Multi-step random noise attenuation

In order to overcome the problem of plane-wave destruction in estimating conflicting dips that is involved in traditional seislet thresholding, I propose a new multi-step processing algorithm. I first use an adaptive empirical mode decomposition (EMD) based dip filter to separate the seismic data into several dip bands (5 or 6). Next, I apply seislet thresholding to each separated dip component to remove random noise. Finally I combine all the denoised data to form the final denoised data. In the step of denoising each dip component using the seislet transform, I first apply plane-wave destruction to each separated dip component to calculate the local slopes, and then apply the forward seislet transform, soft thresholding, and the inverse seislet transform on each dip component. Because of the dip separation, there are no dip conflicts in the data, thus plane-wave destruction can obtain more precise dip estimation, which will result in better compression by the seislet transform and better thresholding-based denoising performance than the alternatives. Figure 4 shows the detailed workflow chart of the proposed dip-separated denoising framework. In Table 1, I give a detailed explanation for the meanings of different abbreviations.

flowchart_new
Figure 4. Workflow chart of the proposed dip-separated denoising framework.

Abbreviations	Meanings
PWD	plane-wave destruction
DipC	Dip component after EMD based dip filter
Seis	Seislet domain without thresholding
Dip	Local slope map using plane-wave destruction
TSeis	Thresholded seislet domain
DC	Denoised component after thresholding in the seislet domain
N	Number of dip components after EMD based dip filter

Table 1. Explanation of abbreviations shown in Figure 4.

In this paper, I choose the threshold value by a simple percentile strategy. I do not chose the exact threshold value. Instead, I choose a percentage of low amplitude coefficients to remove. For example, if I choose 10%, I preserve the 90% largest coefficients. Then, when tuning the parameters, I can only tune the percentage, which is convenient to implement in practice.

In order to numerically measure the denoising performance for the synthetic data, I utilize signal-to-noise ratio (SNR) (Liu et al., 2009; Hennenfent and Herrmann, 2006; Chen and Fomel, 2015), as shown below :

$$SNR=10\log_{10}\frac{\Arrowvert \mathbf{s} \Arrowvert_2^2}{\Arrowvert \mathbf{s}-\hat{\mathbf{s}}\Arrowvert_2^2},$$ (13)

where $\mathbf{s}$ is the noise-free signal and $\hat{\mathbf{s}}$ is the denoised signal. For the field data example, as I do not know the exact answer, I cannot judge by numerical measurement. Instead, I only evaluate by visual observation, which is still effective.