Ground-roll noise attenuation using a simple and effective approach based on local bandlimited orthogonalization

Bandpass filtering and the frequency-overlap problem

A bandpass filtering process can be simply summarized as:

$$\mathbf{\hat{d}} = \mathbf{F}^{-1} \mathbf{B}_{fl,fh} \left(\mathbf{F} \mathbf{d}\right),$$ (1)

where $\mathbf{d}$ and $\mathbf{\hat{d}}$ denote the unfiltered and filtered data, respectively. $\mathbf{F}$ and $\mathbf{F}^{-1}$ denotes a pair of forward and inverse Fourier transforms. $\mathbf{B}_{fl,fh}$ denotes the bandpass filter with a high-bound-frequency (HBF) $fh$ , and low-bound-frequency (LBF) $fl$ . For the purpose of removing ground-roll noise, $fh$ is usually chosen as Nyquist frequency, the only parameter to choose is the LBF. The actual filtering in this paper is implemented by recursive (Infinite Impulse Response) convolution in the time domain following the Butterworth algorithm.

The problem of bandpass filtering for removing ground-roll noise is the difficulty of choosing an optimal LBF, because of the frequency-overlap problem of ground-roll noise and primary reflections. Figure 3 shows a demonstration of the frequency-overlap problem. When $fl=25$ Hz, all the ground-roll noise has been removed, and the denoised section (Figure 3a) does not contain any ground-roll noise. However, the noise section (Figure 3b) contains a lot of coherent signals: both direct waves and primary reflections. When $fl=10$ Hz, the noise section (Figure 3d) does not contains any coherent reflection or direct waves, however, the denoised section (Figure 3c) still contains a large amount of ground-roll noise.

One of the most commonly used approaches to solve the frequency-overlap problem is to use matched filtering. The removed ground-roll noise after a common bandpass filtering is used as an initial guess for the ground-roll noise. A least squares (LS) based matching filter is then calculated to match the initial ground-roll noise to the raw seismic data based on the least-energy assumption. The matched ground-roll noise is then subtracted from the raw seismic data to obtain the ground-roll noise attenuated profile. However, this adaptive subtraction method depends highly on the initial prediction of the ground-roll noise. Besides, in the case of highly non-stationary primary reflections and ground-roll noise, a conventional stationary matched filtering is not physically reasonable, and thus will not likely provide a satisfactory performance. In the next sections, we will introduce a novel approach for attenuating ground-roll noise based on bandpass filtering, which can remove more ground-roll noise and preserve more useful primary reflections.

Ground-roll noise attenuation using a simple and effective approach based on local bandlimited orthogonalization