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.