Seismic interferometry involves the crosscorrelation of responses at different receivers to obtain the Green's function between these receivers. For the simple situation of an impulsive plane wave propagating along the x-axis, the crosscorrelation of the responses at two receivers along the x-axis gives the Green's function of the direct wave between these receivers. When the source function of the plane wave is a transient ͑as in exploration seismology͒ or a noise signal ͑as in passive seismology͒, then the crosscorrelation gives the Green's function, convolved with the autocorrelation of the source function. Direct-wave interferometry also holds for 2D and 3D situations, assuming the receivers are surrounded by a uniform distribution of sources. In this case, the main contributions to the retrieved direct wave between the receivers come from sources in Fresnel zones around stationary points. The main application of direct-wave interferometry is the retrieval of seismic surface-wave responses from ambient noise and the subsequent tomographic determination of the surfacewave velocity distribution of the subsurface. Seismic interferometry is not restricted to retrieving direct waves between receivers. In a classic paper, Claerbout shows that the autocorrelation of the transmission response of a layered medium gives the plane-wave reflection response of that medium. This is essentially 1D reflected-wave interferometry. Similarly, the crosscorrelation of the transmission responses, observed at two receivers, of an arbitrary inhomogeneous medium gives the 3D reflection response of that medium. One of the main applications of reflected-wave interferometry is retrieving the seismic reflection response from ambient noise and imaging of the reflectors in the subsurface. A common aspect of direct-and reflected-wave interferometry is that virtual sources are created at positions where there are only receivers without requiring knowledge of the subsurface medium parameters or of the positions of the actual sources.

S U M M A R YSeismic interferometry, also known as Green's function retrieval by crosscorrelation, has a wide range of applications, ranging from surface-wave tomography using ambient noise, to creating virtual sources for improved reflection seismology. Despite its successful applications, the crosscorrelation approach also has its limitations. The main underlying assumptions are that the medium is lossless and that the wavefield is equipartitioned. These assumptions are in practice often violated: the medium of interest is often illuminated from one side only, the sources may be irregularly distributed, and losses may be significant. These limitations may partly be overcome by reformulating seismic interferometry as a multidimensional deconvolution (MDD) process. We present a systematic analysis of seismic interferometry by crosscorrelation and by MDD. We show that for the non-ideal situations mentioned above, the correlation function is proportional to a Green's function with a blurred source. The source blurring is quantified by a so-called interferometric point-spread function which, like the correlation function, can be derived from the observed data (i.e. without the need to know the sources and the medium). The source of the Green's function obtained by the correlation method can be deblurred by deconvolving the correlation function for the point-spread function. This is the essence of seismic interferometry by MDD. We illustrate the crosscorrelation and MDD methods for controlled-source and passive-data applications with numerical examples and discuss the advantages and limitations of both methods.

One application of seismic interferometry is to retrieve the impulse response ͑Green's function͒ from crosscorrelation of ambient seismic noise. Various researchers show results for retrieving the surface-wave part of the Green's function. However, reflection retrieval has proven more challenging. We crosscorrelate ambient seismic noise, recorded along eight parallel lines in the Sirte basin east of Ajdabeya, Libya, to obtain shot gathers that contain reflections. We take advantage of geophone groups to suppress part of the undesired surface-wave noise and apply frequency-wavenumber filtering before crosscorrelation to suppress surface waves further.After comparing the retrieved results with data from an active seismic exploration survey along the same lines, we use the retrieved reflection data to obtain a migrated reflection image of the subsurface.

[1] The retrieval of the earth's reflection response from cross-correlations of seismic noise recordings can provide valuable information, which may otherwise not be available due to limited spatial distribution of seismic sources. We cross-correlated ten hours of seismic background-noise data acquired in a desert area. The cross-correlation results show several coherent events, which align very well with reflections from an active survey at the same location. Therefore, we interpret these coherent events as reflections. Retrieving seismic reflections from background-noise measurements has a wide range of applications in regional seismology, frontier exploration and long-term monitoring of processes in the earth's subsurface.

S U M M A R YRelations 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 theorems of the convolution type and of the correlation type. We obtain relations between reflection and transmission responses, including their codas, due to internal multiple scattering. These relations can be used for deriving the reflection response from transmission measurements (which is useful for seismic imaging of the subsurface, using passive recordings of noise sources in the subsurface, also known as acoustic daylight imaging) as well as for deriving the transmission coda from the reflection measurements (which is useful for seismic imaging schemes that take internal multiple scattering into account). Furthermore, following the same approach, we obtain mutual relations between reflection responses with and without free-surface multiples. The convolution-type relations are similar to those used by Berkhout and others for surface-related multiple elimination, whereas the correlation-type relations resemble Schuster's relations for seismic interferometry. Last, but not least, we obtain expressions for the reflection response at a boundary below an inhomogeneous medium, which may be useful for imaging the medium 'from below'. The main text of this paper deals with the acoustic situation; the Appendices provide extensions to the elastodynamic situation.In this paper we present a unified approach for deriving relationships between seismic reflection and transmission responses in 3-D inhomogeneous acoustic and full elastic media. In all relations, the codas due to internal multiple scattering are included. We consider situations with and without a free surface on top of the configuration; below a specific depth level we assume that the medium is homogeneous. Hence, the responses of interest are:(1) reflection responses at the upper boundary, with and without free-surface multiples at the upper boundary;(2) transmission responses between the upper and lower boundaries, with and without free-surface multiples at the upper boundary;(3) reflection responses at the lower boundary, with and without free-surface multiples at the upper boundary.Apart from relations between reflection and transmission responses we will encounter relations between reflection responses with and without free-surface multiples and relations between reflection responses at the upper and lower boundaries.The relations between reflection and transmission responses are the basis for deriving the reflection response from the transmission response, and the coda of the transmission response from the reflection response. The former relation is relevant for 'acoustic daylight imaging', that is, for imaging the subsurface from passive recordings of the transmission responses of natural noise sources i...

S U M M A R YCreating new responses from cross-correlations of responses measured at different locations is known as interferometry. Each newly created response represents the field measured at one of the receiver locations as if there were a source at the other. Here, we formulate electromagnetic interferometric Green's functions representations in open configurations. There are in principle no restrictions on the heterogeneity and anisotropy of the medium inside or outside the domain. Time-correlation type formulations rely on conservation of total wave energy and they cannot be used for media showing relaxation of some form in a straightforward way. Time-convolution type propagation invariants are independent of the medium relaxation mechanisms and they can be used for interferometry by cross-correlating a measured response with the time-reverse of another response. This type of interferometry can only be formulated in the configuration with one receiver outside the domain. For time-convolution interferometry no restrictions on the medium heterogeneity, anisotropy or relaxation mechanisms are made. For these interferometric formulations to be of practical use, the main simplification is to make a high-frequency approximation for the normal derivative in the source coordinate. These approximations of the exact result lead to two different types of errors. We discuss the causes and consequences of these errors and illustrate them with numerical examples.

[1] The successful surface waves retrieval in solid-Earth seismology using long-time correlations and subsequent tomographic images of the crust have sparked interest in extraction of subsurface information from noise in the exploration seismology. Subsurface information in exploration seismology is usually derived from body-wave reflections > 1 Hz, which is challenging for utilization of ambient noise. We use 11 h of noise recorded in the Sirte basin, Libya. First, we study the characteristics of the noise. We show that the bulk of the noise is composed of surface waves at frequencies below 6 Hz. Some noise panels contain nearly vertically traveling events. We further characterize these events using a beamforming algorithm. From the beamforming, we conclude that these events represent body-wave arrivals with a fairly rich azimuthal distribution. Having body-wave arrivals in the noise is a prerequisite for body-wave reflections retrieval. We crosscorrelate and sum the recorded ambient-noise panels to retrieve common-source gathers, following two approaches-using all the noise and using only noise panels containing body-wave arrivals likely to contribute to the reflections retrieval. Comparing the retrieved gathers with active seismic data, we show that the two-way traveltimes at short offsets of several retrieved events coincide with those of reflections in the active data and thus correspond to apexes of reflections. We then compare retrieved stacked sections of the subsurface from both approaches with the active-data stacked section and show that the reflectors are consistent along a line. The results from the second approach exhibit the reflectors better.Citation: Draganov, D., X. Campman, J. Thorbecke, A. Verdel, and K. Wapenaar (2013), Seismic exploration-scale velocities and structure from ambient seismic noise (> 1

S U M M A R YIn recent years, there has been an increase in the deployment of relatively dense arrays of seismic stations. The availability of spatially densely sampled global and regional seismic data has stimulated the adoption of industry-style imaging algorithms applied to converted-and scattered-wave energy from distant earthquakes, leading to relatively high-resolution images of the lower crust and upper mantle. We use seismic interferometry to extract reflection responses from the coda of transmitted energy from distant earthquakes. In theory, higher-resolution images can be obtained when migrating reflections obtained with seismic interferometry rather than with conversions, traditionally used in lithospheric imaging methods. Moreover, reflection data allow the straightforward application of algorithms previously developed in exploration seismology. In particular, the availability of reflection data allows us to extract from it a velocity model using standard multichannel data-processing methods. However, the success of our approach relies mainly on a favourable distribution of earthquakes. In this paper, we investigate how the quality of the reflection response obtained with interferometry is influenced by the distribution of earthquakes and the complexity of the transmitted wavefields. Our analysis shows that a reasonable reflection response could be extracted if (1) the array is approximately aligned with an active zone of earthquakes, (2) different phase responses are used to gather adequate angular illumination of the array and (3) the illumination directions are properly accounted for during processing. We illustrate our analysis using a synthetic data set with similar illumination and source-side reverberation characteristics as field data recorded during the 2000-2001 Laramie broad-band experiment. Finally, we apply our method to the Laramie data, retrieving reflection data. We extract a 2-D velocity model from the reflections and use this model to migrate the data. On the final reflectivity image, we observe a discontinuity in the reflections. We interpret this discontinuity as the Cheyenne Belt, a suture zone between Archean and Proterozoic terranes.