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.

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We study the wave properties at a fluid/porousmedium interface by using newly derived closed-form expressions for the reflection and transmission coefficients. We illustrate the usefulness of these relatively simple expressions by applying them to a water/porousmedium interface (with open-pore or sealed-pore boundary conditions), where the porous medium consists of (1) a water-saturated clay/silt layer, (2) a water-saturated sand layer, (3) an air-filled clay/silt layer, or (4) an airfilled sand layer. We observe in the frequency range 5 Hz-20 kHz that the fast P-wave and S-wave velocities in the four porous materials are indistinguishable from the corresponding frequency-independent ones calculated using Gassmann relations. Consequently, for these frequencies we would expect the reflection and transmission coefficients for the four water/porous-medium interfaces to be similar to the ones for corresponding interfaces between water and effective elastic media (described by Gassmann wave velocities). This expectation is not fulfilled in the case of an interface between water and an air-filled porous layer with open pores. A close examination of the expressions for the reflection and transmission coefficients shows that this unexpected result is because of the large density difference between water and air.

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, using small depth steps, also demands that the operators do not amplify the wavefield at every depth step.Weighted least squares is an appropriate method to use for designing extrapolation operators that are accurate and efficient and that remain stable in a recursive algorithm. The extrapolated wavefields calculated with these operators are comparable with the extrapolation results obtained with other known operator design techniques as the Remez exchange method and nonlinear optimization. In this paper, the weighted leastsquares technique is refined by using different model functions. By smoothing the phase and amplitude transition at the evanescent cutoff, we can stabilize the resulting operators.The accuracy of the operators is shown in zero-offset migration impulse responses in 2D and 3D media. The Sigsbee2A data set is used to illustrate the quality of the extrapolation operators in prestack depth migration in a complex medium.