Dayboro’s 5D interpolation program regularizes Pre-stack 3D seismic data in 5-Dimensions; Time, CMPX, CMPY, Azimuth, and Offset. The result of this program is a set of regularized CDP gathers fully populated for each azimuth and all offsets for every CDP. Regularization will help pre-stack migration with cancelation, help remove acquisition imprints and since only the dominant spectral events are being extracted for the output, many forms of noise are left behind. Moreover, the Azimuth Sectors are well populated so that accurate Azimuthal analysis becomes feasible.

This program regularizes Prestack 3D seismic data in five dimensions. The five dimensions involved are time, CMPX, CMPY, azimuth, and offset. Time refers to trace sample time and is regular to start with. CMPX and CMPY are the common mid points between the shot and the receiver in the X and Y directions respectively. Azimuth is the bearing of the shot to receiver vector. Offset is the absolute distance from shot to receiver. The end product of this program is a set of regularized CDP gathers. Each output gather has the same number of traces. Each trace in each output gather has a CMPX and CMPY equal to that of the output CDP bin centre coordinate that it belongs to. Within each azimuth bin, in each output gather, there are traces with offsets incrementing in an orderly fashion.

For example the regularized output might have:

CDP gather every 50 meters in inline and xline directions

8 symmetric azimuth bins centered at 0, 22.5, 45, 67.5 90, 112.5, 135 and 157.5 degrees

32 offsets incrementing by 50 meters from 50 to 1600 meters

There are many benefits of regularized data such as:

- Regularized data will help prestack migration with cancelation
- Regularized data will tend to remove aquistion imprints
- Since only the dominant spectral events are being extracted for the output, many forms of noise are reduced

The method that this program uses to regularize the data is as follows:

- Prestack data is broken up into overlapping temporal and spatial blocks
- For each block each trace is converted into the Fourier domain.
- Each frequency slice is transformed into a 4 dimensional Fourier domain of CMPX, CMPY, AZIMUTH, and OFFSET, using a non-uniform Fourier transform
- The Fourier transform of the frequency slice is reshaped to represent the frequency slice with the least number of significant spectral events

- A reverse 4 dimensional transform is performed to produce the regularized frequency slice

- Reverse Fourier transforms are performed to produce the regularized traces in the block

- All the regularized blocks of data are combined to create the output regularized CDP gathers.

References used in the development of this program are:

Fessler, J. A.,Bradley P. Sutton, 2003, Nonuniform Fast Fourier Transforms Using Min-Max Interpolation:IEEE T-SP,51(2):560-74, Feb. 2003.

Greengard, L., 2004, Accelerating the Nonuniform Fast Fourier Transform: SIAM REVIEW,Vol. 46, No. 3, pp. 443-454

Press W. P., Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, 1994, NUMERICAL RECIPIES in C, The Art of Scientific Computing, Second Edition: Chapters 12 and 13.

Poole, G., Philippe Herrmann ,CGGVeritas, 2007, Multi-dimensional data regularization for modern aquisition geometries: SEG/San Antonio 2007 Annual Meeting

Poole, G., 2010, 5d Data Reconstruction Using The Anti-Leakage Fourier Transform, Barcelona ’10

Sacchi M.,2011, ABC’s of Seismic Data Regularization: CSEG Convention Short Course, May 4, 2011

Sheng XU, Yu Zhang, Don Pham, and Gilles Lambare, 2005, Antileakage Fourier transform for seismic data regularization: GEOPHYSICS, VOL. 70, NO. 4

Trad, D. Five-dimensional interpolation: Recovering from acquistion constraints:GEOPHYSICS, VOL. 74, NO.6

On the all 3D datasets we have processed the 5D Interpolation provided a significant uplift to the data.