Comparison of wavelet estimation methods - Springer Link

Geosciences Journal Vol. 17, No. 1, p. 55 − 63, March 2013 DOI 10.1007/s12303-013-0008-0 ⓒ The Association of Korean Geoscience Societies and Springer 2013

Comparison of wavelet estimation methods Bo Y. Yi Gwang H. Lee* Han-Joon Kim Hyeong-Tae Jou Dong G. Yoo Byong J. Ryu Keumsuk Lee

Korea Institute of Geoscience and Mineral Resources, Daejon 305-350, Republic of Korea Department of Energy Resources Engineering, Pukyong National University, Busan 608-737, Republic of Korea

} Korea Institute of Ocean Science and Technology, Ansan 426-744, Republic of Korea } Korea Institute of Geoscience and Mineral Resources, Daejon 305-350, Republic of Korea Korea National Oil Corporation, Anyang 431-711, Republic of Korea

ABSTRACT: Wavelet estimation is a very important task in seismic data processing and analysis such as deterministic deconvolution, seismic-to-well tie, and seismic inversion, among others. We investigated the wavelets estimated from four different methods: (1) the wavelet estimated from the seafloor signal; (2) the wavelet estimated fully from well-log data; (3) the wavelet estimated using seismic and well-log data; and (4) the wavelet estimated from sparse-spike deconvolution. The wavelets estimated from 2-D seismic data using the four methods are quite comparable to one another. The results of the deconvolution and inversion of the 2-D seismic data using the four wavelets show that the wavelet estimated from the seafloor signal can be as effective as those estimated from the more rigorous methods. Key words: wavelet estimation, deconvolution, inversion

1. INTRODUCTION The reflectivity or the impulse response of the earth can be obtained by deconvolution of seismic data if the source wavelet is known and the noises can be removed. Zerophase wavelet-shaping correction to reshape the source impulse response from near minimum or mixed phase to zero phase requires the wavelet. Zero-phase seismic data improve the accuracy of the interpreted subsurface geology and provide the correct input to many important seismic data analysis procedures including the amplitude-variationwith-offset (AVO) and seismic attribute analyses (Henry, 1997). Most modern seismic inversion methods require the wavelet information. The solution of the inversion, which is not unique, can be constrained by comparing the seismic traces with synthetic traces constructed from the convolution of the inversion model and the wavelet. The wavelet is also the key input to seismic-to-well tie. The wavelet can be measured directly during seismic data acquisition but it requires special acquisition techniques (Ikelle et al., 1997). The use of controlled-phase acquisition and processing strategies can help control seismic phase *Corresponding author: [email protected]

(Trantham, 1994), but mismatches between recorded seismic data and synthetic traces constructed from well-log data occur very frequently (Edgar and Baan, 2011). The wavelet is more commonly estimated from seismic and well-log data. The wavelet estimation methods fall largely into two categories: (1) purely statistical ways and (2) the use of well-log data (White and Simm, 2003; Hampson-Russell, 2007). The statistical method estimates the wavelet using the amplitude spectrum or autocorrelation functions of the recorded seismic data but cannot determine the phase of the wavelet without further assumptions, such as minimum phase. The reflectivity series computed from sonic and density logs can be used to estimate the wavelet with proper amplitude and phase spectra. In this study, we compared four different methods of wavelet estimation: (1) estimation from the seafloor signal; (2) estimation fully from well-log data; (3) statistical estimation of the amplitude spectrum from seismic data and estimation of the phase spectrum from well-log data; and (4) estimation as part of sparse-spike deconvolution. First, we estimated the wavelets using the four methods. Next, we performed seismic-to-well tie using the four estimated wavelets to test how well the synthetic traces based on these wavelets are correlated with the seismic traces at the well. Then, we applied the four wavelets to deconvolution and inversion of a 2-D seismic profile to test each wavelet against the rest. Our results show that the wavelet estimated from mathematically simple methods can be as effective as those estimated from more computationally rigorous methods. 2. DATA Data used in this study consist of a 2-D multi-channel seismic profile and sonic and density logs from a well in the Ulleung Basin, East Sea (Japan Sea) (Fig. 1). The seismic profile was acquired in 2005 by the Korea Institute of Geoscience and Mineral Resources (KIGAM) on the R/V Tamhae II as part of the pre-drill study for the Ulleung Basin

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Bo Y. Yi, Gwang H. Lee, Han-Joon Kim, Hyeong-Tae Jou, Dong G. Yoo, Byong J. Ryu, and Keumsuk Lee

Fig. 1. (a) N-S seismic profile from the Ulleung Basin, East Sea (Japan Sea). The vertical line indicates the position of the UBGH01-09 well. (b) Sonic (left) and density (right) logs from the UBGH01-09 well. The insets are the East Sea (Japans Sea), bathymetry of the Ulleung Basin, and data locations. Contour interval in meters.

Gas-Hydrate Drilling Expedition 2007. A 240-channel (3000m long) streamer recorded shots from a 1035-in3 (2000 psi) six air-gun array. The hydrophone group interval and shot spacing were 12.5 and 25 m, respectively, yielding 60-fold coverage. The sampling interval is 1 ms. Data processing included resampling, frequency filtering, true amplitude recovery, velocity analysis, dip-moveout correction, radon filtering, stacking, and time-variant band-pass filtering. Zero-phase shaping filter was not applied to the data. The sonic and density logs are from the UBGH01-09 well drilled on a buried seismic chimney during the 2007 expedition. 3. DATA ANALYSIS AND RESULTS 3.1. Wavelet Estimation We extracted 100-ms long wavelets, conditioned by the cosine taper with 20% wavelet length at both start and end of the wavelets to limit side-lobe amplitudes. The estimated wavelets are not zero phase because the seismic data were not processed for zero phase. The simplest method of estimating the wavelet is to derive it from the seafloor signal. Because the seafloor is typically

a simple, sharp interface, its seismic response should approximate the source wavelet. We extracted the wavelet from the average of 300 traces centered at the well location along the seafloor reflection (Figs. 2a and b) to increase the signal-to-noise ratio of the wavelet. The wavelet derived from the seafloor signal is of mixed-phase, characterized by a leading trough followed by the main peak and waning side lodes. The average phase is –35 degrees. Both the amplitude and phase spectra of the wavelet can be obtained by minimizing the difference between the seismic trace at the well and the synthetic trace constructed from well-log data. The wavelet is estimated by finding the operator or shaping filter which, when convolved with the reflectivity from the well, closely approximates the seismic trace. The wavelet (Fig. 2c) estimated from this full-estimation method is generally similar to that from the seafloor signal although the leading side lobes are characterized by a relatively large peak and double troughs. The peak in the trailing side lobes seen in the wavelet from the seafloor signal is not present. The amplitude spectrum of the full-estimation wavelet (Fig. 2d) looks quite different from that of the wavelet from the seafloor signal, characterized by large energy in the low frequency range. The average phase of the

Comparison of wavelet estimation methods

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Fig. 2. (a) Wavelet estimated from the seafloor signal. (b) Amplitude and phase spectra of the wavelet estimated from the seafloor signal; the average phase is −35 degrees. (c) Wavelet estimated fully from the well-log data. (d) Amplitude and phase spectra of the wavelet estimated fully from the well-log data; the average phase is −31 degrees. (e) Wavelet estimated from the hybrid method. (f) Amplitude and phase spectra of the wavelet estimated from the hybrid method; the average phase is −40 degrees. (g) Wavelet estimated from sparsespike deconvolution. (h) Amplitude and phase spectra of the wavelet estimated from sparse-spike deconvolution; the average phase is –32 degrees.

full-estimation wavelet is –31 degrees. The purely statistical estimation of the wavelet derives the amplitude spectrum from seismic data, assuming that the reflectivity is a random process. This assumption means that the autocorrelation of the recorded seismic data is approximately equal to the autocorrelation of the wavelet.

Thus, the amplitude spectrum of the wavelet is approximately equal to that of the recorded seismic data. The phase of the wavelet is assumed to be either minimum phase or zero phase depending on how the seismic data have been processed. The third method estimates the amplitude spectrum purely statistically and the phase spectrum from the well-

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log data for constant phase (Hampson-Russell, 2007). First, a series of constant phase rotations is applied to the statistically-estimated wavelet. Then, the synthetic trace is constructed for each rotation and correlated with the seismic trace at the well. Finally, the phase rotation that produces the maximum correlation is selected for the phase of the wavelet. This technique is called the hybrid method. The wavelet from the hybrid method (Fig. 2e) is similar more to that from the seafloor signal than that from the full estimation; its leading side lobes are more evident whereas the trailing side lobes are subdued compared with the wavelet from the seafloor signal. The phase spectrum of the wavelet from the hybrid method (Fig. 2f) is also quite similar to that of the wavelet from the seafloor signal. The average phase of the wavelet estimated from the hybrid method is –40 degrees. The fourth method is based on the iterated window maximization (IWM) algorithm for sparse-spike deconvolution, introduced by Kaaresen and Taxt (1998). This method assumes: (1) the reflectivity series is sparse (Kormylo and Mendel, 1982) and follows the Bernoulli-Gaussian distribution (Mendel, 1983); (2) the earth is horizontally layered; and (3) the wavelet is common to several traces. These assumptions provide a priori information as the unknowns (i.e., the reflectivity and wavelet) can be considered as realizations of stochastic variables. A Bayesian framework is used and a maximum a posteriori estimate is derived to combine the a priori information and the seismic data. The procedure alternates steps of wavelet estimation and reflectivity estimation. Thus, an optimal wavelet is obtained as an integral part of the process. The wavelet estimation requires a simple least-squares fit while the reflectivity is recovered by the IWM. The wavelet (Fig. 2g) from this method is very similar to that from the seafloor signal. Its phase spectrum (Fig. 2h) is somewhat narrower than those of other wavelets. The average phase of the wavelet is –32 degrees. The wavelet was computed from 11 traces centered at the well location. 3.2. Seismic-to-well Tie Seismic-to-well tie is a very important part of seismic data analysis and interpretation, providing a means of correctly identifying horizons to pick and estimating the wavelet (White and Simm, 2003) and helping obtain time-depth relationships. We performed seismic-to-well tie to examine how well the synthetic traces constructed from the convolution of the estimated wavelets and the reflectivity series computed from the well-log data are correlated with the seismic data (Fig. 3). The correlations for the full-estimation wavelet (Fig. 3b) and the hybrid wavelet (Fig. 3c) are very high (0.883 and 0.857, respectively). The correlations for the wavelets from the seafloor signal and sparse spike deconvolution are also quite high (0.831 and 0.832, respectively). The correlations greater than 0.7 are considered to be good

for most seismic data analysis procedures (Hampson-Russell, 2007). 3.3. Deconvolution The objective of deconvolution or wavelet processing is to make the output wavelet to be as closely as broadband and zero phase to ensure optimum resolution and ease of interpretation. We applied two-sided, deterministic Wiener deconvolution to the seismic data, using the estimated wavelets, to convert them into zero phase (Fig. 4). Then, the presumably zero-phase wavelets were extracted from each of the four deconvolved data sets, using the four wavelet-estimation methods (Fig. 5). The results of the deconvolution are quite comparable to one another and show a significantly increased temporal resolution compared with the original non zero-phase data. The reflectors stand out more distinctively on the deconvolved data since deconvolution has compressed the waveform at the reflections. The positivepolarity reflection immediately below the seafloor is of higher amplitude in the result using the full-estimation wavelet than other results (Fig. 4b). The layers in the interval between 2900 and 2960 ms in two-way travel time (TWTT) are better imaged in the results using the wavelets estimated from the seafloor signal (Fig. 4a) and sparse-spike deconvolution (Fig. 4d). The result using the hybrid method (Fig. 4c) is similar to that using the full-estimation wavelet but the 2900–2960 ms TWTT interval is more blurry. Overall, the results using the wavelets estimated from the seafloor signal and sparse-spike deconvolution provide better resolution. The wavelets extracted from the deconvolved data are approximately zero phase and largely comparable to one another except for the full-estimation wavelet which shows comparable characteristics only in the data deconvolved using the full-estimation wavelet (the black curves in Figs. 5c and d). The full-estimation wavelet is characterized by a large trough in the trailing side lobes that is delayed by about 10 ms compared with other wavelets (Figs. 5a, e, and g). The amplitude spectrum of the full-estimation wavelet is also different from other wavelets in that its low-frequency components contain larger energy than its high-frequency components. The amplitude spectra of the wavelets from the seafloor and sparse-spike deconvolution are very similar to each other. 3.4. Seismic Inversion The main objective of seismic inversion is to transform seismic reflection data into quantitative rock properties, descriptive of the reservoir (Pendrel, 2006). Post-stack inversion transforms the stacked seismic data into P-impedance (the product of density and P-wave velocity). In pre-stack inversion, P-impedance, S-impedance (the product of density and S-wave velocity), and density are computed. Many avail-


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Fig. 3. Seismic-to-well ties using the wavelets estimated from: (a) the seafloor signal; (b) the full-estimation method; (c) the hybrid method; and (d) sparse-spike deconvolution. Seismic-to-well correlations are very good for all cases. The synthetic trace (blue) and the corresponding seismic trace at the well (red) are repeated five times to help the correlation procedure.

able inversion methods are based on forward convolution of a reflectivity model with the known or estimated wavelet, comparison of the modeled output with the observed seismic trace and then updating the reflectivity model to minimize the difference between the modeled and observed traces (EERL, 2006).

We applied post-stack, model-based inversion to the original non zero-phase data to test the four non zero-phase wavelets (Fig. 2). The model-based inversion is known to work well on most data (Hampson-Russell, 2007). It requires the wavelet and thus the result can be significantly affected by the choice of the wavelet. The wavelet is convolved with

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Fig. 4. Seismic profiles after zero-phase shaping deconvolution using: (a) the wavelet estimated from the seafloor signal; (b) the fullestimation wavelet; (c) the wavelet estimated from the hybrid method; and (d) the wavelet estimated from spare-spike deconvolution. The results of deconvolution using the wavelets estimated from the seafloor signal and sparse-spike deconvolution largely provide better resolution than other wavelets especially at depths of 2900–2960 ms TWTT. See Figure 1a for the same seismic profile before zero-phase shaping deconvolution.

the reflectivity, computed from the impedance model of the well, to generate synthetic traces. An initial impedance model, constructed from the interpolation of the impedance values at the wells guided by the interpreted horizons, is perturbed iteratively until the resulting synthetic traces match the real traces within some tolerance level. The inversion results (Fig. 6) are generally comparable to one another but, overall, the inversion using the wavelet from the seafloor signal provides slightly better resolution than the rest. In particular, the high-impedance layers between 2900 and 2960 ms TWTT are better resolved across the profile in the inversion using the wavelet from the seafloor signal. However, the high-impedance layers between about 2970 and 2990 ms TWTT to the north of the seismic chimney are not clearly resolved compared with the results from other wavelets. 4. DISCUSSION AND CONCLUSIONS The wavelet estimated fully from well-log data provides slightly better images at very shallow depths compared with

other estimated wavelets. The synthetic-to-well correlation for the full-estimation wavelet is very good because the phase of the wavelet is obtained by forcing the well-derived synthetic to match the seismic. However, the full-estimation method calculates an exact wavelet only in a statistical sense and only works if the seismic-to-well tie is very good. Moreover, a timing or stretch error can cause rapid degradation, characterized by loss of high frequency in the wavelet, distortion of the phase spectrum, and production of unrealistic side lobes (Hampson-Russell, 1999). This is probably why the full-estimation wavelet shows large energy in the low frequency and its side lobes are quite different from those of other wavelets. The zero-phase wavelets estimated from the deconvolved data using the fullestimation wavelet are also different from the rest. The hybrid method has been found to be the most robust when seismic-to-well tie is poor (Hampson-Russell, 2007). However, the randomness assumption of reflectivity to estimate the amplitude spectrum is good only in practice. Reflectivity is not entirely a random process but rather high-


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Fig. 5. The zero-phase wavelet and its phase spectrum were estimated from each of the deconvolved profile shown in Figure 4 using the four methods (the red curves for the seafloor signal; the black curves for the full-estimation wavelet; the blue curves for the hybrid wavelet; and the cyan curves for the sparse-spike deconvolution). (a) and (b) for the seismic profile in Figure 4a. (c) and (d) for the seismic profile in Figure 4b. (e) and (f) for the seismic profile in Figure 4c. (g) and (h) for the seismic profile in Figure 4d. The estimated zero-phase wavelets are largely comparable to one another except for that (c and d) estimated using the full information from the well-log data, which has a large peak after the main peak and exhibits relatively lower amplitudes for the low frequencies.

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Fig. 6. Inversion results of the original non zero-phase data using the wavelets estimated from: (a) the seafloor signal; (b) the full-estimation method; (c) the hybrid method; and (d) sparse-spike deconvolution. The inversion results are comparable to one another, but overall the result using the wavelet from the seafloor signal is slightly better than the rest.

frequency components have a tendency to strengthen gradually (Yilmaz, 2001). The randomness assumption of reflectivity is closely tied to lithology of an area (Dey and Lines, 1998). If an exploration area has periodic properties, its reflectivity does not have the required statistical property of randomness (Dey and Lines, 1998). The phase is obtained by assuming that the well-log data provides ground truth but well-log data are not always available especially in a typical exploration project. The wavelets estimated from welllog data at nearby locations can also be significantly different (Edgar and Baan, 2011). Our results show that the wavelets estimated from the seafloor signal and sparse-spike deconvolution are a good representation of the seismic data, providing overall better resolution than the wavelets estimated from the well-log data. The wavelet estimation from sparse-spike deconvolution is a sophisticated technique, requiring commercial or proprietary tools and specialist skills to implement correctly. The wavelet estimation from an average of the seafloor reflections has been used widely because it can be done without any special skills or additional software packages and the result can be obtained very quickly. However, the

wavelet estimated from the seafloor signal has rarely been tested quantitatively against those estimated from more rigorous methods. We showed that the wavelet from the seafloor signal can be as effective as those from other methods. For onshore seismic data, any reflectors from uniform and continuous boundaries such as the top surface of carbonate rocks or igneous sills or volcanic flows can be used to estimate the wavelet. ACKNOWLEDGMENTS: Financial support to G.H. Lee was provided by the Ministry of Knowledge Economy of Korea (Reservoir Evaluation for Optimal Estimation of Unproduced Hydrocarbons) and the Ministry of Land, Transport and Maritime Affairs of Korea (Development of Technology for CO2 Marine Geological Storage Program). We thank two anonymous reviewers for their constructive comments. Hampson-Russell®, provided by CGGVeritas, was used for seismic data analysis.

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standing Stochastic Seismic Inversion. Earthworks Technical Note, 27 p. Edgar, J.A. and van der Baan, M., 2011, How reliable is statistical wavelet estimation? Geophysics, 76, V59–V68. Ikelle, L.T., Roberts, G., and Weglein, A.B., 1997, Source signature estimation based on the removal of first-order multiples. Geophysics, 62, 1904–1920. Hampson-Russell, 1999, Strata Theory. Hampson-Russell, 64 p. Hampson-Russell, 2007, Strata Guide 2007. CGGVeritas, 89 p. Henry, S.G., 1997, Catch the (seismic) wavelet. AAPG Explorer (March), 36–38. Kaaresen, K.F. and Taxt, T., 1998, Multichannel blind deconvolution of seismic signals. Geophysics, 63, 2093–1207. Kormylo, J.J. and Mendel, J.M., 1982, Maximum likelihood detection and estimation of Bernoullli-Gaussian processes. IEEE Transactions on Information Theory, 28, 482–488.

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Mendel, J.M., 1983, Optimal seismic deconvolution: An estimationbased approach. Academic Press, New York, 254 p. Pendrel, J., 2006, Seismic inversion – a critical tool in reservoir characterization. Scandinavian Oil-Gas Magazine, 5/6, 19–22. Trantham, E.C., 1994, Controlled-phase acquisition and processing 64th Annual International Meeting, SEG, Expanded Abstracts, 890–894. White, R. and Simm, R., 2003, Tutorial: Good practice in well ties. First Break, 21, 75–83. Yilmaz, Ö., 2001, Seismic Data Analysis – Processing, Inversion, and Interpretation of Seismic Data Volume I. SEG, Investigations in Geophysics, 1000 p. Manuscript received February 18, 2012 Manuscript accepted November 29, 2012