Random noise suppression in seismic data by empirical mode decomposition

The quality of seismic data varies tremendously, from areas where excellent reflections(or refractions) are obtained to areas in which the most modern equipment, complex fieldtechniques, and sophisticated data processing do not yield usable data. Between theseextremes, lie most areas in which useful results can be obtained. Seismic records aregenerally affected by various types of noise, such as ground rolls, multiples, randomnoise, and reflection and reflected refraction from near surface structures. Random noiseresultiing from random oscillation during data acquisition is one of the most importantand harmful noises that exists in seismic data over all times and frequencies. Many effortshave been made to remove this type of noise from seismic data. The predictive filter is anordinary method commonly used for random noise attenuation from seismic data. Thisfilter can be used in various domains, such as the f-x domain (Haris and White, 1997) andthe discrete Cosine domain (Lu and Liu, 2007). Jones and Levy (1987) removed events which were not coherent trace-to-trace events by means of the Karhunen-Loevetransform. The empirical mode decomposition (EMD) method is an algorithm for the analysis of multicomponent signals that breaks them down into a number of amplitude and frequency modulated zero-mean signals, termed intrinsic mode functions (IMFs). An IMF must fulfill two requirements: (1) the number of extrema and the number of zero crossings are either equal or differ at most by one; (2) at any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero. In contrast to conventional decomposition methods such as wavelets, which performthe analysis by projecting the signal under consideration onto a number of predefinedbasis vectors, EMD expresses the signal as an expansion of basic functions that aresignal-dependent and estimated via an iterative procedure called sifting. Apart from thespecific applications of EMD, a more generalized task in which EMD can prove useful issignal denoising (Kopsinis and McLaughlin, 2009). When EMD is used for denoising, theproblem is to identify properly which IMFs contain noise characteristics. Certain modeswill consist mainly of noise, whereas other modes will contain both signal and noisecharacteristics. In the case of white Gaussian noise, the noise-only energy of the modesdecreases logarithmically. The first mode, carrying the highest amount of noise energy,will consist mainly of noise, and the effect of noise should gradually weaken with highermodes. In this paper, a new signal denoising method based on the empirical modedecomposition framework is used to suppress random noises in seismic data. A Noisysignal is decomposed into oscillatory components (IMFs). The empirical modedecomposition denoising method involves filtering each intrinsic mode function andreconstructing s the estimated signal using the processed intrinsic mode functions. Thedirect application of wavelet-like thresholding to the decomposition modes is, inprinciple, wrong and can have catastrophic consequences regarding the continuity of thereconstructed signal. This arises as a result of the special attributes of IMFs; namely, theyresemble an AM/FM modulated sinusoid with zero mean. Consequently, we used theinterval thresholding method instead of direct theresholding method to denoise seismicsignal. the efficiency of the proposed method was tested on both synthetic and real seismic data. In every case, results show that the denoising algorithm can suppress random noise significantly.