Marchenko redatuming, imaging, and multiple elimination and their mutual relations
TL;DR: The different approaches to Marchenko redatuming, imaging and multiple elimination are discussed, using a common mathematical framework.
Abstract: With the Marchenko method, it is possible to retrieve Green’s functions between virtual sources in the subsurface and receivers at the surface from reflection data at the surface and focusi...
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01 Jan 2021
TL;DR: ADVI automatic differential variational inference c a subset of variables (clique) C a set of cliques, i.e., c C det determinant dobs observed data vector ELBO evidence lower bound EM Expectation-Maximization F(q;Θ) evidence lower Bound of probability distribution.
Abstract: In a variety of scientific applications, we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has nonunique solutions so uncertainty must be quantified in order to define the family of all possible solutions. Bayesian inference provides a powerful theoretical framework which defines the set of solutions to inverse problems, and variational inference is a method to solve Bayesian inference problems using optimization while still producing fully probabilistic solutions. This chapter provides an introduction to variational inference, and reviews its applications to a range of geophysical problems, including petrophysical inversion, travel time tomography, and full-waveform inversion. We demonstrate that variational inference is an efficient and scalable method which can be deployed in many practical scenarios.
14 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
TL;DR: In this article, a novel approach named surrogate-reformulation-assisted multitasking knowledge transfer (SRAMT) was proposed for production optimization, where multiple surrogate models, which can imitate the landscape of the initial production optimization problem, are constructed with diverse samples as reformulations of the target problem.
7 citations
TL;DR: Wang et al. as mentioned in this paper proposed logging data representation enhancement approach for lithology identification based on feature decomposition, selection and transformation, converting the raw logging curves into an improved high dimensional representation with more effective information and less noise.
7 citations
References
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Book•
01 Jan 1980
1,373 citations
"Marchenko redatuming, imaging, and ..." refers background in this paper
...It is a 3D generalization of the ‘fundamental solution’ in 1D scattering problems (Lamb, 1980)....
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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
"Marchenko redatuming, imaging, and ..." refers background in this paper
...Unlike in seismic interferometry (Campillo and Paul, 2003; Wapenaar, 2003; Schuster et al., 2004; Bakulin and Calvert, 2006; Gouédard et al., 2008), no physical receiver is needed at the position of the virtual source....
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TL;DR: In this paper, a method for the elimination of all surface-related multiples by means of a process that removes the influence of the surface reflectivity from the data is proposed.
Abstract: The major amount of multiple energy in seismic data is related to the large reflectivity of the surface. A method is proposed for the elimination of all surface-related multiples by means of a process that removes the influence of the surface reflectivity from the data. An important property of the proposed multiple elimination process is that no knowledge of the subsurface is required. On the other hand, the source signature and the surface reflectivity do need to be provided. As a consequence, the proposed process has been implemented adaptively, meaning that multiple elimination is designed as an inversion process where the source and surface reflectivity properties are estimated and where the multiple-free data equals the inversion residue. Results on simulated data and field data show that the proposed multiple elimination process should be considered as one of the key inversion steps in stepwise seismic inversion.
740 citations
"Marchenko redatuming, imaging, and ..." refers background in this paper
...Hence, the reflection response R in equations 4 and 5 contains no surface-related multiples, which complies with the situation after surface-related multiple elimination (Verschuur et al., 1992; van Groenestijn and Verschuur, 2010)....
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Book•
01 Jan 1980
TL;DR: In this article, a user-oriented discussion on Seismic Migration Technique is presented, where the authors discuss the influence of errors in the input data and the effect of field patterns on the migration result.
Abstract: Introduction. 1. Basic Concepts. 2. Principles of Seismic Inversion. 3. User-Oriented Discussion on Seismic Migration Technique. 4. Choice of the Proper Migration Technique. 5. Influence of Velocity Errors. 6. Influence of Errors in the Input Data. 7. Effect of Field Patterns on the Migration Result. 8. Interpretive Migration. Appendices. Subject Index.
519 citations
"Marchenko redatuming, imaging, and ..." refers background or methods in this paper
...Note the similarity with the classical redatuming scheme (Berkhout, 1982; Berryhill, 1984; Berkhout and Wapenaar, 1993), which in the compact operator notation reads Rtar ≈ f+t1,dRf+1,d. (29) Recall that f+1,d is the direct contribution of focusing operator f+1 , see Figures 1a and 1b....
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...Traditionally this is done with one-way wave field extrapolation operators (or ‘focusing operators’) which account for primaries only (Berkhout, 1982; Berryhill, 1984)....
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...When the reflectivity is angle-dependent, r(xA) should actually be replaced by a kernel r(x′A,xA, t), and extra integrals along SA and time should be included in equation 89 (Berkhout, 1982; de Bruin et al., 1990)....
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TL;DR: In this paper, a multidimensional multiple-attenuation method is presented that does not require any subsurface information for either surface or internal multiples. But it does not consider the relationship between forward and inverse scattering.
Abstract: We present a multidimensional multiple‐attenuation method that does not require any subsurface information for either surface or internal multiples. To derive these algorithms, we start with a scattering theory description of seismic data. We then introduce and develop several new theoretical concepts concerning the fundamental nature of and the relationship between forward and inverse scattering. These include (1) the idea that the inversion process can be viewed as a series of steps, each with a specific task; (2) the realization that the inverse‐scattering series provides an opportunity for separating out subseries with specific and useful tasks; (3) the recognition that these task‐specific subseries can have different (and more favorable) data requirements, convergence, and stability conditions than does the original complete inverse series; and, most importantly, (4) the development of the first method for physically interpreting the contribution that individual terms (and pieces of terms) in the inv...
497 citations