The effects of oscillatory behavior of the mother wavelet in the discrete wavelet transform in order to suppress seismic random noise

Document Type : Research


1 Ph.D. Student, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran

2 Professor, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran

3 Assistant Professor, Department of Earth Sciences, Faculty of Sciences and Modern Technologies, Graduate University of Advanced Technology, Kerman, Iran


Seismic data have a variable characteristic. Overlooking this important characteristic will reduce the effectiveness of any signal processing tool. Wavelet transform is a useful tool in seismic data processing and in recent years it has been the subject of attention of geophysicists. In this study we investigate the role of the resolution of the wavelet transform and the Q-factor (Q-factor in band-pass filters is the ratio of central frequency to the bandwidth) of the mother-wavelet on the filter performance with the goal of reducing the random noise and examining the effects of the mother wavelet Q-factor and its oscillatory behavior on the filter performance. We use Rational-Dilation Wavelet Transform (RADWT) and Dual-tree RADWT. These methods have the capability to achieve variable frequency resolution that can also provide a variety of Q-factors. To evaluate the effect of Q-factor of mother wavelet on filter function, the DT-RADWT with different Q-factors is applied on a Ricker Wavelet and synthetic shot gathers and the results are discussed in the manuscript. In the following, we investigate the relationship between seismic signal Q-factor and suitable Q-factor for seismic data processing. The method is applied to high-frequency shallow Sub-Bottom Profiler data and land data. In this study, a new wavelet transform called Rational Dilation Wavelet Transform (RADWT) and its Dual Tree analytical version DT-RADWT is used to attenuate random noise in seismic data. These transforms can achieve a limited range of Q-factor by selecting appropriate parameters p, q and s. The advantage of this transform over the common discrete wavelet transforms is that its rational sampling which provides higher time-frequency resolution. We also investigate the effect of Q-factor of mother wavelet on the performance of wavelet transform filters, and the relation between seismic signal Q-factor and Wavelet transform filter Q-factor.
Increasing the Q-factor can reduce the bandwidth of wavelet in each scale. We test the effect of random noise on Q-factor of Ricker wavelet, with different noise levels. The results showed that by changing the level of random noise, the range of Q-factor remains constant. Next, we added the constant noise to Ricker wavelet, and we analyzed the noise-infected wavelet by RADWT and DT-RADWT with different Q-factors, here the soft threshold was used. The result of denoising is presented in Table 2. In last part of manuscript high Q-factor Dual Tree Rational wavelet transform was used to attenuate random noise from synthetic shot gather and marine and land seismic data (figures 9 & 11& 14& 15). Suitable parameters for random noise attenuation, p, q, and s was selected respectively 7, 8, 1 that made WT Q-factor 7.48. This research investigated the role of Q-factor value in suppressing random noise from reflection seismic data. Many Q-factors were tested to evaluate the effect of wavelet transform Q-factor on random noise denoising, and it was observed that with an increase in the Q-factor of the wavelet transform, the signal-to-ratio of filtered trace was improved. The data Q-factor was also calculated, but there was no significant correlation between the appropriate Q-factor of WT for noise reduction and the signal Q-factor. DT-RADWT was better than RADWT in distinguish was the random noise from the signal, due to the use of two parallel filter banks. DT-RADWT with high Q-factor was applied to synthetic data with a variable level of random noise and results are summarized in table4. In addition, the method was also applied to real shallow marine data from sub-bottom profiler with a wide frequency content. Results confirm the effectiveness of WT filter which is increased with the increase of wavelet transform Q-factor.


Main Subjects

ایرانی‌‌مهر، م. و ریاحی، م. ع.، 1393، تضعیف نوفه تصادفی با تبدیل موجک گسسته ضریب اتساع گویا، مجله ژئوفیزیک ایران، دوره 8، شماره 3، 25-35.
روشندل کاهو، ا. و نجاتی کلاته، ع.، 1389، تضعیف نوفه‌های اتفاقی در داده‌های لرزه‌ای با استفاده از تجزیة مد تجربی، مجله فیزیک زمین و فضا، 9، 1390، صفحه 61-68.
شکفته زوارم، م.، روشندل کاهو، ا. و گرایلو، ه.، 1394، تضعیف نوفه‌های تصادفی در دادههای لرزه‌ای بازتابی با استفاده از فیلتر انتشار ناهمسانگرد غیرخطی تانسوری، نشریه پژوهشهای ژئوفیزیک کاربردی، دوره1شماره2، 105-118.
Aiswarya, K. and Jayaraj, V., 2014, Image Denoising Based On Symmetrical Fractional Overcomplete Wavelet Transform, Unique Journal of Engineering and Advanced Sciences, Vol. 02, no. 1, 101-109.
Askari, R. and Siahkoohi, H. R., 2008, Ground roll attenuation using the S and x-f-k transforms, Geophysical Prospecting, 56, 105-114.
Auscher, P., 1992, Wavelet bases for L2(R) with rational dilation factor, Wavelets and Their Applications. Jones and Barlett,439-451.
Bagheri, M. and Riahi, M. A., 2016, Seismic data random noise attenuation using DBM filtering, Bollettino di Geofisica Teorica ed Applicata Vol. 57, No. 1, 1-11.
Barnes, A. E., 1993, Instantaneous spectral bandwidth and dominant frequency with applications to seismic reflection data, Geophysics, Vol. 58, No. 3, P. 419-428.
Baussard, A., Nicolier, F. and Truchetet. F., 2004, Rational multiresolution analysis and fast wavelet transform: application to wavelet shrinkage denoising, Signal Processing, Vol., 84, No.10,1735–1747.
Bayram, I. and Selesnick, I., 2009, Frequency-domain Design of Overcomplete Rational-Dilation Wavelet Transforms, IEEE Trans. Signal Process, Vol. 57, No. 8, 2957–2972.
Bayram, I. and Selesnick, I., 2011, A Dual-Tree Rational-Dilation Complex Wavelet Transform, IEEE Transactions on Signal Processing, Vol. 59, No.12, 6251 – 6256.
Borhani, M. and Sedghi, V., 2004, 2-D Dual-Tree Wavelet Based Local Adaptive Image Denoising, The 12nd Iranian Conference on Electrical Engineering, P. 12_017
Canales, L., 1984, Random noise reduction: Presented at the 54th Annual International Meeting, SEG. 525–527.
Chase, M. K., 1992, Random noise reduction by 3‐D spatial prediction filtering. SEG Technical Program Expanded Abstracts 1992: pp. 1152-1153
Donoho, D. L. and Johnstone, I. M., 1994, Ideal spatial adaptation via wavelet shrinkage: Biometrika, Vol. 81, P. 425–455.
Fugal, L. D., 2009, Conceptual Wavelets in Digital Signal Processing, Space & Signals Technologies LLC.
Goudarzi, A. and Riahi, M. A., 2013, TQWT and WDGA-Innovative methods for ground roll attenuation, J. Geophys. Eng., Vol 10, No. 6, P. 065007.
Irani Mehr, M. and Abedi, M. M., 2017, Random Noise Attenuation Using Variable WQ-factor Wavelet Transform, 79th EAGE Conference and Exhibition, Paris.
Johnstone, I. M. and Silverman, B. W., 1997, Wavelet threshold estimators for data with correlated noise: J. R. Statist. Soc. B, Vol. 59, P. 319– 51.
Kingsbury, N., 2002, Complex wavelets for shift invariant analysis and filtering of signals, Applied and Computational Harmonic Analysis, Vol. 10, No.3, P. 234-253.
Lari, H. and Gholami, A., 2014, Curvelet-TV regularized Bregman iteration for seismic random noise attenuation, Journal of Applied Geophysics, Vol 109, no. 1: 233-241.
Mallat, S., 2008, A Wavelet Tour of Signal Processing, Academic Press, 3rd edition.
Merklin, L. and Levchenko, O., 2005, Seismic Engineering Survey in the Caspian Sea for Oil and Gas Companies, 2nd Workshop “Seabed Acoustics” in Rostock-Warnemünde.
Meyer, Y., 1992, Wavelets and Operators, Cambridge: Cambridge University Press.
Sheriff, R. E. and Geldart, L. P., 1995, Exploration seismology, 2nd ed, Cambridge university press.
Selesnick, I., 2001, Hilbert transform pairs of wavelet bases, IEEE Signal Processing Letters, Volume 8, No.6, P.170-173.
Selesnick I., 2004, The Double-Density Dual-Tree DWT, IEEE Transactions on Signal Processing, Volume: 52, Issue: 5. P. 1304-1314.
Yilmaz, Ö., 2001, Seismic Data Analysis, Society of Exploration Geophysicists, second edition.