Consider the following magnetic dataset (Fig. 1) which has been extracted from a Zmap+ database as a regularized grid of information. In this example the null value [-999.999] has been inserted anywhere that no data existed. This is necessary to keep the output grid rectangular. To covert this tabular data to a USP dataset (Fig. 2) the following command line was used
All samples containing the null value specified on the command line have be replaced by 0.0 thus leaving a dataset with some very distinct edges.
The above combination of muting operations is required as the polymute routine is constrained to mute using polygons whose interior angles never become greater than 180 degrees. The process is effective however as the resulting record (Fig. 3) has no remaining hard edges. The effect that this edge smoothing has on the Fourier transform of the data is worth noting.
fftxy -N
tapereddata -O fftdata
Note the amount of energy concentrated on the Kx and Ky axes (Fig. 4) due to the hard edges. This effect is dramatically reduced after the data has been conditioned. There is still a significant amount of energy associated with edges on the Ky axis (Fig. 5) as the principle orientation of the data (Fig. 3) is in that direction
Several approaches may now be taken to filtering this data. One may again use the polymute routine to mute out a certain portion of the FK transform. One may also use the fkkstrip routine to apply a Bessel type filter to the input dataset. What will be demonstrated here is the utility of applying a user defined radial filter designed through observation of a radial power spectral display (Fig. 6) of the data.
The vertical axis is the normalized log of the power while the horizontal axis is the radial wavenumber. The actual frequency of each trace is stored in the trace header mnemonic TrcNum and the multiplier used to make that value an integer for display is stored in the trace header mnemonic DpPtLt. From this display the user man pick a filter or any number of filters by creating as many individual xsd pick segments as desired. For this example only one filter was chosen (Fig. 7) to attempt to isolate the regional gradient from the input dataset. Once picked this segment can be saved as a standard XSD pick file.
The resulting dataset (Fig. 8) is a filtered version of the input 2D FFT. The filtering has been applied to the amplitude portion of the transform only. To view the filtered data (Fig. 9) simply apply the inverse 2D FFT by:
The residual component may be obtained in either of two ways. The regional component may be subtracted from the original input data using:
or at the filtering stage the residual may be output directly by using the command line flag [-diff] during execution of fftshape.
of course it is still necessary at this point to apply the inverse FK transform as done previously. The regional component preserves the overall trends of the input data but lacks the detailed contours. The residual component (Fig. 10) contains the difference between the two. The veracity with which the residual resembles reality is of course a matter of interpretation. How close did the filter design resemble anything approaching a Weiner filter? How much is known of the predicted residual based on modelling? The answers to these questions are up to you. These tools are here to give you a very quick method of performing a large variety of filtering in your never-ending quest for the subsurface solution.
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