Seismic exploration using exactly invertible discrete transformation into tau-p space
First Claim
1. A method of seismic exploration of subsurface formations comprising:
- deriving a first seismogram of selected subsurface formations;
transforming said first seismogram to tau-p space through a discrete transformation process which permits exact discrete inverse-transformation and which in processing in the frequency domain can be completed frequency-by-frequency and in processing in the spatial domain can utilize a transformation matrix having a block-circulant structure;
processing the tau-p space seismogram to enhance desirable features thereof and effect an exact discrete inverse transformation from tau-p space to generate an improved seismogram; and
providing a tangible representation of the improved seismogram.
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Abstract
Disclosed are a method and a system for discrete transformation of measurements such as seismic data into and out of tau-p space which is both exact and practical in terms of processing time. The measurements can be filtered or otherwise processed in tau-p space in ways which are not practical or possible in their original space. Since the transformations into and out of tau-p space are exact, the filtered and transformed measurements are free of errors and distortions that perturb known approximate transforms which can be performed in a reasonable time. When the transformation process is carried out in frequency space, it is done frequency-by-frequency, and when it is carried out in the spatial domain, it can utilize a transformation matrix having a block-circulant structure. In each case, the transformation process and matrix have a structure which substantially reduces storage and processing requirements as compared with known prior art.
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Citations
47 Claims
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1. A method of seismic exploration of subsurface formations comprising:
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deriving a first seismogram of selected subsurface formations; transforming said first seismogram to tau-p space through a discrete transformation process which permits exact discrete inverse-transformation and which in processing in the frequency domain can be completed frequency-by-frequency and in processing in the spatial domain can utilize a transformation matrix having a block-circulant structure; processing the tau-p space seismogram to enhance desirable features thereof and effect an exact discrete inverse transformation from tau-p space to generate an improved seismogram; and providing a tangible representation of the improved seismogram. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
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13. A method of seismic exploration of subsurface formations comprising:
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deriving a seismogram of subsurface formations which is in discrete form in a selected space; transforming the seismogram through the use of a discrete form of a transform to generate a seismogram in tau-p space, in a process which comprises utilizing a transformation matrix having the property of being block circulant when represented in the spatial domain; filtering the seismogram in tau-p space to generate a filtered seismogram; inverse-transforming the filtered seismogram from tau-p space through the use of an exact discrete form of an inverse transform to thereby generate a filtered seismogram in the selected space; and providing a tangible representation of the filtered seismogram in the selected space. - View Dependent Claims (14, 15, 16, 17)
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18. A method of seismic exploration of subsurface formations comprising:
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deriving an original seismogram of selected subsurface formations which is represented as a set of traces each comprising discrete samples of a selected seismic parameter over time for a selected spatial parameter; transforming the original seismogram into tau-p space by transforming the original seismogram into the frequency domain, multiplying the frequency domain version of the original seismogram by selected transformation matrices for respective frequencies to derive respective product arrays, and inverse transforming the product arrays out of the frequency domain to derive a representation of the original seismogram in discrete form in tau-p space and allowing exact discrete inverse-transformation; and providing a tangible representation of the seismogram in tau-p space in form suitable for modifying or display in tau-p space. - View Dependent Claims (19, 20, 21, 22, 23, 28)
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24. A method comprising:
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deriving a two-dimensional array xl (n) of seismic traces in (l,n) space, where l is an integer index which identifies a respective one of (2L+l) traces which are rows in the array and ranges from -L to +L, L being an integer, each row of the array comprises discrete samples of a selected seismic parameter, each sample being identified by an index n=1, 2, . . . , N, and xl (n) is a periodic sequence with the period N, N being an integer; deriving transformation matrices Rjl (k), where j is an integer index which identifies a respective one of (2J+l) rows of a transform matrix and ranges from -J to +J, l is an integer index which identifies a respective one of (2L+l) columns of a transformation matrix and ranges from -L to +L, and where k is a frequency index and J and L are integers; transforming the array xl (n) into the frequency domain to derive the array xl (k+1); matrix-multiplying the array xl (k+1) by the matrices Rjl (k) to derive the array yj (k+1) allowing exact discrete inverse-transformation; and modifying the array yj (k+1) to derive a modified array. - View Dependent Claims (25, 26, 27, 29)
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32. A method comprising:
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deriving an original record of measurements of a selected parameter of energy propagating in a medium and sampled in time and in space; transforming the original record to a record in tau-p space through a discrete transformation process which permits exact discrete inverse-transformation and which in processing in the frequency domain can be completed frequency-by-frequency and in processing in the spatial domain can utilize a transformation matrix having a block-circulant structure; processing the tau-p space record to enhance desirable features thereof and effect an exact discrete inverse transformation from tau-p space to generate an improved record; and providing a tangible representation of the improved record. - View Dependent Claims (30, 31, 33, 34, 35, 36, 37, 38, 39, 40)
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41. A method comprising:
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deriving an original record of data for a selected parameter sampled with respect to two independent variables defining an original domain; transforming the original record to a record in a different domain in which each point results from a sum of values of said parameter taken over a corresponding pattern in said original domain, through a discrete transformation which permits exact discrete inverse-transformation and which in processing in a frequency domain corresponding to one of said independent variables can be completed frequency-by-frequency and in processing in said original domain with respect to the other of said independent variables can utilize a transformation matrix having a block-circulant structure; processing said different domain record to enhance desirable features thereof and effect an exact discrete inverse transformation from said different domain to generate an improved record; and providing a tangible representation of the improved record. - View Dependent Claims (42, 43, 44, 45, 46, 47)
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Specification