5D Interpolation

Our 5D interpolation method is based on Fourier reconstruction by Minimum Weighted Norm Interpolation (MWNI). This method is called 5D interpolation because it operates on 5 dimensions of the seismic data, one temporal dimension and four spatial dimensions. The four spatial dimensions are either inline/crossline/inline-offset/crossline-offset, or, inline/crossline/offset/azimuth. Choosing inline-offset and crossline-offset as spatial dimensions leads to a Common Offset Vector (COV) or Offset Vector Tile (OVT) description of the data.

5D interpolation uses a neighbourhood of acquired seismic data to predict the missing data. Ideally, data that are missing in one or two of the spatial dimension can be reconstructed using data that are present and well sampled in the other spatial dimensions. Interpolation has become an important part of our 3D processing flow for a number of reasons:

  • It corrects for the effects of an irregular acquisition geometry by regularizing the geometry and filling in small gaps within the geometry.
  • It equalizes geometries from multiple 3D datasets in 3D merges. In a merge project, the acquisition geometry can have different shot and receiver line spacing, different CDP bin sizes or the azimuth of acquisition may vary from survey to survey. As well some surveys may be acquired with an orthogonal geometry and others with Megabin. Minimizing these differences is an important step towards an optimally merged dataset.
  • Interpolation increases offset/azimuth fold of data for subsequent azimuthal analysis.
  • For cases where base line and monitor surveys are acquired with different geometries, the geometries can be regularized and equalized to common grid for improved time lapses seismic processing and subsequent 4D analysis.
  • The 5D interpolation is also applied to PS datasets by the same technique, but with conversion point locations used as the inline and crossline coordinates.

The output of 5D interpolation is well sampled COV gathers that can be pre-stack time migrated, in the COV domain, to preserve offset and azimuth for subsequent azimuthal analysis, including velocity variation with azimuth (VVAZ). If an offset plane pre-stack time migration is required, the increased fold of the data will allow us to migrate to more offset planes which should improve subsequent AVO analysis.

The following figures show interpolation results where a survey was acquired with a coarser bin grid than the grid required for the merged survey.

fig. 1.1 - Gather Before Interpolation fig. 1.2 - Gather After Interpolation
Figure 1. A CDP gather before and after 5D interpolation.

fig. 2.1 - Stack Before Interpolation fig. 2.2 - Stack After Interpolation
Figure 2. An inline stack before and after 5D interpolation.

fig. 3.1 - Timeslice Before Interpolation fig. 3.2 - Timeslice After Interpolation
Figure 3. A time slice before and after 5D interpolation.