5.2. The Median-dip-filter
The median dip filter is a data-driven tool and yields a cleaned-up seismic data volume in which coherent events are enhanced and randomly distributed noise is suppressed. The filter increases the general interpretability of the seismic data and improves the performance of automatic horizon trackers. Basically the filter collects all amplitudes inside a disc with user-specified search radius and replaces the value at the center by the median value of the amplitudes. The search disc follows the local dips from the steering cube.
The filter, in combination with the steering cube works as follows:
A search radius is defined.
From a starting position we extract the first amplitude.
The local dip and azimuth is followed to the next trace.
The interpolated amplitude at this point is extracted.
Step 3 and 4 are repeated for all traces inside the search radius (see Figure).
The amplitude at the starting position is replaced with the median value of all extracted amplitudes.
Points 2 to 6 are repeated for all samples in the cube.
Filter input for a 4-trace radius which corresponds to 57 points. Note that the disk is neither flat, nor horizontal but follows the seismic events from trace to trace.
A median value can be defined as the value associated with the central position of a ranked series. So, if we rank all N amplitudes from smallest to largest number than we find the median value by taking the value at position (N+1)/2, where N is an odd number. To understand the effect of a median filter, let us assume we are filtering a seismic event with a 3-points median filter. The event, e.g. the amplitudes along a horizon is given by the following series:
...0,0,1,0,0,1,1,3,1,0,1,1,1,.......
The 3-points median filtered response is given by:
....0,0,0,0,0,1,1,1,1,1,1,1,1,.......
To check this take 3 consecutive input numbers, rank them and output the value in the middle, then slide your input set one position and repeat the exercise.
Please observe that:
Events smaller than half the filter length are removed (e.g. the 1 on the left and 0 on the right)
Noise bursts are also removed (the value 3) and
Edges are preserved (the break from mainly zeros to mainly ones stays exactly at the same position. In other words no filter tails are introduced).
5.2.1. Example results
The following figures show an example of the effect of a 57-points (4 trace radius) filter.
5.2.2. Create the Median dip filter yourself
In OpendTect filters are integrated with attribute extractions. The advantage of this approach is that all attributes can be filtered separately without creating intermediate results first. To apply a median filter to a seismic data set you define the median filter as an attribute in the active attribute set. Start the attribute definition module (icon or Attributes option, Processing menu). Select an existing attribute set, or create a new one. Specify Volume statistics as attribute type, select the input seismic and specify output = median. Set the search radius e.g. 4x4 and specify the time gate as [0,0]. Select the steering cube and specify Full steering as the steering mode. A time-gate of [0,0] means that effectively the filter input is collected along a disk. Full steering means that the disk is curved according to the local dip information (see also Section 2.2).
To apply the filter interactively, use the plane viewers in one or more scenes. For a good comparison between filtered and unfiltered displays, scale the data similarly (clipping option, right-hand mouse button on the color bar). To apply to a volume, select Volume output from the Processing menu, specify the median dip filter attribute as 'Quantity to output'.
5.2.3. Note
As an alternative, one could also use the Edge Preserving filter described by Li You et al. in The Leading Edge of February 2002. Just like the median dip filter, this Edge Preserving filter is included in the Evaluate Attributes default attribute set. It uses the Position attribute to locate the area where the variance in seismic amplitude is lowest, and outputs the average amplitude at that location to the current sample location.