In this paper we present a new coherent and random noise attenuation method in the (t-x) domain, based on the à trous wavelet decomposition (ATWD). The filtered signal in the spatial direction is obtained as the noiseless scales reconstruction of the decomposition. The à trous wavelet filter is effective for data where coherent events can be aligned laterally as NMO (normal move out) corrected CMP (common-midpoint) gathers. This processing is successfully applied on the synthetic and real seismic data.
The recovery of the signal and attenuation of the noise is of key importance in the seismic processing. Normal move out (NMO) stacking is an effective noise attenuator for random noise. However, such a technique does not always provide sufficient noise attenuation. Furthermore different techniques were used, involving band-pass filtering, multichannel filters and the non linear filter as the median filter and the empirical mode decomposition (EMD) filter, the wavelet transform-based filters have been proposed in 1d and 2d, (Various specialized methods are available to remove coherent noise and random noise). These filters are applied before stack or after stack. In this paper we present a new method, based on à trous wavelet decomposition algorithm, (Holschneider et al (1988), Shensa (1992)), to remove the random and the coherent noise. The method works optimally where coherent events can be aligned laterally as NMO (normal move out) corrected CMP gathers; the filtered or denoised CMP is obtained by a simple suppression or mute of the low scales (high wavenumber content of the data). A comparison with the empirical mode decomposition (EMD) is shown.
The à trous wavelet algorithm represents a discrete approach to the classical continuous wavelet transform (Mallat 1998). In wavelet analysis, a signal(S) is decomposed into an approximation (C) and a detail (D) as S=C1+D1=C2+D1+D2=C3+D1+D2+D3. The approximations are the high-scale, low-frequency components of the signal. The details are the low-scale, high-frequency components. The approximation is then itself split into a second-level approximation and detail, and the process is repeated.
The principle of this technique is to decompose adaptively a given signal x(t) into oscillating components, called intrinsic mode functions (IMF) obtained from the signal by an algorithm called sifting. The algorithm identifies the IMF by characteristic time scales, defined locally by the time lapse between two extrema of an oscillatory mode or by the time lapse between two zero crossings of such mode. For sifting procedure: construct high and low envelope functions that interpolate the local maxima and minima, take the mean of these envelopes, subtract this mean from x(t) , and yield a signal with local zero mean, the first intrinsic mode function. The residual is treated similarly to obtain the second mode function.
Both of the method, work on pre-processing data by first aligning the event considered to be signal for seismic data (an NMO correction for CMP data in seismic), then this event is enhanced via the à trous wavelet filter or EMD filter.