True Amplitude Extraction Technology and Its Application in Pre-Stack Seismic Data

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1 Journal of Earth Science, Vol. 26, No. 4, p , August 25 ISSN X Printed in China DOI:.7/s True Amplitude Extraction Technology and Its Application in Pre-Stack Seismic Data Xiaohui Yang, Siyuan Cao*, Dian Yuan CNPC Key Laboratory of Geophysical Prospecting, China University of Petroleum, Beijing 2249, China ABSTRACT: Common-reflection-point (CRP) gather is a bridge that connects seismic data and petrophysical parameters. Pre-stack attributes extraction and pre-stack inversion, both of them are important means of reservoir prediction. Quality of CRP gather usually has great impact on the accuracy of seismic exploration. Therefore, pre-stack CRP gathers noise suppression technology becomes a major research direction. Based on the vector decomposition principle, here we propose a method to suppress noise. This method estimates optimal unit vectors by searching in various directions and then suppresses noise through vector angle smoothing and restriction. Model tests indicate that the proposed method can separate effective signal from noise very well and suppress random noise effectively in single wavenumber case. Application of our method to real data shows that the method can recover effective signal with good amplitude preserved from pre-stack noisy seismic data even in the case of low signal to noise ratio (SNR). KEY WORDS: vector decomposition, noise suppression, angle smooth, spline function. INTRODUCTION In China, oil and gas resources are mainly deposited in the Midwest region, where the natural geographical environment is abominable. And the topography of the Midwest is characterized with concave and convex land, deeply buried target layers and complex geological structure. The biggest difficulty in seismic data processing of these complicated regions is that there are a lot of regular interference wave and scattering wave in pre-stack seismic gathers. It is hard for us to differentiate effective wave from the low signal-to-noise ratio (SNR) original seismic data. Therefore, an innovative technology which can extract weak signal from strong noise background is needed urgently. At present, the most important task is looking for subtle oil and gas reservoirs. Pre-stack inversion is a major means for exploration of subtle traps and SNR is the main factor which affects pre-stack inversion results. Therefore, the noise suppression process is one of the most important contents in the research of seismic exploration; and it has great significance in oil and gas exploration and development. Generally speaking, noise in seismic exploration can be divided into three parts: linear interference, multiple wave and random noise. Conventional denoising methods can be divided into two categories. One category is transform-based method. This method separates effective wave from noise by mathematical transformation, such as f-k transform (Sheriff and Geldart, 995), Radon transform (Kabir and Marfurt, 999; *Corresponding author: siyuan.caoff@gmail.com China University of Geosciences and Springer-Verlag Berlin Heidelberg 25 Manuscript received September 2, 24. Manuscript accepted December 3, 24. Foster and Mosher, 992; Hampson, 986; Thorson and Claerbout, 985), etc.. After transformation, there are some differences between effective wave and noise in transformation domain. Using these differences, effective wave can be distinguished from noisy wave. Another category is model-based denoising method, such as bunching filter method (Özbek, 2; Hu and White, 998) and wave equation extrapolation method (Zhou and Greenhalgh, 996). Such methods predict noise through simulation and inversion and then subtract the predicted noise in original noisy data. In such methods, there is no need to know subsurface structure and lithology. Wu and Cao (22) removed random noise of seismic data using orthogonal multiwavelets transformation. Based on this method, Cao et al. (22) recovered break-point information in seismic data and achieved good results. Lu (2) proposed a seismic random noise suppression method using the predictive filter in the discrete cosine transform (DCT) domain and pointed out that seismic data can be represented with fewer coefficients by DCT. Liu et al. (2) introduced a noise suppression method using nonstationary polynomial fitting (NPF), which is based on the assumption that effective signal is coherent along the offset axis in a normal move out (NMO) corrected CMP gather. The coherent components with amplitude variation along the event can adaptively be estimated by NPF while the smoothness of the polynomial coefficients is controlled by shaping regularization. Results indicate that this method can effectively suppress random noise and coherent noise in addition it can preserve seismic signals very well. There are some conventional methods for random noise suppression, e.g., F-X prediction filtering technology (Canales, 984), F-K domain filtering method, polynomial fitting method (Yu et al., 988), and vector decomposition technique, etc.. Each method has its own applicability and limitation. F-X prediction Yang, X. H., Cao, S. Y., Yuan, D., 25. True Amplitude Extraction Technology and Its Application in Pre-Stack Seismic Data. Journal of Earth Science, 26(4): doi:.7/s

2 True Amplitude Extraction Technology and Its Application in Pre-Stack Seismic Data 523 filter can effectively suppress random noise. However, this method not only enhances the energy of all reflected events but also strengthens coherent noise. F-K filtering method, is suitable for linear coherent noise suppression. Frequency band of noise in real data is usually wide so that it is difficult for F-K filtering method to remove noise drastically and because its effective signals are usually damaged (Ma et al., 2). Besides that, this method cannot achieve ideal effect, especially for data which is acquired in complicated geological structure region. Polynomial fitting noise suppression technique can effectively suppress random noise and preserve AVO (amplitude versus offset) character of reflected events. However, it cannot separate lower-order signal from noise effectively. Vector decomposition noise suppression method is conducted by restraining unrelated components to increase the relevance of the adjacent channel signal (Wang, 99, 989). Signal vector is usually orthogonal to noise vector so it is easy to separate signal vector from noise vector. After vector decomposition noise suppression, relative amplitude relations are preserved both in lateral and vertical directions. This method can be successfully used in pre-stack and post-stack denoising process. But, it is usually used in post-stack process and not suitable for pre-stack process because of large amount of calculation. Its denoising effect is affected by many factors, including relevant unit vector, DC (direct current) component, and selection of denoising parameters and so on. Coincidentally there is lack of quality control means to evaluate denoising effect. Therefore, the vector decomposition noise suppression method is needed to be improved in some aspects. Xia et al. (2) introduced a noise elimination method by combining median filtering and vector resolution. The new method overcomes the shortcomings of median filtering and vector decomposition for noise suppression, such as lowing the dominant frequency, difficulties of calculating relevant vectors. He (2) analyzed the denoising effect of vector decomposition method for single-component and multi-component signals noise suppression. Application in real data indicates that this method can suppress random noise very well, while the result is affected by the broadness of time window and the number of traces. Difficulty in separation of effective signals from noise usually exists in denoising methods. If the method is not performed well, there is still noise in signal and the effective signal is usually damaged. In this article, theory about vector decomposition method is studied first and it indicates that effective signal vectors are usually perpendicular to noise signal vector. Based on this, the modified vector decomposition method for noise suppressing is proposed. It improves capability for signal and noise separation by spline interpolation, dip search and vector smoothing. Finally, model tests and field data application show the feasibility of our method. VECTOR DECOMPOSITION Generally speaking, there is a high correlation between adjacent seismic traces. Single channel seismic data can be assumed to be a high-dimension vector. Here, we define value of each sample in a single channel seismic data as a, a 2, a n. n Then the single data can be expressed as A ai k k and k i k ( k, 2, n ) is a unit vector. These unit vectors are orthogonal to each other. Therefore, the correlation between adjacent seismic traces is consistent with the correlation between adjacent vectors. It is well known that when the directions of two unit vectors are close to each other or the angle between two unit vectors is close to zero, they have a high correlation. The angle of a single seismic trace will change when the seismic trace contains noise (expressed as B ). The angle between vectors A and B is defined as α and it can be calculated through the following formula A B cos () A B where denotes the dot product of vectors. To investigate the degree of direction deviation of a noisy signal, here we select Ricker wavelets with various SNR to study. The dominant frequency for Ricker wavelet is 3 Hz. We have three kinds of noisy signal (shown in Figs. a, b and c) and the SNR is 5,, and.5, respectively. The angle between the noisy Ricker and noise-free Ricker is a function of SNR and it is displayed in Fig. d. With the increasing of noise, the angle ranges from to 5. This indicates that the degree of direction deviation is more and more serious when the SNR decreases. From many tests we can find that when SNR is low enough, the angle is close to 9. Therefore, the random noise is usually orthogonal to effective signal. Figure 2 is a schematic diagram of vector composition. The noisy signal vector B can be regarded as the composition of two mutually orthogonal signals B // and B, where B // represents effective signal vector and B is random noise vector. The denoising method by vector decomposition is to preserve the projection component ( B // ) of B and suppress the projection component ( B ) of B. Vector C is a vector after denoising and is expressed as B B C cos B, B // B mcos B, B B B (2) // B where, ab, represents the angle between vectors a and b, and m is the coefficient of noise attenuation, ranging from to. When m is equal to, this method does not suppress the vertical component. When m is equal to, it will fully suppress the vertical component. The unit vector that parallels to the vector B // is defined as the unit correlate vector, and how to exactly extract this vector is a key technology of vector decomposition denoising method. When there are some errors in the estimated unit correlate vector, parts of the effective signal will exist in the vertical component (the second term of Eq. 2 on the right). In a word, parameter m will play a regulatory role, as much as possible to preserve the effective signal. 2 NOISE SUPPRESSION PROCESS In this section, the vector decomposition noise suppression method is applied to pre-stack NMO corrected gathers. In the gathers, primary reflection events are flat. Flow chart of process is shown in Fig. 3. The specific steps are as follows. (a) Data preprocessing and analyzation: SNR and dominant

3 524 Xiaohui Yang, Siyuan Cao and Dian Yuan SNR= 5 (a) SNR= (b) SNR=.5 (c) Amplitude Amplitude Amplitude (d) Angle (º) SNR Figure. Ricker wavelets with different SNR. SNR of (a), (b) and (c) are 5, and.5 respectively. (d) Angle between noisy Ricker wavelet and noise-free Ricker wavelet is plotted as a function of SNR B B Input pre stack gathers CRP Pretreatment and analysis B// Figure 2. A schematic diagram of vector decomposition. The transverse interpolation and vector angle estimation of adjacent trace frequency bands of effective waves are estimated. It is benefit for the selection of parameters for subsequent processing. (b) Interpolation: We interpolate seismic gathers horizontally with a proper function and estimate angles between adjacent channel signals. (c) Estimate the unit correlation vector in multiple directions. Amplitude extraction in lateral direction for primary reflections is the first step. Then we sum the multiple adjacent vectors together to obtain the unit correlation vector. If some residual NMO correction exists in the pre-stack CRP gather, then the reflection events are no longer horizontal. In order to obtain a unit correlation vector, which is parallel to the reflection events, amplitude for primary reflections are extracted in various dip directions rather than transversely. Then we calculate the summation of reflection amplitude in each direction and maximum summation indicates the dip angle of the reflection event. After that, correlation vector for the dip events is computed in the dip direction by the method used before. (d) Separate noise from signal. Parameter m is chosen reasonably for noise suppression. (e) Smooth: Angle between adjacent channels after noise suppression is needed to be smoothed out. The specific reason is shown in Fig. 4. (f) Quality control is done to determine whether the effective signal is damaged or not. (g) Down-sampling: The interpolated gather should be down-sampling as the same sampling rate of the original Select denosing parameters Multi directional search unit correlation vector Separation of signal and noise Constraint of vector angle smoothing Is the signal damaged? No Resampling Output pre-stack gathers CRP Yes Figure 3. Flow chart of pre-stack vector decomposition noise suppression method. gathers and the new gather is the data after noise suppression. Wedge models with different SNR are used in angle smooth analysis between adjacent channel data. The synthetic record of wedge model without any noise is shown in Fig. 4a and the sampling interval is ms. With an increase in trace number, the

4 True Amplitude Extraction Technology and Its Application in Pre-Stack Seismic Data Angle (º) 7 (a) (b) 8 9 Angle (º) (c) (d) Angle (º) 6 4 (e) Trace number 2 (f) Trace number Figure 4. Wedge model with different SNR are displayed in (a), (c) and (e). Angles between adjacent channels of corresponding models are plotted as a function of trace number in (b), (d) and (f). difference in arrival time of the two interfaces becomes larger and larger. Angles of adjacent channel signals at various offsets range from 5 to 2 and are displayed in Fig. 4b. With an increase in offset, the angle curve changes slowly and smoothly. SNR of seismic data shown Fig. 4c is and its angle curve is plotted in Fig. 4d. There are two differences between Figs. 4b and 4d. First, angles range from 2 to 4 and are larger than those of seismic data without noise. Second, the angle curve is no longer smooth. Figure 4e is a section with SNR of.25. Figure 4f shows the adjacent channel vector angle, and the angle distributed within [4, 6 ] range. Figure 5 shows the derivative of three angle curves together. The blue line represents noise-free case (SNR= ). Red and black lines correspond to SNR= and SNR=.25, respectively. The derivative curve of noise-free section is smooth and changes slowly, while that of noisy signal changes dramatically. By comprehensive comparison, the results indicate that the trend of three angle curves are basically consistent. With a decrease of SNR, the value of vector angle of adjacent channel section increases and the angle curve is no longer smooth and changes more and more dramatically. Based on this, it is necessary to smooth the vector angle curve for noisy gathers. 3 MODEL TEST The first set of model test is based on the analog recording. As shown in Fig. 6a, we set a five layer model with two kinds of regular noises (linear noises and linear hyperbolic interference). There are two difficulties in denoising process for this model. First, partial interference signals in this synthetic seismic data are single wavenumber signals. Besides, primary wave and noise almost completely overlap (as red circle shown). Figure 6b displays the seismic gather after denoising process by the modified vector decomposition. And it is easy to find that effective signals are effectively recovered. In the regular noise profile (Fig. 6c) obtained by noise suppression process, red circles indicate that noise is effectively suppressed and blue circles show that there is little damage on effective signal during the denoising process. To analyze the effect on random noise suppression by our method, some random noise is added to Fig. 6a. The data with SNR of.8 is shown in Fig. 7a. In this data, both random noise and regular noise exist. From Figs. 7b and 7c, it can be concluded that both random noise and regular noise are suppressed effectively while the damage on effective signal is relatively very little. The derivatives of angle (º) SNR= SNR= SNR= Trace number Figure 5. Derivative curves of vector angle corresponding to various SNR.

5 526 Xiaohui Yang, Siyuan Cao and Dian Yuan (a) (b) (a) (b) (c) Figure 6. (a) A seismic data with regular noise, (b) seismic data profile after denoising process, (c) noise obtained by denoising process. To analyze the amplitude preservation character of our method, five models with various SNR are used here. SNR of five models are,.8,.53,.4, and.2, respectively. After denoising process, amplitude versus offset of the fourth lateral event for five models are plotted respectively in Fig. 8a and corresponding relative errors are plotted as a function of offset in Fig. 8b. As shown in Fig. 8a, the blue line (labeled as d2) represent the real amplitude and c,c,c2,c3,c4 represent (c) Figure 7. (a) A noisy seismic data with regular and random noise, (b) seismic data after denoising, (c) noise obtained by denoising process. amplitude recovery from the original data with SNR.8,.53,.4 and.2. In Fig. 8b, it is easy to notice that the relative error is less %. Generally speaking, SNR of field data is usually lower than. Therefore, it is hard for conventional methods to process field data denoising. Model tests indicate that our method can achieve an acceptable result even if SNR is.2 (e.g., the forth event).

6 True Amplitude Extraction Technology and Its Application in Pre-Stack Seismic Data 527 Amplitude ( 4 ) Relative error (a) (b) d2 c c c2 c3 c4 c c c2 c3 c4 Figure 8. Amplitude analysis. (a) The fourth event amplitude with various SNR after denoising process; (b) relative error of the fourth event with various SNR. 4 PRE-STACK SEISMIC DATA PROCESSING The data shown in Fig. 9a is a pre-stack gather acquired from a land field. Figures 9b and 9c represent data profile after denoising and noise profile, respectively. In the real data, it is easy to see random noise and tilt events, which make it difficult to track seismic events. This interference noise results in a reduction in accuracy of amplitude extraction and AVO analysis. After denoising, continuities of seismic events and the SNR have been greatly improved. In Fig. 9a, at about 925 ms (labeled with an ellipse), feature of amplitude change is not obvious which is harmful for the subsequent process, such as inversion and attributes extraction. After processing by our method, feature changing of seismic reflection wave amplitude with offset (labeled with an ellipse in Fig. 9b) is more apparent than before. Tilt noise and random noise removed here are displayed in Fig. 9c, which indicates that our method does little harm to effective wave during denoising process. Figure displays the second application in the land data. Figure a is the original gather, b is the synthetic pre-stack gather based on wells information, and c is the gather after noise suppression. SNR of the original data is seriously low and feature changing of seismic wave amplitude with offset are complicated, disorderly. There is no obviously consistency between synthetic gather and real data. Obviously, it is too hard to find the effective wave and track the maker bed events and is impossible to conduct the pre-stack inversion based on this real data. Compared with original data, the SNR after denoising displayed in Fig. c is improved greatly and data after denoising is highly consistent with forward seismic gather. The features of events are clear and the continuity is better than before. Figures a and b show the partial angle-stack gathers before and after denoising process separately. Black wiggles represent the near partial angle-stack seismic data. Blue wiggles and red wiggles represent the middle and far partial angle-stack seismic data separately. The incident angle of the near, middle and far partial angle-stack seismic data range from 5, 5 3 and 3 48, respectively. Blue lines and green lines in lateral direction represent two reflections we ever picked up. It is easy to find that the correlation of different angle stack gathers in Fig. a is much poor than Fig. b. This indicates that amplitude of different offsets in the gather denoising by our method is reasonable and credible and therefore it is acceptable for subsequent pre-stack inversion and interpretation process. (a) Trace number (b) Trace number (c) Trace number Figure 9. (a) A CRP gather; (b) the CRP gather after denoising; (c) noise obtained by denoising process.

7 Xiaohui Yang, Siyuan Cao and Dian Yuan 528 Figure. (a) A CRP gather, (b) synthetic CRP gather based on well data, (c) CRP gather after denoising (a) (b) Kq Kq In6jd_kq_xq J2x Js3 Js2 Js2oilt Js2bot js J5 In6jd_kq_xq 2.65 Time (s) Js2 Js2oilt Js2bot In6jd_kq_xq J2x Js Time (s) js J5 In6jd_kq_xq Figure. Partial angle-stack gathers. The original pre-stack gather is before (a) and after (b) denoising. 5 CONCLUSION The improvement on computational accuracy of angle between vectors and angle smooth process are keys to the improved vector decomposition noise suppression method. Some operations such as collection of statistics features of angle change between adjacent seismic traces and selection of high-dimension vector function and spline function have great influences on the improvement of our method. Meanwhile, calculated amount of our method is large because of high-dimension calculation, especially in pre-stack data denoising process. Therefore, how to improve the computational efficiency and optimize the selection of denoising parameter will be the subject in the future. Then the improved vector decomposition method will be applied broadly in the denoising process. ACKNOWLEDGMENT This study was supported by the National Science and Technology Major Project of China (No. 2ZX524--). REFERENCES CITED Cao, S. Y., Liu, H. W., Sa, L. M., 22. A Study on the Restoration of the Original Fracture Information. Petroleum Exploration and Development, 29: 3 5 (in Chinese with English Abstract) Canales, L. L., 984. Random Noise Reduction. SEG International Exposition and 54th Annual Meeting, Atlanta Foster, D. J., Mosher, C. C., 992. Suppression of Multiple Reflectors Using the Radon Transform. Geophysics, 57(3): Hampson, D., 986. Inverse Velocity Stacking for Multiples

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