عنوان مقاله [English]
Seismic records are generally affected by various types of noise, such as ground rolls, multiples, random noise, reflection and reflected refraction from near surface structures. Random noise resulting from random oscillation during data acquisition is one of the most important and harmful noises that exist in seismic data over all times and frequencies. Much effort has been made to attenuate this type of noise from seismic data. The predictive filter is commonly used for random noise attenuation from seismic data. This filter can be used in various domains such as the f-x domain (Haris and White, 1997) and the discrete Cosine domain (Lu and Liu, 2007). Bekara and van der Ban (2009) attenuated the coherent and random noises using a combination of empirical mode decomposition (EMD) and Fourier transform.
EMD decomposes a time series into a finite set of signals called intrinsic mode functions (IMFs). They represent different oscillations embedded in the data. They are built to satisfy two conditions: (1) The number of extrema and the number of zero crossings must be equal or differ at most by one, and (2) at any point the mean value of the local maxima envelope and the local minima envelope must be zero.
Bekara and van der Ban (2009) transformed seismic section from the t-x domain to an f-x domain by Fourier transform. Then, they applied EMD to a constant-frequency slice in the f-x domain and removed the first IMF. In the FX-EMD method, the denoised seismic section can be obtained by reversing the EMD and Fourier transform, respectively.
The time–frequency transform of a signal shows a variation in the frequency contents of a signal with time. Ideally, the time-frequency representation only provides information about the frequency moments without mutual information about the adjacent instants. Stockwell (1996) introduced the S-transform which is a combination of short-time Fourier (STFT) and wavelet transforms. It uses a variable window length and the Fourier kernel. However, the S-transform suffers from a poor energy concentration in the time-frequency domain. It has a poor time resolution at lower frequencies and a poor frequency resolution at higher frequencies. Sahu et al. (2009) proposed a modified Gaussian window which scales with the frequency in an efficient way to obtain a better energy concentration of the S-transform.
Han-peng et al. (2011) used the time-frequency transform instead of Fourier transform (TFX-EMD) for considering the nonstationary property of the seismic data. They obtained the denoised seismic section by applying the EMD to a constant-frequency slice and removing the first IMF in t-f-x domain.
Due to the presence of random noise in the other IMFs, removing the first IMF is not always an appropriate approach. One of the best algorithms in EMD-based noise attenuation is the interval thresholding of the IMFs. The main idea of this algorithm is to determine an aproperiate threshold value and to apply it to the considered IMFs.
In this study, we modified the TFX-EMD algorithm by changing the EMD denoising strategy. We used the interval thresholding of IMFs instead of removing the first IMF in the t-f-x domain. We evaluated the efficiency of our method on both synthetic and real seismic sections and compared the obtained results with those of the FX-EMD and traditional TFX-EMD methods. The comparison shows that the new EMD denosing strategy in the t-f-x domain can effectively suppress random noise and has a better performance than the other two approaches. Also, in our method, unlike the FX-EMD and traditional TFX-EMD, the steep events are preserved.