A theoretical overview of model-based and correlation-based redatuming methods

Abstract

We review the equations for correlation-based redatuming methods. A correlation-based redatuming method uses natural-phase information in the data to time shift the weighted traces so they appear to be generated by sources ͑or recorded by geophones͒ shifted to a new location. This compares to model-based redatuming, which effectively time shifts the traces using traveltimes computed from a prior velocity model. For wavefield redatuming, the daylight imaging, interferometric imaging, reverse-time acoustics ͑RTA͒, and virtualsource methods all require weighted correlation of the traces with one another, followed by summation over all sources ͑and sometimes receivers͒. These methods differ from one another by their choice of weights. The least-squares interferometry and virtual-source imaging methods are potentially the most powerful because they account for the limited source and receiver aperture of the recording geometry. Interferometry, on the other hand, has the flexibility to select imaging conditions that target almost any type of event. Stationary-phase principles lead to a Fermat-based redatuming method known as redatuming by a seminatural Green's function. No crosscorrelation is needed, so it is less expensive than the other methods. Finally, Fermat's principle can be used to redatum traveltimes.

Interferometry by Deconvolution of Multicomponent Multioffset GPR Data

“…A similar inversion is used for transforming acoustic surface-related multiples into primaries [34]. Equations (16) and (17) describe 3-D IbD and are similar to the least squares redatuming method [35]. When we ignore the inverse matrix in (17), we arrive at…”

Target-enclosed seismic imaging

“…It is well-known that multiple reflections in the medium are not addressed by this procedure, which can lead to the emergence of spurious arrivals in the redatumed data space (Malcolm et al, 2007). In theory, more accurate results can be achieved if propagators are computed in the physical medium (Bakulin and Calvert, 2006;Schuster and Zhou, 2006), and if upgoing and downgoing wavefields are separated (Mehta et al, 2007). However, to eliminate all spurious events from redatumed gathers, reflection data should be acquired along a closed boundary surrounding the new subsurface datum (Snieder et al, 2006).…”

Interferometric identification of surface-related multiples

“…Mathematical representations of seismic interferometry are based on Rayleigh's reciprocity theorems (Claerbout, 1976;Wapenaar, 2004;Schuster and Zhou, 2006). A generalization of the theory to 3D elastodynamic media is derived by Wapenaar and Fokkema (2006).…”