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The theory of Green's function retrieval essentially requires homogeneously distributed noise sources. Even though these conditions are not fulfilled in nature, low-frequency (<1 Hz) surface waves generated by ocean–crust interactions have been used successfully to image the crust with unprecedented spatial resolution. In contrast to low-frequency surface waves, high-frequency (>1 Hz) body waves have a sharper, more localized sensitivity to velocity contrasts and temporal changes at depth. In general, their retrieval using seismic interferometry is challenging, and recent studies focus on powerful, localized noise sources. They have proven to be a promising alternative but break the assumptions of Green's function retrieval. In this study, we present an approach to model correlations between P waves for these scenarios and analyse their sensitivity to 3-D Earth structure. We perform a series of numerical experiments to advance our understanding of these signals and prepare for an application to fault monitoring. In the considered cases, the character of the signals strongly diverges from Green's function retrieval, and the sensitivity to structure has significant contributions in the source direction. An accurate description of the underlying physics allows us to reproduce observations made in the context of monitoring the San Jacinto Fault in California using train-generated seismic waves. This approach provides new perspectives for detecting and localizing temporal velocity changes previously unnoticed by commonly exploited surface-wave reconstructions. [ABSTRACT FROM AUTHOR]

Cross correlation of ambient seismic noise has begun to provide detailed images of the Earth that are not possible to attain using earthquake-based or active-source imaging techniques. However, the theoretical justification for the ambient noise correlation or seismic interferometry approach typically relies on an equipartition or diffuse field assumption that is not expected to be satisfied on Earth. Here we demonstrate that a Bayesian inference approach to calculating the expected cross correlation of seismic signals leads to an improved understanding of its relationship with the Green's function. The Bayesian derivation is found to exactly replicate the equipartition result under a global energy constraint, and is able to accommodate any number of other constraints that typically cannot be utilized in other approaches. With these stronger constraints, the cross correlation is found to deviate more and more strongly from the 'expected' Green's function, but nonetheless a specific prediction can be made regarding the expected cross correlation which can be used as a more reliable point of comparison with observations than the Green's function. The approach therefore provides a path forward for how to use seismic cross correlation data under more and more realistic conditions and improvements in knowledge, and should eventually help improve the accuracy of resulting images of the Earth. [ABSTRACT FROM AUTHOR]

Beamforming and backprojection methods offer a data-driven approach to image noise sources, but provide no opportunity to account for prior information or iterate through an inversion framework. In contrast, recent methods have been developed to locate ambient noise sources based on cross-correlations between stations and the construction of finite-frequency kernels, allowing for inversions over multiple iterations. These kernel-based approaches show great promise, both in mathematical rigour and in results, but are less physically intuitive and interpretable. Here we show that these apparently two different classes of methods, beamforming and kernel-based inversion, are achieving exactly the same result in certain circumstances. This paper begins with a description of a relatively simple beamforming or backprojection algorithm, and walks through a series of modifications or enhancements. By including a rigorously defined physical model for the distribution of noise sources and therefore synthetic correlation functions, we come to a framework resembling the kernel-based iterative approaches. Given the equivalence of these approaches, both communities can benefit from bridging the gap. For example, inversion frameworks can benefit from the numerous image enhancement tools developed by the beamforming community. Additionally, full-waveform inversion schemes that require a window selection for the comparisons of misfits can more effectively target particular sources through a windowing in a beamform slowness domain, or might directly use beamform heatmaps for the calculation of misfits. We discuss a number of such possibilities for the enhancement of both classes of methods, testing with synthetic models where possible. [ABSTRACT FROM AUTHOR]

We introduce open-source tool noisi for the forward and inverse modeling of ambient seismic cross-correlations with spatially varying source spectra. It utilizes pre-computed databases of Green's functions to represent seismic wave propagation between ambient seismic sources and seismic receivers, which can be obtained from existing repositories or imported from the output of wave propagation solvers. The tool was built with the aim of studying ambient seismic sources while accounting for realistic wave propagation effects. Furthermore, it may be used to guide the interpretation of ambient seismic auto- and cross-correlations, which have become pre-eminent seismological observables, in light of non-uniform ambient seismic sources. Written in the Python language, it is both accessible for usage and further development, as well as efficient enough to conduct ambient seismic source inversions for realistic scenarios. Here, we introduce the concept and implementation of the tool, compare its model output to the output of cross-correlations computed with SPECFEM3D_globe, and demonstrate its capabilities on selected use cases: A comparison of observed cross-correlations of the Earth's hum to a forward model based on hum sources from oceanographic models, and a synthetic noise source inversion using full waveforms and signal energy asymmetry. [ABSTRACT FROM AUTHOR]

We propose a theory for rotational and strain ambient noise interferometry, motivated by the recent development of rotational ground motion sensors and distributed acoustic sensing (DAS) technology. In this context, we demonstrate that displacement, strain and rotation interferograms can be generically written in the form of a representation theorem, that is, as a solution to the seismic wave equation that we refer to as the interferometric wavefield. The physical quantity (displacement, strain or rotation) determines the distributed source of the interferometric wavefield, as well as an observational operator that extracts the correct type of noise correlation function. The proposed interferometric equations are free of assumptions on the distribution of noise sources or the equipartitioning of the ambient field, typically required for Green's function retrieval. In addition to being valid for any kind of heterogeneous source and viscoelastic medium, they allow us to account for measurement details, such as the gauge length in DAS. We illustrate the practical feasibility of our approach with a series of numerical examples, based on regional-scale, spectral-element simulations of the interferometric wavefield. Specifically, we compare displacement and strain interferograms for homogeneous and heterogeneous earth models, and for homogeneous and heterogeneous noise sources. Ultimately, our developments are intended to enable adjoint-based waveform inversion with emerging measurement technologies that provide spatial gradient information in addition to conventional seismic displacement recordings. [ABSTRACT FROM AUTHOR]

We present a computational framework for the assimilation of local to global seismic data into a consistent model describing Earth structure on all seismically accessible scales. This Collaborative Seismic Earth Model (CSEM) is designed to meet the following requirements: (i) Flexible geometric parametrization, capable of capturing topography and bathymetry, as well as all aspects of potentially resolvable structure, including small-scale heterogeneities and deformations of internal discontinuities. (ii) Independence of any particular wave equation solver, in order to enable the combination of inversion techniques suitable for different types of seismic data. (iii) Physical parametrization that allows for full anisotropy and for variations in attenuation and density. While not all of these parameters are always resolvable, the assimilation of data that constrain any parameter subset should be possible. (iv) Ability to accommodate successive refinements through the incorporation of updates on any scale as new data or inversion techniques become available. (v) Enable collaborative Earth model construction. The structure of the initial CSEM is represented on a variable-resolution tetrahedral mesh. It is assembled from a long-wavelength 3-D global model into which several regional-scale tomographies are embedded. We illustrate the CSEM workflow of successive updating with two examples from Japan and the Western Mediterranean, where we constrain smaller scale structure using full-wave form inversion. Furthermore, we demonstrate the ability of the CSEM to act as a vehicle for the combination of different tomographic techniques with a joint full-waveform and travel time ray tomography of Europe. This combination broadens the exploitable frequency range of the individual techniques, thereby improving resolution. We perform two iterations of a whole-Earth full-waveform inversion using a long-period reference data set from 225 globally recorded earthquakes. At this early stage of the CSEM development, the broad global updates mostly act to remove artefacts from the assembly of the initial CSEM. During the future evolution of the CSEM, the reference data set will be used to account for the influence of small-scale refinements on large-scale global structure. The CSEM as a computational framework is intended to help bridging the gap between local, regional and global tomography, and to contribute to the development of a global multiscale Earth model. While the current construction serves as a first proof of concept, future refinements and additions will require community involvement, which is welcome at this stage already. [ABSTRACT FROM AUTHOR]

We develop and apply a novel full-waveform ambient noise inversion that jointly constrains 3D Earth structure and heterogeneous noise sources. The fundamental idea is to drop the principle of Green's function retrieval, which is the basis for current noise tomographic studies, and to establish correlation functions as self-consistent observables in seismology. Our method is valid for arbitrary noise source distributions in both space and frequency, and it accounts for the complete seismic wave propagation physics in 3D heterogeneous and attenuating media. Extracting waveform information from correlation functions allows us to improve the resolution of ambient noise tomography and to refine noise source location, which is essential for a better understanding of noise generation.The forward problem of modeling correlation functions and the computation of sensitivity kernels for noise sources and Earth structure are implemented based on the spectral-element solver Salvus. As a first application, we consider a global dataset focusing on the Earth's hum period band and invert for both the distribution of noise sources and Earth structure. In order to validate our approach, we assess the quality of the obtained tomographic model with an independent dataset comprised of earthquake recordings.The successful application of full waveform ambient noise inversion opens new possibilities in tomographic imaging due to the continuous and ubiquitous nature of ambient noise sources. [ABSTRACT FROM AUTHOR]

Ambient noise auto-correlations have been successfully used in a small number of recent studies in order to image crustal reflectors. This idea, which goes back to Claerbout, holds great potential for passive imaging: the naturally occurring ambient noise penetrates to large depths and can be measured continuously even in seismically quiet regions, and at low expense. Reflection profiles obtained from auto-correlations could supplement the sharp boundaries to the generally smooth images obtained with ambient noise tomography. However, the interpretation of the auto-correlation traces in terms of crustal reflectors often appears far from straightforward. Some studies have relied on additional information such as well logs or active seismic profiles in order to delineate reflectors. We suggest to utilize additional information about the source distribution of the ambient seismic noise in order to interpret noise auto-correlations. To do so, we investigate the influence of the source distribution on auto-correlations by means of a synthetic sensitivity study. We make use of our recently developed method to model auto-correlations for various Earth models – from layered to fully 3-D – and for various distributions of sources with spatially varying spectra. This also allows us to quantify the sensitivity of the auto-correlations to noise sources, as well as to variations in subsurface structure. We firstly show and discuss the sensitivity of auto-correlation envelopes to proximal and distant ambient seismic sources. Cross-terms between signals arriving directly at the seismic sensor and signals reflected in between sources and the receiver give rise to signals in the auto-correlation, but not necessarily those one would expect by assuming subvertically incident ambient noise body waves. The auto-correlation sensitivity to sources provides an overview of these signals and could therefore be used to facilitate interpretation.In this context, it is necessary to account for the role of processing applied to the continuous seismic data in order to retrieve auto-correlations, since it has been shown that the successful recovery of reflectors depends on it. We then investigate the sensitivity of auto-correlation envelopes to Earth structure. It depends on the given ambient source distribution. Thus, we compare structural sensitivities for different scenarios of ambient source distributions to complement the first part of the sensitivity study, and to add to the understanding of this new passive imaging tool. [ABSTRACT FROM AUTHOR]