Ground-roll noise suppression by time-frequency filtering based on variational mode decomposition

Summary Seismic imaging is highly dependent on the quality of seismic data. Structural and stratigraphic interpretation of seismic sections that contain the least amount of noise is much easier. Reflection seismic data are often associated with noise. Coherent noise is a major category of noise that accompanies seismic data, and has the same trend in different seismic traces of the data. Ground roll is one of the main coherent noises that has a low frequency, high amplitude and low velocity. Various methods, such as frequency filters and frequency-wavenumber filter, have been used for ground-roll attenuation. Different advantages and disadvantages are mentioned for each of the methods. In this paper, we have used time – frequency transform and variational mode decomposition to attenuate the ground-roll.
Introduction Generally, seismic noises are divided into two categories: coherent and incoherent. Coherent noise attenuation has always been a serious challenge for seismic data processors. Ground-roll is the main type of coherent noise in seismic data and is characterized by dispersive wave, low frequency, high amplitude relative to other events of interest in land seismic surveys, and propagates along and near the surface of the earth and obscures useful information in seismic exploration. The ground-roll noise often masks the shallow reflections at near offset and deep reflections at far offset and must be attenuated before the succeeding processing procedure. Therefore, ground-roll removal is an essential part of land seismic data processing. There have been many researches about eliminating ground-roll noise published in literature, and many authors have introduced various methods for handling the ground-roll noise problem. A most straightforward and commonly used method for suppressing the ground-roll noise is band-pass filtering. In many cases, ground-roll has significant amplitudes only at frequencies lower than the signal. In such cases, a simple frequency band-pass filter will provide suitable noise removal. In the case of the frequency overlap of primary reflections and ground-roll, the band-pass frequency filter either fails to attenuate all the ground-roll noise or removes much useful reflection energy. Dip filtering also known as f-k filtering, which is based on the 2D Fourier transform, is another commonly used technique to attenuate ground-roll. In the 2D Fourier transform of a seismic pre-stack gather, there is no a clear separation border between signal and noise region, consequently it leads to signal distortion. Radon, tau-p, and radial trace transforms have also been applied to ground-roll removal. Another widely used method to remove ground-roll noise from seismic data is singular value decomposition (SVD)-based method. Nevertheless, all of the above-mentioned approaches disagree with seismic data natural behavior because of stationary signal assumptions. Several methods have been introduced that consider the non-stationary nature of seismic data. The time-frequency denoising algorithm is an effective method for handling noise problems. A high resolution time-frequency map can be very helpful in unwanted energy filtering in time-frequency domain. In this paper, we have used variational mode decomposition method to create a high resolution time-frequency map of seismic trace and ground-roll attenuation.
Methodology and Approaches The goal of variational mode decomposition method is to decompose a real input signal,   xt, into a number of modes that have specific sparsity properties while each being band-limited about a center frequency, k 
, and reproducing the
input. Each intrinsic mode function,   k ut, can be calculated by solving an optimization problem as:         2 , 2 s.t. min                  k kk jt tk u k k k j t u t e t u t x t     Time-frequency filter has been widely used to attenuate the ground roll components. Based on the time-frequency map obtained from the variotional mode decomposition of seismic data and instantaneous frequency,   i ft, and instantaneous bandwidth,   i bt, of seismic data, an effective time-frequency filter can be designed based on the difference between seismic signals and ground roll in time-frequency map as:  
        1 , , 22 0 otherwise             ii ii b t b t f f t f t H t f The de-noised seismic trace can be obtained by applying the above time-frequency filter on time-frequency map of seismic trace and transfer back the filtered time-frequency map to time domain.
Results and Conclusions The proposed algorithm has been tested on a real seismic shot gather and the results have been compared to the results of applying frequency–wavenumber method on the seismic data. The obtained results show that the proposed method attenuates the ground-roll effectively while minimal harm to the reflected signal incurs. Hence, it can be an excellent alternative technique to attenuate the ground-roll noise.