Arab J Geosci (2017) 10: 440 DOI 10.1007/s12517-017-3224-5 ORIGINAL PAPER Denoising and improving the quality of seismic data using combination of DBM filter and FX deconvolution Majid Bagheri 1 & Mohammad Ali Riahi 1 & Hosein Hashemi 1 Received: 21 August 2016 / Accepted: 26 September 2017 / Published online: 11 October 2017 # Saudi Society for Geosciences 2017 Abstract Seismic data denoising, random noise attenuation (RNA) and spike-like noise suppression, is a main consideration for improving the quality of records. RNA could increase signal to noise ratio (S/N) to avoid misinterpretation of seismic data. In this research, a novel method is created by using the combination of frequency-offset deconvolution (FXD) and decision-based median (DBM) filter for RNA from seismic data. The method is applied in two main phases; FXD is focused to remove the Gaussian noise and DBM filter is focused to attenuate the impulsive noise and spikes. To implement and verify the method, three types of data are used: two synthetic models (a model with linear events and a model with hyperbolic events) and an observed seismic section. The ability of the proposed method (FXD-DBM) in comparison of applying each in seismic RNA application is proven. The noise level is reduced obviously, and hence, the S/N of all examined seismic records is increased considerably after denoising by the combination of FX deconvolution and DBM filter. About the real seismic section, suppressing random noise and spikes show up improving the seismic reflector continuity and hence enhancing the interpretability of data. Moreover, some masked events by random noise are clarified in different parts of data after denoising using the planned method. Keywords FX deconvolution . DBM filter . Random noise attenuation . Seismic data . Signal to noise ratio * Majid Bagheri majidbagheri@ut.ac.ir 1 Institute of Geophysics, University of Tehran, PO Box 14115-6466, Tehran, Iran Introduction Impulsive and seismic random noise elimination is always an important and a challenging field in seismic processing to enhance the interpretability of data. Random and impulse noise could be generated by unspecific sources and could be recorded during data acquisition, so it is hard to predict and reduce the noise from seismic data. To achieve the goal, till now, many strategies have been introduced by different researchers (Spitz 1991; Abma and Claerbout 1995; Liu and Liu 2006; Cai et al. 2008; Bekara and Baan 2007, 2009; Sacchi and Naghizadeh 2009). The main common consideration of all is to eliminate random and spike noise while preserving the signal. Some other well-known examples of enormous researches for RNA consist of conventional median filter which is a simple and strong filter (Bednar 1983) that is broadly used as an effective filter. Deconvolution as an old technique is introduced by different researchers (i.e., Dimri 1992) and is improved for inverting and denoising data; for instance, a new filter is recently developed for inverting geophysical models (Ganguli et al. 2016). Curvelet transform appertains to a family of multiscale and also multidirectional data extensions that capable to attenuate incoherent noise from seismic records with low level of S/N (Starck et al. 2002). The curvelet domain is strongly appropriate for denoising since the incoherent energy is spreading almost equally between all curvelet coefficients whereas the coherent seismic energy maps to a relatively small number of significant curvelet coefficients. F-X prediction is well known and is the most common techniques in seismic processing to suppress noise (Spitz and Deschizeaux 1994; Abma and Claerbout 1995). In this method, the prediction filter is applied in a window and predicts a dip for an example, and tries to attenuate all other dips in that window. For impulsive seismic noise attenuation, a 440 Page 2 of 8 Arab J Geosci (2017) 10: 440 time-varying median filter is proposed by Liu et al. (2009). To enhance removing spikes, a decision method (DM) is planned which is capable to identify noise preceding to use of the median filter (Arastehfar et al. 2013). DM is simple and effective to reduce the impulsive noise level while preserving the signal samples. Application mainly consists of two stages, a synthetic study containing two models, and a real data seismic section. Synthetic data helps to evaluate the noise suppression using frequency-offset deconvolution (FXD) and decision-based median (DBM) filter and indicate the advantages of the planned method. Incoherent noise in the real seismic section that degrades the quality of the data is attenuated considerably using the proposed method. not. Hence, from Eq. 2, random noised can be estimated. A simple way to estimate white noise is possible using Eq. 3 by estimation error filter. However, for a problem if Eq. 3 is not satisfied, for instance when the signal not predicted well, Eq.2 will not be able to estimate random noise. On the other words, using the Fourier transform, a prediction filter is calculated for the spatial series created at each frequency. In general, the calculated filter can be applied in two stages in order to separate predictable signal from unpredictable noise in each frequency slice: first, finding the filter h by solving Eq. (1), and second, applying the filter to each frequency slice. Each filter is applied forward and then reversed in space, and the results are averaged to maintain a symmetrical application similar to the T-X prediction case (Abma and Claerbout 1995). The method DBM filter FX deconvolution The conventional median filter is based on a smoothing process. After positioning traces with their true dip, median filter replaces the sample in the center of the search window by the median value of all samples within this window (Tukey 1977). Having its drawback, median filter reduces the random noise and spikes significantly. In general, the filter works in offset (X) direction, and the running window slides down in the time axis. For data with high level of noise, conventional median filter will be smearing the details and edges and random noise could not be removed simply. To solve the problem, this strategy should be used that noisy samples initially be recognized and then median filtering be performed, whereas other samples reserved unaffected (Arastehfar et al. 2013). In other words, this strategy which called DBM method is planning a median operator where it will be applied just on noisy samples and the identity filter will be performed on the noise-free samples. In this method, the seismic record is considered as an image (S) which is supposed to be a vector (R) made by the rows of the image. In this way, the column vector R is constructed with the rows of matrix S. It should be remembered that the first and the last row along with the first and the last column must be ignored in this method. So, an image Sa × b of size a × b becomes a vector RN × 1 of size N × 1 in the vector outline, where N = (a − 2) × (b − 2). Wx(y) is defined as a processing window of size x × x, where x is an odd integer and y is the central pixel within the window (Kulkarni and Bhaskar 2013). In DM technique, one can detect a noisy pixels by comparing each pixel in the image with its neighboring pixels. Two successive pixels in R are compared to see whether the difference if greater than the threshold d which is a factor related to the noise level of data and the ‘Step’ parameter. The parameter ‘Step’ is also a pre-defined value, added to d depending on the The method was introduced by Canales (1984) firstly and is developed later by Gulunay (1986). The FX deconvolution prediction process depends on the form of linear events in frequency versus space direction. Linear events in the t–x domain apparent is a superposition of periodic events in the f–x domain where they could be predicted simply by an autoregression filter in this domain. The F-X prediction filter for 2D data, A(t,n), can be expressed as follows: m Að f ; nÞ ¼ ∑ hk Að f ; n−k Þ ; n ¼ 1; 2; …; N ð1Þ k¼1 if each data point can be expressed as a linear combination of previous ones. Here, A is a frequency slice with spatial sequential index n and h is a filter operator with the length m. The strategy of FX focuses to predict noise, and the denoised data is the result of subtracting the noise from the input noisy data (Sacchi and Kuehl 2001). To formulate the method, this assumption should be considered that A = S + W, where S is the clean signal and W is the added white noise to signal, hence: m m k¼0 k¼0 ∑ pk An−k ¼ ∑ pk W n−k ð2Þ Here, p is the filter estimation error with p(0) = 1 and p(1:m) = − h(1:m). The Eq. 2 needs the: m ∑ hk S ð f ; n−k Þ ¼ 0 ð3Þ k¼1 The prediction error of the pure signal is white because it is predictable, but about random noise as unpredictable event is Arab J Geosci (2017) 10: 440 condition |ri – 1 − ri| > d, where |·| indicates the absolute operator and ri denotes the ith component of R. The chance to identify a sample as noisy is approximately impossible when the level of noise is low. By rising d, it will be getting harder to consider a sample as noisy when the previous one is detected as noisy sample. Otherwise, the parameter d is changed to the pre-defined value of threshold. It should be noted that the ‘Step’ is a main factor in exact detection of noisy samples and in protecting edges. So, this filter is an adaptive median filter which determines the affected noisy pixels of an image. Based on this procedure, when the difference between two successive pixels is greater than the threshold d, the pixel is considered as a noisy pixel which makes it necessary to apply the median operation. It incomes that the noisy sample will be replaced by the median value of the samples in its surrounding while all the other samples leave unaffected. The sample is not noisy and the identity filter will be applied when the condition |ri – 1 − ri| > d is not satisfied. The proposed method is planned using combination of FX deconvolution and DBM filter. In other words, the method is applied into two main phases. FXD is focused to remove the white noise using prediction strategy, and DBM filter is focused to attenuate the impulsive (spike-like) noise and spikes using decision-based strategy. Application Page 3 of 8 440 Fig. 2. The close-up confirms the ability of combination of FXD and DBM filter for random noise elimination, and the noise level is reduced more using this trick. Synthetic model 2 The second synthetic model consisting of four hyperbola events is created to check the ability of the proposed method face to hyperbola events (Fig. 3a) with random noise. For this model, a high level of random noise is added to noise-free data to create the noisy data, as shown in Fig. 3b. Figure 3c indicates the result of RNA from the second synthetic model. It is clear that S/N ratio is increased after FX deconvolution but again, some random noise is kept. If the DBM filter implemented as the second step of the presented method is applied, the result of Fig. 3d is obtained. To implement the method, the window size is fixed on 5 × 5, the threshold d is set to 90, and the parameter ‘Step’ is set to 5. Comparing Figs. 3c and 3d clarifies the power of the planned method for RNA by improving the S/N ratio of the second synthetic model. For investigating the result for this model better, again, a zoom of a part of this model is selected and is shown in Fig. 4. The close-up could confirm the positive effect of the presented method for RNA from this model too. Comparing Figs. 4b and 4c shows that using the combination of FXD and DBM, random noise is removed significantly and S/N ratio is increased. Synthetic model 1 Field data example The first synthetic data consists of four linear events with different dips to evaluate the proposed method to linear events containing random noise. As shown in Fig. 1a, a Ricker wavelet is used to generate this model of 100 traces. Noisy synthetic data (Fig. 1b) is created by adding random noise to noise-free data. The random noise is white Gaussian noise type with SNR value of 4, which the scalar SNR specifies the signal to noise ratio per sample. Figure 1b displays where linear events are covered by adding random noise and thereafter, the signal to noise ratio is decreased. In Fig. 1c, the result of RNA using FX deconvolution is shown; FXD succeeded to decrease the noise level of data, but there is some remained noise. To diminish the remained random noise, the DBM filter is applied with the window size of 5 × 5, the threshold d of 80, and the parameter ‘Step’ of 6. After applying DBM filter in the second step of noise attenuation, the noise level is reduced again and the S/N ratio is improved greatly (Fig. 1d). Comparing Figs. 1c and 1d indicates that the combination of FXD and DBM filter is more successful for RNA compare to each one of the methods. To validate the outcomes better, a close-up of a part of synthetic model 1 before and after denoising is shown in A real seismic section is selected to further study the performance of the suggested method. The real data is related to Marun oil field, located in the Khuzestan Province of Iran, and is the second-largest oil field in Iran. It consists of two oil reservoirs and one gas reservoir named Asmari, Bangestan, and Khami, respectively. The Bangestan oil reservoir is located deeper than the Asmari oil reservoir and has been producing sour oil. This field is an anticline with NW-SE trend. The dimensions of Marun oil field at the Asmari oil reservoir horizon are 67 and 7 km in length and width, respectively. The seismic section with 4-ms time sampling interval, and trace spacing of 50 m is selected from this oil field (see Fig. 5a). From Fig. 5a, random noise is evident in most parts of the section and all events are masked with random noise. The denoised seismic section using FX deconvolution is shown in Fig. 5b, where high level of noise is eliminated. Using DBM filter in the second step of the proposed method, some remained impulse noise is attenuated (see Fig. 5c). Calculating the difference between Figs. 5a and 5c results the eliminated noise (Fig. 5d). The difference confirms the suppression of high level of noise from data and the performance of presented method for RNA. 440 Page 4 of 8 Arab J Geosci (2017) 10: 440 Fig. 1 a Noise-free synthetic data consist of four linear events with deferent dips. b Noisy synthetic data and linear events are covered after adding noise. c Synthetic data after denoising using FXD. d Denoised synthetic data using combination of FXD and DBM. Comparing c and d indicates that the combination of FXD and DBM filter is more successful in RNA To investigate the results better, a zoom of the section before and after denoising using FXD and the combination of FXD and DBM filter is shown in Fig. 6. Comparing Figs. 6a and 6c clarifies the power of the proposed method Fig. 2 A close-up of a part of synthetic model 1 from Fig. 1. a Noisy data. b Denoised data using FXD. c Denoised data using FXD + DBM filter. Comparing b and c shows the power of planned method for RNA from data Arab J Geosci (2017) 10: 440 Page 5 of 8 440 Fig. 3 a Noise-free synthetic data consists of four hyperbola events. b Noisy synthetic and hyperbola events are masked by adding random noise. c Synthetic data after denoising using FXD. d Denoised synthetic data by combination of FXD and DBM. Comparing c and d clarifies the power of the planned method for RNA and improving S/N ratio in removing random noise and an obvious increase in signal to noise ratio. The final result gives a much clearer lateral continuity than original data and hence improving the interpretability of data. consider a sample as noisy when the previous one is detected as noisy sample. Otherwise, the parameter d is changed to the pre-defined value of threshold. Also, it should be noted that the ‘Step’ is a main factor in exact detection of noisy samples and in protecting edges. DBM filtering can lead to a well removal of spike-like noise by increasing the window size (Arce 2005). However, this may affect the signal and distort it during filtering. DBM filtering is an attractive method because its application is much simpler and it needs less computational time in comparison to FX deconvolution. However, it is not able to handle complicated seismic events such as conflicting dips versus FX deconvolution can deal with conflicting dips and discontinuous seismic events (Sacchi 1999). Clearly, the combination of FX deconvolution and DBM filtering creates more powerful method to suppress white and impulsive noise better. Combination strategy may causes too smoothed seismic images; however, covered seismic will be largely preserved. Discussion The FX deconvolution with this assumption that seismic events are linearly continuous and noise is random can be applied. Therefore, the F-X prediction should be performed to small windows to guarantee that seismic events are almost linear, and thereafter, the Fourier transform will be operated within each window. This process proved effective in reducing much of the white noise; however, some leftover noise may be still not fully attenuated. For DBM implementation, the chance to identify a sample as noisy is approximately impossible when the level of noise is low. By rising d, it will be getting harder to 440 Page 6 of 8 Arab J Geosci (2017) 10: 440 Fig. 4 A zoom of a part of second synthetic model from Fig. 3. a Noisy data. b Denoised data using FXD. c Denoised data using FXD + DBM filter. Comparing b and c shows that using the combination of FXD and DBM, random noise is removed significantly and S/N ratio is increased Fig. 5 a A real seismic section. Random noise is observable in most parts of the data and events are masked with them. b The section after denoising using FXD. c The section after denoising using FXD + DBM, random noise is suppressed significantly. d With the difference between a and c, result shows that proposed method is powerful for RNA Arab J Geosci (2017) 10: 440 Page 7 of 8 440 Fig. 6 a A close-up of a part of the section. b Denoised data using FXD. c Denoised data using FXD + DBM filter. Comparing b and c clarifies that random noise is attenuated and the S/N is improved considerably. The lateral continuity of events is increased, and hence, the interpretability of data is enhanced significantly Conclusion presence of strongly curved events. The final result gives a much clearer lateral continuity than original data and hence enhancing the interpretability of data. Moreover, some masked events by random noise were clarified in different parts of the data after denoising with high signal-protection ability. Generally, the picked results showed that random and impulsive noise in seismic data can be effectively attenuated by the combination of FXD and DBM filter. Results of both synthetic and field seismic data have demonstrated reasonable noise attenuation while the signal was preserved during denoising. The original seismic data must be denoised from random noise in order to acquire high-quality seismic data to form a reliable basis for subsequent geological interpretation. A new approach was planned here by using the combination of FX deconvolution and DBM filter to reduce the random noise and spikes from seismic data. The proposed method is divided into two main steps; the first step uses FX deconvolution to eliminate the Gaussian random noise. In the second step, other noise type including impulsive noise will be removed using DBM filter. FX deconvolution automatically calculates the signal with spatial variations in dip or amplitude using f-x regularized auto-regression. To overcome the supposition of linearity of the signal in the f-x domain prediction technique, the f-x domain prediction for non-linear events uses windowing tricks. The DBM filter is an adaptive strategy that just operates the median filter to noisy samples and not affects healthy seismic samples. This makes the DBM filter an appropriate choice for detecting and suppressing impulsive noise. To evaluate the method, two types of synthetic model were created, and also, a real seismic section was used. The results of the presented method on the different examined seismic data (synthetic data include linear events, synthetic data include hyperbola events, a real seismic section) identified the method as really powerful for RNA. About synthetic models, the noise level was reduced obviously; also, the S/N of data was improved considerably after denoising using the combination of FX deconvolution and DBM filter. About the real seismic section, experiment showed that the proposed strategy is really successful for random noise attenuation in the Acknowledgments University of Tehran would be acknowledged for financial support of this work under the research grant number of 28322/ 1/01. References Abma R, Claerbout J (1995) Lateral prediction for noise attenuation by tx and f-x techniques. Geophysics 60:1887–1896 Arce, G. R., 2005, Nonlinear signal processing: Wiley Interscience, Hoboken Arastehfar S, Pouyan AA, Jalalian A (2013) An enhanced median filter for removing noise from MR images. J AI Data Min 1(1):13–17 Bednar JB (1983) Applications of median filtering to deconvolution, pulse estimation, and statistical editing of seismic data. Geophysics 48:1598–1610 Bekara M, Baan MV (2007) Local singular value decomposition for signal enhancement of seismic data. Geophysics 72(2):V59–V65 Bekara M. and Baan, M. 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