Seismic interferometry by crosscorrelation and by multidimensional deconvolution: a systematic comparison
01 May 2010-pp 5758
Abstract: SUMMARY Seismic 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 wave field 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, particularly for EM applications, 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 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.
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Proceedings Article•
01 Jan 1993
TL;DR: In this article, invariant imbedding, wave field splitting and phase space methods are reformulated in terms of an operator scattering matrix characteristic of the modeled environment, and the subsequent equations for the reflection and transmission operators are of first-order (one-way) in range, nonlinear (Riccati-like), and, in general, nonlocal.
Abstract: Wave field splitting, invariant imbedding, and phase space methods reformulate the Helmholtz wave propagation problem in terms of an operator scattering matrix characteristic of the modeled environment. The subsequent equations for the reflection and transmission operators are of first-order (one-way) in range, nonlinear (Riccati-like), and, in general, nonlocal. The reflection and transmission operator equations provide the framework for constructing inverse algorithms based on, in principle, exact solution methods
45 citations
01 Dec 2016
TL;DR: In this paper, a multidimensional deconvolution (MDD) process is proposed to correct non-uniform illumination patterns by means of a so-called point-spread function (PSF).
Abstract: Obtaining new seismic responses from existing recordings is generally referred to as seismic interferometry (SI). Conventionally, these seismic interferometric responses are retrieved by simple crosscorrelation of recordings made by separate receivers: a first receiver acts as a 'virtual source' whose response is retrieved at the other receivers. When surface waves are retrieved, the newly retrieved responses can be used to extract receiver-receiver phase velocities. These phase velocities often serve as input parameters for tomographic inverse problems. Another application of SI exploits the temporal stability of the multiply scattered arrivals (the coda). For all applications, however, the accuracy of the retrieved responses is paramount. In practice, this accuracy is often degraded by irregularities in the illumination pattern: correct response retrieval relies on a uniform illumination of the receivers. Reformulating the theory underlying seismic interferometry by crosscorrelation as a multidimensional deconvolution (MDD) process, allows for correction of these non-uniform illumination patterns by means of a so-called point-spread function (PSF). We apply SI by MDD to surface-wave data recorded by the Malargue seismic array in western Argentina. The aperture of the array is approximately 60 km and it is located on a plateau just east of the Andean mountain range. The array has a T-shape, which makes it very well suited for the application of SI by MDD. We select time windows dominated by surface-wave noise traveling in a favorable direction, that is, traversing the line of virtual sources before arriving at the receivers at which we aim to retrieve the virtual-source responses. These time windows are selected based upon the slownesses along the two receiver lines. From the selected time windows, virtual-source responses are retrieved by computation of ensemble-averaged crosscorrelations. Similarly, ensemble-averaged crosscorrelations between the positions of the virtual sources are computed: the PSF. We use the PSF to deconvolve the effect of illumination irregularities and the source function from the virtual-source responses retrieved by crosscorrelation. The combined effect of time-window selection and MDD results in more accurate and temporally stable surface-wave responses.
16 citations
01 Apr 2019
TL;DR: In this paper, the authors discuss a variety of imaging methods in a systematic way, using a specific form of Green's theorem (the homogeneous Green's function representation) as the common starting point.
Abstract: Abstract. The solid earth and exploration communities independently developed a variety of seismic imaging methods for passive- and active-source data. Despite the seemingly different approaches and underlying principles, many of those methods are based in some way or another on Green's theorem. The aim of this paper is to discuss a variety of imaging methods in a systematic way, using a specific form of Green's theorem (the homogeneous Green's function representation) as the common starting point. The imaging methods we cover are time-reversal acoustics, seismic interferometry, back propagation, source-receiver redatuming and imaging by double focusing. We review classical approaches and discuss recent developments that fully account for multiple scattering, using the Marchenko method. We briefly indicate new applications for monitoring and forecasting of responses to induced seismic sources, which are discussed in detail in a companion paper.
8 citations
Cites background from "Seismic interferometry by crosscorr..."
...The main approximation is that evanescent waves are neglected (Zheng et al., 2011; Wapenaar et al., 2011)....
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...(7) The main approximation is that evanescent waves are neglected (Zheng et al., 2011; Wapenaar et al., 2011)....
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01 Jan 2019
TL;DR: In this article, the authors proposed a method for seismic interferometry, referred to as full waveform ambient noise inversion, which incorporates the heterogeneous nature of ambient noise sources in space and frequency, and models the full wave propagation physics.
Abstract: This thesis deals with the development and application of a novel method for seismic interferometry, referred to as full waveform ambient noise inversion. It incorporates the heterogeneous nature of ambient noise sources in space and frequency, and models the full wave propagation physics. By dropping the principle of Green’s function retrieval, the basis of traditional ambient noise tomography, we establish correlation functions as selfconsistent observables. A more accurate description of the physics of the problem allows us to extract additional information, to advance our understanding of correlation wavefields and to quantify inherent source-structure trade-offs. We generalize the theoretical formulation, thus facilitating the application of adjoint techniques, and investigate the prerequisites for its application to real data in a synthetic 2-D study. We then follow with a framework for modeling correlations in 3-D attenuating media with arbitrary noise source distributions and for the computation of sensitivity kernels for changes in source and structure. In a pilot use case, we look into a commonly encountered difference between the observation of body waves and surface waves, and reveal fundamentally different conditions for their reconstruction. For a final synthesis of all results and a proof of concept we invert a global dataset focusing on the long-period ambient noise field, called the Earth’s Hum, for the distribution of ambient noise sources, and for Earth structure. We confirm existing models for the source power-spectral density and recover tomographic features well known from global Earth models.
7 citations
Cites background from "Seismic interferometry by crosscorr..."
...…and Snieder , 2008a,b), multi-dimensional deconvolution (Wapenaar et al., 2008; Wapenaar and van der Neut, 2010; van der Neut et al., 2011; Wapenaar et al., 2011a,b), higher-order correlations (Stehly et al., 2008; Spica et al., 2016; Sheng et al., 2018) and wavefront tracking (Lin et…...
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...The quality of the retrieved Green’s function is improved by deconvolving the cross-correlation function with a so-called pointspread function that captures the illumination pattern of the sources (Wapenaar and van der Neut, 2010; van der Neut et al., 2011; Wapenaar et al., 2011a,b)....
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01 Jan 2020
TL;DR: In this paper, a target-oriented FWI (full-waveform inversion) was proposed by using Marchenko focusing to extrapolate the wavefields from the acquisition surface to the vicinity of the target.
Abstract: Measuring wave motion on the surface of an unknown medium can help us infer the physical properties of the medium through which waves propagate without intrusion. In many applications, multiple scattering and high computational cost prevent state-of-the-art data processing techniques from delivering a high-quality image of the medium, especially when it is complex. The recently developed Marchenko focusing technique has potential to overcome these challenges by performing data processing and imaging in a target-oriented fashion. Superior to conventional redatuming methods, Marchenko focusing retrieves multiply-scattered waves from single-sided reflection data with minimal a priori knowledge of medium properties. By iteratively re-emitting a time-reversed and time-windowed wavefield from a single side of the unknown medium, we can focus the wavefield at a prescribed virtual source position inside the medium. The redatumed wavefields in response to the virtual source can be used for imaging free from artefacts related to multiple scattering and interference from the medium surrounding the target. In this thesis, I work on practical implementation and applications of the Marchenko focusing technique. I first review the theory and methodology of the standard Marchenko scheme using 1D and 2D acoustic numerical examples. Then, I investigate its potential application to the hDVS (heterodyne distributed vibration sensing) technology, which records wavefields semi-continuously in space using an optical fibre. The hDVS signal is focused by the Marchenko method in the optical frequency regime, based on an analytical hDVS model. With a hypothesis of strong scattering inside the fibre, the redatumed hDVS signal may contribute to improving strain estimation. Next, I implement Marchenko focusing in a dissipative medium by both numerical modelling and laboratory implementation. To accommodate dissipation which is not accounted for in the standard Marchenko scheme, double-sided reflection data are required to derive an effectual reflection response. Physical focusing of the sound wave is achieved in a 1D variable-diameter tube. Finally, I conduct target-oriented FWI (full-waveform inversion) by using Marchenko focusing to extrapolate the wavefields from the acquisition surface to the vicinity of the target. Based on the representation theorem of the convolution type, a local forward modelling operator couples the target and the surrounding medium acoustically. I invert for the optimal target model, whose seismic response to the Marchenko retrieved areal sources best matches the Marchenko retrieved observed data. Given a sufficiently accurate initial velocity model, local FWI saves computational
6 citations
Cites background from "Seismic interferometry by crosscorr..."
...seismic interferometry (Wapenaar et al., 2011), wavefield injection (Robertsson et al....
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...The convolution-type representation theorem has wide geophysical applications, e.g. seismic interferometry (Wapenaar et al., 2011), wavefield injection (Robertsson et al., 2015; Vasmel and Robertsson, 2016), immersive wave experimentation (van Manen et al., 2007; Vasmel et al., 2013; Becker et al.,…...
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"Seismic interferometry by crosscorr..." refers methods in this paper
...(f) MDD result (red) compared with directly modeled response (black). of the Rayleigh-wave for the upper 300 km of the PREM model (Dziewonski & Anderson 1981), using the approach described by Wathelet et al. (2004)....
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TL;DR: Cross-correlation of 1 month of ambient seismic noise recorded at USArray stations in California yields hundreds of short-period surface-wave group-speed measurements on interstation paths that are used to construct tomographic images of the principal geological units of California.
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TL;DR: Proxy curves relating observed signal-to-noise ratios to average measurement uncertainties show promise to provide useful expected measurement error estimates in the absence of the long time-series needed for temporal subsetting.
Abstract: SUMMARY Ambient noise tomography is a rapidly emerging field of seismological research. This paper presents the current status of ambient noise data processing as it has developed over the past several years and is intended to explain and justify this development through salient examples. The ambient noise data processing procedure divides into four principal phases: (1) single station data preparation, (2) cross-correlation and temporal stacking, (3) measurement of dispersion curves (performed with frequency‐time analysis for both group and phase speeds) and (4) quality control, including error analysis and selection of the acceptable measurements. The procedures that are described herein have been designed not only to deliver reliable measurements, but to be flexible, applicable to a wide variety of observational settings, as well as being fully automated. For an automated data processing procedure, data quality control measures are particularly important to identify and reject bad measurements and compute quality assurance statistics for the accepted measurements. The principal metric on which to base a judgment of quality is stability, the robustness of the measurement to perturbations in the conditions under which it is obtained. Temporal repeatability, in particular, is a significant indicator of reliability and is elevated to a high position in our assessment, as we equate seasonal repeatability with measurement uncertainty. Proxy curves relating observed signal-to-noise ratios to average measurement uncertainties show promise to provide useful expected measurement error estimates in the absence of the long time-series needed for temporal subsetting.
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"Seismic interferometry by crosscorr..." refers background in this paper
...…(Campillo & Paul 2003; Shapiro & Campillo 2004; Shapiro et al. 2005; Sabra et al. 2005a,b; Larose et al. 2006; Gerstoft et al. 2006; Yao et al. 2006; Bensen et al. 2007, 2008; Yao et al. 2008; Gouédard et al. 2008a,b; Liang & Langston 2008; Ma et al. 2008; Lin et al. 2009; Picozzi et al. 2009)....
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...2006; Bensen et al. 2007, 2008; Yao et al. 2008; Gouédard et al. 2008a,b; Liang & Langston 2008; Ma et al. 2008; Lin et al. 2009; Picozzi et al. 2009). Usually one considers the retrieval of the fundamental mode only. It is well known that in a layered medium, surface waves consist of a fundamental mode and higher-order modes (e.g. Nolet (1975); Gabriels et al. (1987)). Halliday & Curtis (2008) and Kimman & Trampert (2010) carefully analyze interferometry of surface waves with higher-order modes....
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TL;DR: This seismological example shows that diffuse waves produced by distant sources are sufficient to retrieve direct waves between two perfectly located points of observation and has potential applications in other fields.
Abstract: The late seismic coda may contain coherent information about the elastic response of Earth. We computed the correlations of the seismic codas of 101 distant earthquakes recorded at stations that were tens of kilometers apart. By stacking cross-correlation functions of codas, we found a low-frequency coherent part in the diffuse field. The extracted pulses have the polarization characteristics and group velocities expected for Rayleigh and Love waves. The set of cross-correlations has the symmetries of the surface-wave part of the Green tensor. This seismological example shows that diffuse waves produced by distant sources are sufficient to retrieve direct waves between two perfectly located points of observation. Because it relies on general properties of diffuse waves, this result has potential applications in other fields.
1,139 citations
"Seismic interferometry by crosscorr..." refers background in this paper
...…the most widely used applications of direct-wave interferometry is the retrieval of seismic surface waves between seismometers from ambient noise (Campillo & Paul 2003; Shapiro & Campillo 2004; Shapiro et al. 2005; Sabra et al. 2005a,b; Larose et al. 2006; Gerstoft et al. 2006; Yao et al. 2006;…...
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