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We introduce seismic interferometry of passive data by multidimensional deconvolution (MDD) as an alternative to the crosscorrelation method. Interferometry by MDD has the potential to correct for the effects of source irregularity, assuming the first arrival can be separated from the full response. MDD applications can range from reservoir imaging using microseismicity to crustal imaging with teleseismic data.

The methodology of surface‐wave retrieval from ambient seismic noise by crosscorrelation relies on the assumption that the noise field is equipartitioned. Deviations from equipartitioning degrade the accuracy of the retrieved surface‐wave Green's function. A point‐spread function, derived from the same ambient noise field, quantifies the smearing in space and time of the virtual source of the Green's function. By multidimensionally deconvolving the retrieved Green's function by the point‐spread function, the virtual source becomes better focussed in space and time and hence the accuracy of the retrieved surface‐wave Green's function may improve significantly. We illustrate this at the hand of a numerical example and discuss the advantages and limitations of this new methodology.

With seismic interferometry reflections can be retrieved between station positions. In the classical form, the reflections are retrieved by an integration over sources. For a specific dataset, however, the actual source distribution might not be sufficient to approximate the source integral. Yet, there might be a dense distribution of receivers allowing integration over the receiver domain. We rewrite the source integral to an integration over midpoints. With this formulation, a reflection can be retrieved even in the limiting case of only a single source. However, with respect to the classical formulation, an additional stationary-phase analysis is required.

A number of seismic methods exist to image the lithosphere below a collection of receivers, using distant earthquakes. In the current practice, especially mode-conversions in teleseismic phases are utilized. We present a new method that takes advantage of the availability of global phases. This method is called global-phase seismic interferometry (GloPSI). With GloPSI, zero-offset reflections are extracted from reverberations near the array caused by global seismicity. We exemplify GloPSI with data from the Hi-CLIMB experiment (2002–2005) and migrate the obtained reflection responses. This results in a 800 km long reflectivity profile through the Himalayas and a large part of the Tibetan Plateau.

A novel method, based on differential arrival times of diffractions from the core-mantle boundary, swiftly scans for seismic velocity anomalies in the crust and mantle below an array of seismometers. The method is applied to data from the USArray and the large-scale structural features in the western United States are resolved. High lateral resolution is achieved, but structure is averaged over depth. As such, this method is complementary to surface-wave and tomographic body-wave methods, where averaging takes place in the lateral sense. Processing and data-volume requirements involved are minimal. Therefore, this method can be applied during the early stages of array deployment, before the necessary data is acquired to obtain accurate inversion images. The quick scanner can be used to identify features of interest, upon which the array could be refined.

Application of seismic interferometry to records from receivers at the Earth’s surface from sources in wells retrieves the reflection response measured at the receivers as if from virtual sources located also at the surface. When the wavefields experience intrinsic losses during propagation, non-physical arrivals (ghosts) would appear in the retrieved result. These ghosts appear due to waves that reflect inside a subsurface layer. Thus, a ghost contains information about the seismic properties of the specific layer. We show how such ghosts can be used to monitor layer-specific changes in the velocity and intrinsic losses in the subsurface. We show how to identify the ghosts using numerical-modelling results from a vertical well, and how to estimate the layer-specific velocity and quality-factor changes using numerical-modelling results from a horizontal well as well as ultrasonic S-wave laboratory data.

Topography and near-surface heterogeneities lead to traveltime perturbations in surface land-seismic experiments. Usually, these perturbations are estimated and removed prior to further processing of the data. A common technique to estimate these perturbations is the delay-time method. We have developed the “modified delay-time method,” wherein we isolate the arrival times of the virtual refraction and estimate receiver-side delay times. The virtual refraction is a spurious arrival found in wavefields estimated by seismic interferometry. The new method removes the source term from the delay-time equation, is more robust in the presence of noise, and extends the lateral aperture compared to the conventional delay-time method. We tested this in an elastic 2D numerical example, where we estimated the receiver delay- times above a horizontal refractor. Taking advantage of reciprocity of the wave equation and rearranging the common shot gathers into common receiver gathers, isolated source delay times could also be obtained.

Progress in the imaging of the mantle and core is partially limited by the sparse distribution of natural sources; the earthquake hypocenters are mainly along the active lithospheric plate boundaries. This problem can be approached with seismic interferometry. In recent years, there has been considerable progress in the development of seismic interferometric techniques. The term seismic interferometry refers to the principle of generating new seismic responses by cross-correlating seismic observations at different receiver locations. The application of interferometric techniques on a global scale could create sources at locations where no earthquakes occur. In this way, yet unknown responses would become available for the application of travel-time tomography and surface-wave dispersion studies. The retrieval of a dense-enough sampling of source gathers would largely benefit the application of reflection imaging. We derive new elastodynamic representation integrals for global-scale seismic interferometry. The relations are different from other seismic interferometry relations for transient sources, in the sense that they are suited for a rotating closed system like the Earth. We use a correlation of an observed response with a response to which free-surface multiple elimination has been applied to account for the closed system. Despite the fact that the rotation of the Earth breaks source-receiver reciprocity, the seismic interferometry relations are shown to be valid. The Coriolis force is included without the need to evaluate an extra term. We synthesize global-scale earthquake responses and use them to illustrate the acoustic versions of the new interferometric relations. When the sampling of real source locations is dense enough, then both the responses with and without freesurface multiples are retrieved. When we do not take into account the responses from the sources in the direct neighborhood of the seismic interferometry-constructed source location, the response with free-surface multiples can still be retrieved. Even when only responses from sources at a certain range of epicentral distances are available, some events in the Green’s function between two receiver locations can still be retrieved. The retrieved responses are not perfect, but the artefacts can largely be ascribed to numerical errors. The reconstruction of internal events – the response as if there was a source and a receiver on (major) contrasts within the model – could possibly be of use for imaging. With modelling it is possible to discover in which region of the correlation panel stationary phases occur that contribute to the retrieval of events. This knowledge opens up a new way of filtering out undesired events and of discovering whether specific events could be retrieved with a given source-receiver configuration.

In 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.

The last few years there has been a growing number of body-wave observations in noise records. In 1973 Vinnik conjectured that P-waves would even be the dominant wavemode, at epicentral distances of about 40 degrees and onwards from an oceanic source. At arrays far from offshore storms, surface waves induced by nearby storms would not mask the body-wave signal and hence primarily P-waves would be recorded. We measured at such an array in Egypt and indeed found a large proportion of P-waves. At the same time, a new methodology is under development to characterize the lithosphere below an array of receivers, without active sources or local earthquakes. Instead, transmitted waves are used which are caused by distant sources. These sources may either be transient or more stationary. With this new methodology, called seismic interferometry, reflection responses are extracted from the coda of transmissions. Combining the two developments it is clear that there is a large potential for obtaining reflection responses from low-frequency noise. A potential practical advantage of using noise instead of earthquake responses would be that an array only needs to be deployed for a few days or weeks instead of months, to gather enough illumination. We used a few days of continuous noise, recorded with an array in the Abu Gharadig basin, Egypt. We split up the record in three distinct frequency bands and in many small time windows. Using array techniques and taking advantage of all three-component recordings we could unravel the dominant wavemodes arriving in each time window and in each frequency band. The recorded wavemodes, and hence the noise sources, varied significantly per frequency band, and -to a lesser extent- per time window. Primarily P-waves were detected on the vertical component for two of the three frequency bands. For these frequency bands, we only selected the time windows with a favorable illumination. By subsequently applying seismic interferometry, we retrieved P-wave reflection responses and delineated reflectors in the crust, the Moho and possibly the Lehmann discontinuity.

Seismology is the study of the vibration of the Earth. Seismologists pay much attention to the main source of Earth vibration: earthquakes. But also other seismic sources, like mining blasts, ocean storms and windmills, are studied. All these sources induce seismic waves, which can eventually be recorded as ground vibrations. These seismic records contain not only information about the sources, but also about the part of the Earth through which the waves have propagated. This thesis focuses on a main subclass of seismology: seismic imaging. With seismic imaging, seismic records are studied with the aim to unravel the structure and composition of the Earth. Seismic imaging finds its main use in extracting information about the solid Earth that is within our reach. With the current state of the art, we can only mine minerals from the upper 0.2 percent. Imaging the deep (i.e., unreachable) Earth finds its main use in hazard assessment. Through imaging the deep Earth, we can better understand the dynamics of our planet, manifested in, amongst others, earthquakes and volcanism. By forecasting how the Earth will reshape, we can sensibly adapt. Seismic characterization of the subsurface also improves our ability to assess the direct impact of earthquakes. A large part of the current deep-Earth images are obtained through tomographic inversion. These images are successful for identifying large-scale structural anomalies, like (remnants of) subducting slabs. However, they lack the resolution to accurately image discontinuities in space. Sharp discontinuities, like the interface between sedimentary and crystalline rock, lead to conversions and reflections of seismic waves. It is those reflections that are most suitable for imaging the discontinuities. The technique developed to do this is called seismic reflection imaging (SRI). Though SRI is considered to be an advanced technique for imaging the subsurface, the dense and wide source (and receiver) distribution requirement thus far limited the use for deep-Earth imaging. Deep-Earth imaging is done primarily with natural sources. Their limited and irregular distribution and their unpredictable occurrence time is inconvenient for SRI. In this thesis we work on a methodology to alleviate the stringent requirement on the source distribution. This methodology is called seismic interferometry (SI). SI is a remapping operation. With SI, the responses from many sources are combined to create the response as if there were a source at a receiver position. The response from this "virtual" source could contain both surface waves and body waves. We apply SI such that especially (reflected) body waves are retrieved, because it are these waves that are used for SRI. When we apply SI to a regularly-spaced array of receivers, we could turn uncontrolled natural sources into a well-organized succession of virtual sources, which is amenable for SRI. The aim of this work is to improve the imaging of the interior of the Earth by the application of body-wave SI to naturally induced seismic data. A prior study focused on the exploration-scale (i.e., the part of the Earth that is being mined). In this thesis, we focus on low-frequency waves (< 2 Hz), which contain especially information about the deep Earth. In Part I we consider applications to earthquake recordings. In Part II we evaluate the retrieval of reflections using microseisms. Part I starts by looking into the global-scale configuration. For this configuration, two seismic stations (or two arrays of stations) may be located anywhere on the globe and reflectors may be located anywhere in depth. We derive and numerically test relations to retrieve the complete response between two stations, using worldwide seismicity. The SI relations are valid for a closed entity for seismic waves, like the Earth is by approximation. The relations do not account for inelastic losses, by which eventually all seismic energy is transformed to heat. Though normally of negligible influence, the SI relations do account for the rotation of the Earth. In practice, the distribution of the larger earthquakes is not wide enough to retrieve complete responses between any two points on the Earth. However, still relevant primary reflections can be retrieved with a limited dense distribution of seismicity, like from the Tohoku (2011) aftershock sequence. Part I proceeds by zooming in to the lithospheric-scale configuration. The lithosphere is the part of the solid Earth where most (seismic) activity takes place. It makes up the crust and the upper part of the mantle. It is this part of the Earth that, broken into plates and fueled by convection in the mantle, undergoes birth (at midoceanic ridges), collisions (resulting in stunning topography) and death (subduction back into the mantle). Inspecting the Earth in depth unveils a part of the history of the lithosphere and gives an indication of the processes still ongoing. Information about the structure of the lithosphere is hidden in the coda of wavefields that arrive due to distant seismicity. We test a few different SI approaches to extract this information. We use synthetic data with similar characteristics as field data recorded during the Laramie broad-band experiment (2000-2001). This was an array of seismic stations in Wyoming, USA, to study an suture zone. We evaluate the requirements for obtaining multi-offset reflection responses. These multi-offset reflections are important for obtaining a velocity model. We estimate this model for the subsurface below the Laramie array and we use it to map the extracted reflections to a reflectivity image of the lithosphere. In the remainder of part I, we focus again on the lithospheric scale. This time, we assume that a velocity model is already available through other means. Consequently, only single-offset reflection responses are required to make an image. We use global phases to obtain zero-offset reflection responses. We show the robustness of the method with data from the Hi-CLIMB experiment (2002-2005). This was a large and well-sampled seismic array, passing the Himalayas and a significant part of the Tibetan Plateau. The successive application of SRI leads to an image of the Indian-Eurasian Plate collision. The rediscovery of body waves in low-frequency noise (<1 Hz) opened up the research for Part II of this thesis. The noise are in fact microseisms: Earth vibrations that are indirectly caused by ocean gravity waves. High-amplitude ocean waves are caused when storms, leading to persistent wind fields, cross an ocean. We retrieve reflection responses from body-wave noise using SI approaches similar to the ones used for earthquake recordings. The main difference between applications to noise and (large) earthquake responses is that the origin of large earthquakes is known, whereas the origin of noise is generally not known. Therefore, the main challenge for noise applications is to unravel the noise illumination. For this purpose, we use a well-sampled areal array in Egypt to study the noise illumination in different frequency bands. We only select the noise records with a favorable body-wave content and process them into separate reflection responses, of both the lithosphere and the upper crust. We further evaluate what basin-scale information can be extracted from the retrieved reflections. The wavelengths of the reflections extracted from low-frequency noise are too long to image a sedimentary basin in detail. However, the sharp boundary between the sediments and the underlying crystalline rocks can be delineated. For the same dataset from Egypt, we compare the information that is extracted with SI with the information that is obtained when using two other passive seismic techniques, namely horizontal-to-vertical spectral ratio and receiver function. In the appendices we discuss a few spin-off developments from the main research. In Appendix A we work out an alternative SI relation that integrates over midpoints between receiver positions, instead of over sources. Using this relation, reflections can already be retrieved using only a single source. However, a well-sampled array of receivers needs to be available and an additional evaluation needs to be performed. In Appendix B we develop a technique to estimate loss factors from plane-wave transmission responses. The losses are estimated from amplitude ratios, obtained before and after applying autocorrelation. In Appendix C we present a method that was inspired by SI. Crosscorrelations of diffractions from the core-mantle boundary are used to swiftly scan anomalies in the crust and mantle. Finally, in Appendix D we discuss an alternative implementation of SI: SI by multidimensional deconvolution. With this technique the outcome of SI may be improved. However, well-sampled arrays of receivers are required and additional processing needs to be implemented. In this thesis, we show that the application of SI to earthquake recordings is sufficiently mature to yield high-resolution images of the lithosphere. Relations for imaging deeper structures are worked out and modus operandi are thought through. However, the reality check is still to be encountered with field-data applications. Furthermore, we show that the applications of SI to microseisms can be used to yield information about a basin depth. Moreover, we show the great promise of microseism applications for unveiling a lithosphere in depth, using only a few days of noise recordings. The more repetitive character of microseism sources with respect to earthquakes, in fact makes them more amenable for monitoring applications, if their yearly variations and radiation characteristics are well understood.