Kees Wapenaar

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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(More)
S U M M A R Y Relations between reflection and transmission responses of horizontally layered media were formulated by Claerbout in 1968 and by many others. In this paper we derive similar relations for 3-D inhomogeneous media. As the starting point for these derivations, we make use of two types of propagation invariants, based on one-way reciprocity(More)
In 1968, Jon Claerbout showed that the reflection response of a 1D acoustic medium can be reconstructed by autocorrelating the transmission response. Since then, several authors have derived relationships for reconstructing Green’s functions at the surface, using crosscorrelations of noise recordings that were taken at the surface and that derived from(More)
It has recently been shown that the response to a virtual source in the subsurface can be derived from reflection data at the surface and an estimate of the direct arrivals between the virtual source and the surface. Hence, unlike for seismic interferometry, no receivers are needed inside the medium. This new method recovers the complete wavefield of a(More)
It has been shown theoretically and observationally that the Green's function for acoustic and elastic waves can be retrieved by cross-correlating fluctuations recorded at two locations. We extend the concept of the extraction of the Green's function to a wide class of scalar linear systems. For systems that are not invariant under time reversal, the(More)
Despite the strength of seismic interferometry to retrieve new seismic responses by crosscorrelating observations at different receiver locations, the method relies on a number of assumptions which are not always fulfilled in practice. Some practical circumstances that may hamper interferometry by crosscorrelation are: one-sided illumination, irregular(More)
Seismic interferometry deals with the generation of new seismic responses by crosscorrelating existing ones. One of the main assumptions underlying most interferometry methods is that the medium is lossless. We develop an ‘interferometry-bydeconvolution’ approach which circumvents this assumption. The proposed method applies not only to seismic waves, but(More)
Many depth migration methods use one-way frequency–space depth extrapolation methods. These methods are generally considered to be expensive, so it is important to find the most efficient way of implementing them. This usually means making spatial convolution operators that are as short as possible. Applying the extrapolation operators in a recursive way,(More)
One-way wave equations conveniently describe wave propagation in media with discontinuous and/or rapid variations in one direction, but with smooth and slow variations in the complementary transverse directions. In the past, reciprocity theorems have been developed in terms of one-way wave fields. The boundaries of the integration volumes and the variations(More)