, and M. Alfaraj, 2002, Edge-preserving smoothing and applications : The Leading Edge, 21, , Luo, Y., W. G. Higgs, and W. S. Kowalik, 1996, Edge detection and stratigraphic analysis using 3D seismic data: 66 th Annual International Meeting, SEG, Expanded Abstracts, Marfurt, K. J., 2006, Robust estimates of 3D reflector dip and azimuth: Geophysics, 71, no. 4, P29 P40, Marfurt, K. J., R. L. Kirlin, S. H. Farmer, and M. S. Bahorich, 1998, 3D seismic attributes using a semblance-based coherency algorithm: Geophysics, 63, , Marfurt, K. J., V. Sudhakar, A. Gersztnkorn, K. D. Crawford, and S. E. Nissen, 1999, Coherency calculations in the presence of structural dip: Geophysics, 64, , Picou, C., and R. Utzmann, 1962, La coupe sismique vectorielle: Un pointe semi-automatique : Geophysical Prospecting, 10, no. 4, , Page 1663