A correlation-type reciprocity theorem is used to show that the elastodynamic Green's function of any inhomogeneous medium (random or deterministic) can be retrieved from the cross correlation of two recordings of a wave field at different receiver locations at the free surface. Unlike in other derivations, which apply to diffuse wave fields in random media or irregular finite bodies, no assumptions are made about the diffusivity of the wave field. In a second version, it is assumed that the wave field is diffuse due to many uncorrelated sources inside the medium.

The term seismic interferometry refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations. The first version of this principle was derived by Claerbout ͑1968͒, who showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response. For an arbitrary 3D inhomogeneous lossless medium it follows from Rayleigh's reciprocity theorem and the principle of time-reversal invariance that the acoustic Green's function between any two points in the medium can be represented by an integral of crosscorrelations of wavefield observations at those two points. The integral is along sources on an arbitrarily shaped surface enclosing these points. No assumptions are made with respect to the diffusivity of the wavefield. The Rayleigh-Betti reciprocity theorem leads to a similar representation of the elastodynamic Green's function. When a part of the enclosing surface is the earth's free surface, the integral needs only to be evaluated over the remaining part of the closed surface. In practice, not all sources are equally important: The main contributions to the reconstructed Green's function come from sources at stationary points. When the sources emit transient signals, a shaping filter can be applied to correct for the differences in source wavelets. When the sources are uncorrelated noise sources, the representation simplifies to a direct crosscorrelation of wavefield observations at two points, similar as in methods that retrieve Green's functions from diffuse wavefields in disordered media or in finite media with an irregular bounding surface.

Traditionally, the Marchenko equation forms a basis for 1D inverse scattering problems. A 3D extension of the Marchenko equation enables the retrieval of the Green’s response to a virtual source in the subsurface from reflection measurements at the earth’s surface. This constitutes an important step beyond seismic interferometry. Whereas seismic interferometry requires a receiver at the position of the virtual source, for the Marchenko scheme it suffices to have sources and receivers at the surface only. The underlying assumptions are that the medium is lossless and that an estimate of the direct arrivals of the Green’s function is available. The Green’s function retrieved with the 3D Marchenko scheme contains accurate internal multiples of the inhomogeneous subsurface. Using source-receiver reciprocity, the retrieved Green’s function can be interpreted as the response to sources at the surface, observed by a virtual receiver in the subsurface. By decomposing the 3D Marchenko equation, the response at the virtual receiver can be decomposed into a downgoing field and an upgoing field. By deconvolving the retrieved upgoing field with the downgoing field, a reflection response is obtained, with virtual sources and virtual receivers in the subsurface. This redatumed reflection response is free of spurious events related to internal multiples in the overburden. The redatumed reflection response forms the basis for obtaining an image of a target zone. An important feature is that spurious reflections in the target zone are suppressed, without the need to resolve first the reflection properties of the overburden.

The major amount of multiple energy in seismic data is related to the large reflectivity of the surface. A method is proposed for the elimination of all surface‐related multiples by means of a process that removes the influence of the surface reflectivity from the data. An important property of the proposed multiple elimination process is that no knowledge of the subsurface is required. On the other hand, the source signature and the surface reflectivity do need to be provided. As a consequence, the proposed process has been implemented adaptively, meaning that multiple elimination is designed as an inversion process where the source and surface reflectivity properties are estimated and where the multiple‐free data equals the inversion residue. Results on simulated data and field data show that the proposed multiple elimination process should be considered as one of the key inversion steps in stepwise seismic inversion.

Turning noise into useful data-every geophysicist's dream? And now it seems possible. The field of seismic interferometry has at its foundation a shift in the way we think about the parts of the signal that are currently filtered out of most analyses-complicated seismic codas (the multiply scattered parts of seismic waveforms) and background noise (whatever is recorded when no identifiable active source is emitting, and which is superimposed on all recorded data). Those parts of seismograms consist of waves that reflect and refract around exactly the same subsurface heterogeneities as waves excited by active sources. The key to the rapid emergence of this field of research is our new understanding of how to unravel that subsurface information from these relatively complex-looking waveforms. And the answer turned out to be rather simple. This article explains the operation of seismic interferometry and provides a few examples of its application.A simple thought experiment. Consider an example of a horizontally stratified (one-dimensional) acoustic medium, and for the moment let us imagine that it has only a single internal interface. Now, say horizontally planar pressure waves are emitted by two impulsive sources, one after the other, and that one source is above the interface and one below. Vibrations from the resulting propagating waves are recorded at two receivers which can be placed anywhere between the two sources ( Figure 1, left).The recordings are shown in the center of the figure. At each receiver a direct and a reflected wave is recorded for source 1, whereas only one transmitted wave is recorded for source 2.Seismic interferometry of these data involves only two simple steps: The two recorded signals from each source are crosscorrelated and the resulting crosscorrelograms are summed (stacked). The result, shown on the right of Figure 1, is surprising; for positive times it is the seismogram that would have been recorded at either receiver if the other receiver had in fact been a source, and at negative times it is the time reverse of this seismogram. In other words, by this simple, two-step operation we have constructed the seismic trace from a virtual source-a source that did not exist in our initial experiment, and a source that is imagined to be at the location of one of our receivers.To generalize, this simple example placed no constraint on where the receivers were placed, provided they were between the sources. By moving either or both of them (or by using many distributed receivers from the start), it is therefore possible to construct the trace from an infinite number of virtual source and receiver pairs placed at any locations, by recording the signal from only two actual sources. What is more, provided one of the active sources is above the interface and receivers and the other is below, the location of the active sources is also arbitrary, and in order to carry out the process above we do not even need to know where these sources are. Seismic interferometry steps.The fundamental steps of t...