A 1-D time-varying median filter for seismic random, spike-like noise elimination

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## 1-D time-varying median filter (TVMF)

Using the above definitions, a TVMF can be designed. We use the following three steps to determine its parameters:

1. Choose the reference median filter length.

At point , where the filter-window length of the reference median filter is chosen as , output can be expressed as

 (8)

where filter-window length is a large odd number so that random noise could be eliminated as much as possible. is determined by using the SNR estimation method, which will be discussed later.

2. Choose the threshold value.

Using the reference median filter with its large filter-window length, we processed the seismic data first to find . Then we applied the absolute mean value to calculate the threshold value, which is shown as

 (9)

We can evaluate random-noise data versus useful signal data by using the threshold value. When , the point is judged to be random noise, whereas when , the point should be signal data. We can therefore use the threshold value as a judgment norm - data in which should be processed by the median filter having windows smaller than to protect the detailed signal structure. Data in which should be processed by the median filter having windows larger than to strengthen its ability to eliminate random noise.

3. Choose the time-varying filter windows.

Choices involving time-varying windows abound after the threshold value has been chosen. We can define four scales of windows. Detailed time-varying window length is defined as

 (10)

where , , , and are constant even numbers, and and . Specific values for these parameters will be discussed in the next section. Using the above definition, we distinguish between random noise and useful signal, such that we can process the seismic data using different filter scales.

 A 1-D time-varying median filter for seismic random, spike-like noise elimination

Next: Synthetic data tests Up: Theoretical basis Previous: Signal-to-noise ratio (SNR) estimation

2013-07-26