Processing Map Data in USP

Introduction

In the interpretive process it is often helpful to view the data under consideration from a new perspective. USP contains a number of routines tailored to this purpose, not only for seismic data, both pre and post stack, but for any dataset which can be represented by a regularized grid of values. Interpretational maps, be they from potential fields datasets such as gravity and magnetics, or seismic horizon interpretations in time or depth, easily fit this category. In this section we will examine the properties of one subset of these tools whose purpose is to do radial filtering of the 2D FFT of the data.

xyz2sis

Though written specifically to convert to USP format gridded data extracted from a Zmap database, this routine will convert any regularized (x,y,z) dataset. The algorithm employed first scans the input dataset to determine which of the indices [x or y] is incrementing the fastest. This index is associated with the sample index of the resulting USP record. The remaining index is referenced to the trace number. The [z] value becomes the data amplitude at the [x,y | sample,trace] location. Certain extracted grid information is stored in the line and trace headers of the output dataset to aid in data location when viewing the dataset using the X Seismic Display tool XSD.

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

xyz2sis -N zmapdata -O uspdata -null -0.999999e-3

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.

polymute

Since the radial filtering process involves taking a 2D FFT of this dataset it is useful to condition the data by first smoothing these rough edges. This was accomplished by picking a set of polygons to use with the USP routine polymute in such a fashion so as to taper the edges of the mapped data. To apply the routine the following was executed:
polymute -N uspdata -P pick1 -nxtaper 20 -nztaper 20 |
polymute -P picks2 -nxtaper 20 -nztaper 20 -M in |
polymute -P picks3 -nxtaper 20 -nztaper 20 -M in -O tapereddata

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

To apply a 2D FFT to the input data the following was executed:
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.

fkrad

To create this display the following was run:
fkrad -N fftdata -O fkraddata

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.

fkshape

The designed filter was applied to the data using:
fftshape -N fftdata -O fftshapedata -P filterpicks

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:

fftxy -N fftshapedata -O regional -R

The residual component may be obtained in either of two ways. The regional component may be subtracted from the original input data using:

vstak -N1 regional -N2 tapereddata -O residual -amp -1

or at the filtering stage the residual may be output directly by using the command line flag [-diff] during execution of fftshape.

fftshape -N fftdata -O fftshapedata -P filterpicks -diff

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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