Improving Kirchhoff migration with repeated local plane-wave imaging? A SAR-inspired signal-processing approach in prestack depth imaging

A local plane-wave approach of generalized diffraction tomography in heterogeneous backgrounds, equivalent to Kirchhoff summation techniques when applied in seismic reflection, is re-programmed to act as repeated synthetic aperture radar (SAR) imaging for seismic prestack depth migration. Spotlight-mode SAR imaging quickly provides good images of the electromagnetic reflectivity of the ground via fast Fourier transform (FFT)-based signal processing. By calculating only the Green's functions connecting the aircraft to the centre of the illuminated patch, scattering structures around that centre are also recovered. SAR technology requires us to examine seismic imaging from the local point of view, where the quantity and quality of the available information at each image point are what are important, regardless of the survey geometry. When adapted to seismics, a local image of arbitrary size and sampling is obtained by FFT of seismic energy maps in the scattering wavenumber domain around each node of a pre-calculated grid of Green's functions. These local images can be used to generate a classic prestack depth-migrated section by collecting only their centres. However, the local images also provide valuable information around the centre, as in SAR. They can therefore help to pre-analyse prestack depth migration efficiently, and to perform velocity analysis at a very low cost. The FFT-based signal-processing approach allows local, efficient and automatic control of anti-aliasing, noise and resolution, including optimized Jacobian weights. Repeated local imaging could also be used to speed up migration, with interpolation between local images associated with a coarse grid of Green's functions, as an alternative to interpolation of Green's functions. The local images may, however, show distortions due to the local plane-wave approximation, and the velocity variations across their frame. Such effects, which are not necessarily a problem in SAR, should be controlled and corrected to further enhance seismic imaging. Applications to realistic models and to real data show that, despite the distortion effects, the local images can yield similar information to prestack depth migration, including common-image-point gathers for velocity analyses and AVO/AVA effects, at a much lower cost when a small target is considered.