Global solution of a linearized inverse problem for the wave equation

Nolan, Clifford J.; Symes, William W.

doi:10.1080/03605309708821289

Cited by 69 publications

(102 citation statements)

References 8 publications

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“…for which each data bin creates an independent image. This category includes many variants of common shot, common offset and common scattering angle migration (Nolan and Symes, 1996;Nolan and Symes, 1997;Xu et al, 2001;Brandsberg-Dahl et al, 2003;Stolk, 2002;Stolk and Symes, 2004). …”

Section: Introductionmentioning

confidence: 99%

Kinematics of shot-geophone migration

2009

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In contrast to prestack migration methods based on data binning, common image gathers produced by shot-geophone migration exhibit the appropriate semblance property in either offset domain (focussing at zero offset) or angle domain (focussing at zero slope), when the migration velocity is kinematically correct and when events to be migrated arrive in the data along non-turning rays. The latter condition is required for successful implementation via wavefield depth extrapolation ("survey sinking"). Thus shot-geophone migration may be a particularly appropriate tool for migration velocity analysis of data exhibiting structural complexity.

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Section: Introductionmentioning

confidence: 99%

Kinematics of shot-geophone migration

2009

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“…In particular, analysis of wavefront sets can determine whether backprojection will provide an image free of certain artifacts. 16,21,34 In addition, wavefront-set analysis suggests an approach for producing artifact-free, superresolved images: remove all components of the data set except those that correspond to well-understood target features, and form an image from those components only.…”

Section: Discussionmentioning

confidence: 99%

“…Restricting our attention to the singular structure-specifically, to a certain set in phase space called the wavefront set-allows us to use the tools of microlocal analysis. [8][9][10][11] This strategy was first applied to imaging problems by Beylkin 12 ; its uses in seismic prospecting, [13][14][15][16] X-ray tomography, 17,18 sonar, 19 and synthetic-aperture radar 20,21 are active areas of research. An approach similar to the one we pursue here, in which we use microlocal analysis not to do imaging but instead to study the connection between features of the target and the data, was considered for the X-ray tomography problem by Quinto.…”

Section: Introductionmentioning

confidence: 99%

<title>Microlocal high-range-resolution ISAR for low signal-to-noise environments</title>

Cheney

Borden

2003

SPIE Proceedings

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We consider the problem of identification of airborne objects from high-range-resolution radar data. We use high-frequency asymptotics to show that certain features of the object correspond to identifiable features of the radar data. We study the cases of single scattering and scattering from re-entrant structures such as ducts.This work suggests a method for target identification that circumvents the need to create an intermediate radar image from which the object's characteristics are to be extracted. As such, this scheme may be applicable to efficient machine-based radar identification programs.

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“…In the acoustic case, allowing for multipathing (caustics), see Rakesh [82] and Hansen [56]. For the acoustic problem with (non)maximal acquisition geometry, see Nolan and Symes [80]. For the elastic case with maximal acquisition geometry, see De Hoop and Brandsberg-Dahl [33] and Stolk and De Hoop [91].…”

Section: High-frequency Born Modeling and Imagingmentioning

confidence: 99%

“…Stolk [89] simplified the analysis considering a case when the Bolker condition is violated. Nolan and Symes [80] discussed the imaging and inversion of seismic data with different (restricted) acquisition geometries. The mathematical treatment of systems of equations, such as the elastic equations, in the high-frequency approximation has been given by Taylor [98].…”

Section: Synopsis Of Publicationsmentioning

confidence: 99%

Microlocal analysis of seismic inverse scattering in anisotropic elastic media

Stolk¹,

Hoop²

2001

Comm Pure Appl Math

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Abstract. We review applications of microlocal analysis (MA) to reflection seismology. In this inverse method one attempts to estimate the index of refraction of waves in the earth from seismic data measured at the Earth's surface. Seismic imaging creates images of the Earth's upper crust using seismic waves generated by artificial sources and recorded into extensive arrays of sensors (geophones or hydrophones). The technology is based on a complex, and rapidly evolving, mathematical theory that employs advanced solutions to a wave equation as tools to solve approximately the general seismic inverse problem, with complications introduced by the heterogeneity and anisotropy of the Earth's crust. We describe several important developments using MA to generate these wave-solutions by manipulating the wavefields directly on their phase space. We also consider some recent applications of MA to global seismology.

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Global solution of a linearized inverse problem for the wave equation

Cited by 69 publications

References 8 publications

Kinematics of shot-geophone migration

Kinematics of shot-geophone migration

<title>Microlocal high-range-resolution ISAR for low signal-to-noise environments</title>

Microlocal analysis of seismic inverse scattering in anisotropic elastic media

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