Spurious multiples in seismic interferometry of primaries

Abstract

Seismic interferometry is a technique for estimating the Green's function that accounts for wave propagation between receivers by correlating the waves recorded at these receivers. We present a derivation of this principle based on the method of stationary phase. Although this derivation is intended to be educational, applicable to simple media only, it provides insight into the physical principle of seismic interferometry. In a homogeneous medium with one horizontal reflector and without a free surface, the correlation of the waves recorded at two receivers correctly gives both the direct wave and the singly reflected waves. When more reflectors are present, a product of the singly reflected waves occurs in the crosscorrelation that leads to spurious multiples when the waves are excited at the surface only. We give a heuristic argument that these spurious multiples disappear when sources below the reflectors are included. We also extend the derivation to a smoothly varying heterogeneous background medium.

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

“…The original aim of the virtual source method has been to correct only for the primary transmission effects of the overburden. Since internal multiple reflections were not accounted for in the formulation, spurious events could emerge in the retrieved gathers (Snieder et al 2006). This problem has been mitigated to some extent by separating upgoing and downgoing waves prior to redatuming, which was made possible by the deployment of multicomponent receivers (Mehta et al 2007).…”

Green's function retrieval by cross‐correlation in case of one‐sided illumination

“…Various theories have been developed to explain this phenomenon, ranging from diffusion theory for enclosures [Weaver and Lobkis, 2001], multiple scattering theory and stationary-phase theory for random media [Malcolm et al, 2004;Snieder, 2004] and reciprocity theory for deterministic and random media [Wapenaar, 2004;Weaver and Lobkis, 2004;van Manen et al, 2005]. The principle of recovering an acoustic response by cross-correlation is often called Green's function retrieval; in the geophysical literature it is also known as seismic interferometry [Schuster et al, 2004;Wapenaar and Fokkema, 2006;Snieder et al, 2006].…”

“…Impressive results have been obtained by these authors for ballistic waves, but the coda due to internal multiple scattering was not considered. Snieder et al [2006] analyze the cross-correlation method for exploration seismology in more detail and conclude that artifacts appear in the reconstructed Green's function as a result of the fact that the source locations do not constitute a closed surface.…”

Locating Scatterers by Non-physical Scattered Waves Obtained by Seismic Interferometry

“…To obtain the complete Green's function between the receivers whose recorded responses we cross-correlate, the boundary sources (primary or secondary) need to effectively enclose these receivers (Wapenaar and Fokkema, 2006). When the receivers are not equally illuminated from all directions by the boundary sources, non-physical arrivals (ghosts) will appear in the SI result (Snieder et al, 2006;Halliday and Curtis, 2009;Halliday et al, 2010). Because SI effectively redatums sources from places away from the scatterers to the target area, the unwanted extra effects, due to propagation from the active-source locations through possibly laterally changing medium to the receivers close to the target area, are eliminated and non-physical ghost scattered waves are retrieved.…”