GNGTS 2017 - 36° Convegno Nazionale

584 GNGTS 2017 S essione 3.1 The use of Continuous Wavelet Transform for Ground Roll attenuation A. Tognarelli Earth Sciences Department, University of Pisa, Italy Introduction. In seismic reflection land data, Ground-Roll (GR) constitutes an high amplitude and low frequency noise that obliterates the reflected events decreasing the quality of the seimograms and, as a consequence, of the final stack section. Many processing methods are adopted to reduce the GR noise but the dispersive nature of the surface waves makes it difficult to design an optimal window for classical 1D filtering approaches based on short time Fourier Transform or for 2D approaches based on singular value decomposition. Also, 2D methods such as the f-k filtering can generate artifacts or can give poor results if the surface waves are aliased or if the traces are not regularly spaced. An additional difficulty is that the characteristics of the surface waves change depending on the near surface properties so that their features can vary drastically along the seismic line. This, requires to adapt the parameters of the processing operators according to the changing characteristics of the GR. Actual and more sophisticated methods consist in the estimation of the surface waves followed by adaptive subtraction but they are computationally expensive and time consuming. Source and/or receiver array design still remains the less invasive approach to reduce the surface waves noise and, for near surface survey, Tognarelli and Stucchi (2016) proposed an acquisition scheme that permits to perform different array simulations in the processing lab. Arrays are not able to remove the GR, they are effective to partially reduce the GR and at improving the signal window. In the last years, the continuous wavelet transform (CWT) (Daubechies, 1990,1992) has been used in a wide range of geophysical and geological disciplines such as seismic, oceanography, and climatology (Torrence and Compo, 1998; Lau and Weng,1995; Deighan and Watts, 1997; Sinha et al. , 2005; Farge, 1992; Sadowsky, 1996), but also in other contexts like image processing, music and medicine fields (Mallat, 2009). In general, the CWT analysis can be applied successfully to all time or spatial series that represent a non-stationary process, with the aim of investigating the spectral components and how they change over time and/or space. In this work, the CWT is used to analyse the shot gathers from a near surface seismic land survey and an intuitive filtering procedure, applied in the wavelet domain and aimed at attenuating the GR, is presented. The improvement of the data quality is shown and discussed for the shot gathers and finally for the stack section. Method. The CWT is defined as the convolution between a sampled time series x n’ and a scaled and translated version of a mother wavelet ψ: (1) where N is the number of samples in the time series, δt is the sample rate, a is the scale (or dilatation) and nδt is the translation b . The mother wavelet ψ is translated of b and scaled of a during the CWT process and acts on the input series x n’ as a band-pass filter whose central frequency changes as the scale parameter a changes. In this work, the complex Morlet is chosen as mother wavelet, b is set equal to the sample rate and a is defined by the exponential (2) where a o is the smaller scale that can be correctly resolved, j=0,1,…..,J is the scale index and δ j determines the sampling in the scale. For a Morlet wavelet, the relationship between Fourier period 1/f and the scale a can be directly computed. The CWT is a 1Doperator whose computation yields, for each trace, a time-frequency diagram called wavelet spectrum. The wavelet spectrum allows to analyse the frequency content over time of a trace and, if necessary, to remove the W n ( a ) = � x n ψ * [ ––––––– ] N – 1 n ' = 0 ( n'–n ) δt a a j = a 0 2 jδ j