اثر رفتار نوسانی موجک مادر در تبدیل موجک گسسته به‌منظور تضعیف نوفه لرزه‌ای تصادفی

ابزارهای پردازش داده لرزه‌ای ویژگی‌های متنوعی دارند و چشم‌پوشی از این ویژگی‌ها اثرگذاری ابزارهای پردازش سیگنال را کاهش می‌دهد. در این تحقیق نقش تفکیک‌پذیری در تبدیل موجک و نسبت فرکانس مرکزی به پهنای باند موجک (wq-factor) موجک مادر بر عملکرد تضعیف نوفه اتفاقی بررسی خواهد شد. در این تحقیق از نسخه دوشاخه تحلیلی تبدیل موجک اتساع گویا (dt-radwt) به‌منظور بررسی نقش نسبت فرکانس مرکزی به پهنای باند موجک (wq-factor) در تبدیل موجک استفاده شده است. این تبدیل‌ها می‌تواند بازه متنوعی از wq-factor ها را فراهم کنند. برای بررسی تاثیر wq-factor موجک مادر بر روی عملکرد تبدیل موجک dt-radwt با wq-factor های مختلف بر روی داده مصنوعی اعمال می‌شود، در ادامه تحقیق ارتباط بین نسبت فرکانس مرکزی به پهنای باند موجک داده و نسبت فرکانس مرکزی به پهنای باند موجک مناسب برای پردازش داده‌های لرزه‌ای بررسی می‌شود، نتایج نشان داد که نسبت فرکانس مرکزی به پهنای باند موجک نگاشت لرزه‌ای ارتباط معناداری با نسبت فرکانس مرکزی به پهنای باند موجک مناسب برای تجزیه سیگنال ندارد و ضمناً با افزایش نسبت فرکانس مرکزی به پهنای باند موجک تبدیل موجک، پردازش سیگنال بهتر صورت می‌گیرد. در قسمت بعد، این روش بر داده‌های subbottom profiler و همچنین داده‌های خشکی استفاده شده است. نتایج dt-radwt نشان داد که انتخاب wq-factor بالا در تبدیل موجک، موجب کاهش بهتر نوفه تصادفی از داده لرزه‌ای خواهد شد.

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

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 Qfactor (Qfactor in bandpass filters is the ratio of central frequency to the bandwidth) of the motherwavelet on the filter performance with the goal of reducing the random noise and examining the effects of the mother wavelet Qfactor and its oscillatory behavior on the filter performance. We use RationalDilation Wavelet Transform (RADWT) and Dualtree RADWT. These methods have the capability to achieve variable frequency resolution that can also provide a variety of Qfactors. To evaluate the effect of Qfactor of mother wavelet on filter function, the DTRADWT with different Qfactors 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 Qfactor and suitable Qfactor for seismic data processing. The method is applied to highfrequency shallow SubBottom Profiler data and land data. In this study, a new wavelet transform called Rational Dilation Wavelet Transform (RADWT) and its Dual Tree analytical version DTRADWT is used to attenuate random noise in seismic data. These transforms can achieve a limited range of Qfactor 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 timefrequency resolution. We also investigate the effect of Qfactor of mother wavelet on the performance of wavelet transform filters, and the relation between seismic signal Qfactor and Wavelet transform filter Qfactor.Increasing the Qfactor can reduce the bandwidth of wavelet in each scale. We test the effect of random noise on Qfactor of Ricker wavelet, with different noise levels. The results showed that by changing the level of random noise, the range of Qfactor remains constant. Next, we added the constant noise to Ricker wavelet, and we analyzed the noiseinfected wavelet by RADWT and DTRADWT with different Qfactors, here the soft threshold was used. The result of denoising is presented in Table 2. In last part of manuscript high Qfactor 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 Qfactor 7.48. This research investigated the role of Qfactor value in suppressing random noise from reflection seismic data. Many Qfactors were tested to evaluate the effect of wavelet transform Qfactor on random noise denoising, and it was observed that with an increase in the Qfactor of the wavelet transform, the signaltoratio of filtered trace was improved. The data Qfactor was also calculated, but there was no significant correlation between the appropriate Qfactor of WT for noise reduction and the signal Qfactor. DTRADWT was better than RADWT in distinguish was the random noise from the signal, due to the use of two parallel filter banks. DTRADWT with high Qfactor 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 subbottom profiler with a wide frequency content. Results confirm the effectiveness of WT filter which is increased with the increase of wavelet transform Qfactor.