Two-dimensional data provides a more challenging problem, but also a more useful one. Consider the following as an example of two-dimensional data with noise:
For a dataset such as
In the case of real seismic data, the filters are computed from the data. While the filters could be calculated over several traces, I limit the prediction of a trace to include only its immediate neighbors. These filters have the form
Two filter calculations are done for each trace, one for each filter shown above. When these filters are applied, two sets of residuals are created. These two sets of residuals are combined into a single set of residuals by taking a sample-by-sample minimum of the absolute values of the two residuals. This single residual is then used as the diagnostic for noise. The single residual allows a sample to be predicted from either the right or from the left by taking the best of the two original predictions.
Once the set of minima of the absolute values of the residuals is created, the median of all the minima within a window is calculated. Although measures other than the median, such as the RMS of a window, could be used, the median is likely to provide a better diagnostic of a typical value within a window. Zero values are ignored when calculating the median, so that traces that were not present or muted on the input to the process do not contribute to the value of the median. Any value greater than w times the median value calculated is considered to be caused by high-amplitude noise. The value of w is determined by examining the data processed with a range of ws. In the examples shown here, a w of five was used, although the process seems to be somewhat insensitive to the exact values of w, as can be seen with Figure in the electronic version of this thesis. Samples in the original data are eliminated when the corresponding values in the single residual are greater than w times the median within a window. A flowchart describing the entire process is shown in figure .
Figure 1 A flowchart of the sample deletion process.