1887
Volume 38 Number 8
  • E-ISSN: 1365-2478

Abstract

A

The slant‐stack migration formula based on the Radon transform is studied with respect to the depth step Δ of wavefield extrapolation. It can be viewed as a generalized trace‐interpolation procedure including wave extrapolation with an arbitrary step Δ. For Δ= 0 the formula yields the familiar plane‐wave decomposition, while for Δ > 0 it provides a robust tool for migration transformation of spatially undersampled wavefields. Using the stationary phase method, it is shown that the slant‐stack migration formula degenerates into the Rayleigh‐Sommerfeld integral in the far‐field approximation. Consequently, even a narrow slant‐stack gather applied before the diffraction stack can significantly improve the representation of noisy data in the wavefield extrapolation process. The theory is applied to synthetic and field data to perform trace interpolation and dip reject filtration. The data examples presented prove that the Radon interpolator works well in the dip range, including waves with mutual stepouts smaller than half the dominant period.

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