Two-dimensional frequency domain filtering

An automatic computer-implemented process for filtering two-dimensional data including the steps of:

• (a) automatically computing the Fourier transform of said data to produce the values associated with the spatial frequency and wave number corresponding to the time and distance coordinates of said data;
• (b) automatically and selectively zeroing in the transformed data obtained in step (a), all data in only one of two sets collectively comprising the total of said transform data, which sets consist essentially of (1) all transform data the spatial frequency and wave number coordinates of which are within the boundaries of a polygon defined by plurality of arbitrarily chosen vertices of specified spatial frequency and wave number, and (2) the rest of said transform data;
• (c) automatically computing the inverse Fourier transform of the data from step (b), whereby the output data from this step (c) may be plotted to form a visual representation of said travelling waves with the selectively removed data filtered therefrom;
• (d) defining a border of arbitrary width surrounding said polygon;
• (e) automatically modifying the amplitude of all data points the spatial frequency and wave number coordinates of which lie on or within said border by multiplication by an arbitrarily chosen function of maximum value +1 and minimum value 0, which smoothly varies in amplitude, depending on the distance from each of said data points to the nearest point on the perimeter of said polygon, step (e) being completed after step (a) and before the start of step (c);
• and
• (f) plotting the output data from step (c), thus forming said visual representation of the filtered two-dimensional data.

In earth exploration using the arrival of traveling waves at detectors at a plurality of locations spaced in a detector spread, from which a two-dimensional visual display of amplitude of said waves in terms of the position of said detector locations is made, the method of spatially filtering the traveling wave arrival data obtained at said detectors, including the steps of:

• (a) producing a plurality of sets of electric signals corresponding to the arrival of said travelling waves at said detectors so that each set contains in terms of amplitude and time the effect of said waves impinging on one or more detectors positioned at a location in said spread,
• (b) automatically producing in a suitably programmed digital computer (the input data to which is said plurality of sets of electric signals) the Fourier transform of said data into a corresponding plurality of amplitudes in terms of frequency and wave number,
• (c) automatically modifying in a suitably programmed digital computer said amplitudes produced in step (b) to decrease said amplitudes essentially to zero inside or outside a region defined in terms of frequency and wave number in the Fourier transform plane by a plurality of straightline segments defining an area of polygonal shape containing a plurality of vertices (with all internal angles less than 180.degree.) defining in terms of frequency and wave number the perimeter of said area,
• (d) automatically producing in a suitably programmed digital computer, the input data to which is the data produced in step (c), the inverse Fourier transform of said data, from which may be prepared a two-dimensional visual display of amplitude of said waves in terms of the position of said detector locations, from which by spatial filtering the effect of undesired waves has been removed, and
• (e) plotting the output data from step (d), thus forming said visual display of said filtered two-dimensional data.