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

1-D stationary median filter (MF)

The 2-D seismic record can be represented by the following data sequence:

$$x_{i,j} \qquad (i=1,\cdots,m,\cdots,N_x;j=1,\cdots,n,\cdots,N_t)\;,$$ (1)

where $i$ is the spatial sample index, $j$ is the temporal sample index, and $N_x$ and $N_t$ are the numbers of spatial and temporal samples. When filter-window length, $C$, of the stationary median filter is defined (normally $C$ is odd), the result after filtering at the point on the $m^{th}$ trace and the $n^{th}$ sample can be found by

1. Setting the center point at the $m^{th}$ trace and the $n^{th}$ sample, and choosing $C$ samples in the $m^{th}$ trace,

2. Sorting the $C$ samples from smaller to larger, and then

3. Picking the center value, after sequencing, as the output at the point on the $m^{th}$ trace and the $n^{th}$ sample.

Repetition of the process on all data achieves 1-D stationary median filtering of the seismic record. The 1-D stationary median filter can be expressed as $median[x_{i,j}]$.

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