There are several types of 5D interpolation used in the industry. One approach attempts to increase the source and receiver sampling by creating an augmented geometry that includes the original geometry plus desired new source and receiver locations. The output consists of the original data plus new interpolated shots and receivers at the infill locations.


Another method of interpolation replaces the original data with new interpolated traces which are regularized in CMP x- and y-coordinates and in source-to-receiver offset vector x- and y-coordinates.


Statcom uses the Calcoulee Continuum software package to create interpolated traces of regular spacing in CMP x- and y-coordinates, azimuth, and offset.


The output of this full regularization is composed of 100% interpolated traces that are positioned at regular intervals in each of these dimensions. In other words, the original data are replaced totally by interpolated regularly spaced traces, and the output is regular in CMP, offset, and azimuth distribution, providing full uniform coverage of offsets and azimuths.

Freedom From Acquisition limits

The type of interpolation not directly constrained by the surface geometry. It creates the ideal multidimensional trace spacing for the output CMP gathers regardless of the imperfections that exist in the original survey.

Random Noise Cancellation

Improved random noise suppression is attained by interpolation. The numerous weak spectral events expressing random noise tend are left behind. Spatial filtering noise attenuation algorithms may perform better on 5D interpolated Data.

Acquisition Imprint Suppression

The arrangement of interpolated output trades is not closely related to the surface geometry with this type of interpolation. In addition, an ideal (regular and uniform) distribution of traces in offset and azimuth is generated. These two factors improve the suppression of acquisition imprint. 

Wavelet stabilization

The Calcoulee Continuum 5D interpolation and regularization approach helps to stabilize horizon wavelets for prestack and stack volumes. Because the approach suppresses random noise and acquisition imprint, and uses many input traces to model each output trace, more accurate prestack horizon wavelets are achieved. Equal fold and regular trace distribution in all dimensions further help to stabilize wavelet characteristics on stacked volumes.

Calcoulee Continuum software details

The prestack seismic input data are decomposed into input blocks for 5D interpolation. These blocks are extracted CMP gathers that have NMO applied and all the necessary statics. The blocks are CMP super-gathers that overlap in time and space. A typical size for a super-gather is 16 x 16 CMP bins, and 250 msec in length.

The program then interpolates each irregularly sampled input block to a regularly sampled output block. The  interpolation is performed 

on each frequency slice of the input data block. A forward, non-uniform, four dimensional, Fourier transform is performed on the input

 frequency slice being operated upon.

Since the input data are irregularly spaced, the Fourier spectrum will contain what is referred to as spectral leakage. To improve this

 spectrum for interpolation purposes, the Calcoulee Continuum uses the Anti-leakage Fourier Transform (ALFT) as described by Xu et al.,

 2005. This is an iterative procedure. On each iteration, the most significant, highest amplitude, spectral events are extracted from the four 

dimensional Fourier domain and saved. These extracted spectral events are also reconstructed and removed from the input data being

 operated upon. The residual input data are put through the forward, non-uniform Fourier transform again for the start of the next iteration.

​This iterative process is continued until the amplitude of the extracted spectral events falls below the user-specified level.  The collected 

spectral events are put through a reverse four dimensional Fourier transform to construct the regularly sampled output block. Finally,  the

 interpolated regularized output CMP gathers are then constructed from the interpolated output blocks.


The danger exists that an interpolated output trace will be unreliable because it is positioned too far  way from input data in  one or more

 of the four spatial dimensions. To prevent this from happening, dimensional proximity checks are performed on every output trace snippet during the interpolation phase. If a trace snippet fails one of these tests, a kill flag for the dimension in question is set. At the time of

 construction of the output traces, the user can choose which dimensional kill flags are to be activated. This will result in the trace snippets,

 considered to be over extrapolated, not being summed into the final output trace. If this results in a whole trace being killed, a blank trace will be output as a place holder and will be marked as dead.


Another hazard is if the input data are aliased, in one or more of the four spatial dimensions, relative to the desired output spacing

 specified by the user. The Calcoulee Continuum can detect some of the obvious cases of aliasing and take the necessary action 

to prevent the interpolated output from deteriorating. Parameters are also provided for the user to control how the program deals with 

some of these potential aliasing cases.


Calcoulee Corporation,

Email: sjb@xplornet.com