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Microlocal analysis of imaging operators for effective common offset seismic reconstruction

Grathwohl, Christine; Kunstmann, Peer; Rieder, Andreas; Quinto, Eric Todd

Abstract:
The elliptic Radon transform (eRT) integrates functions over ellipses
in 2D and ellipsoids of revolution in 3D. It thus serves as a model for linearized
seismic imaging under the common offset scanning geometry where sources and
receivers are offset by a constant vector. As an inversion formula of eRT is unknown
we propose certain imaging operators (generalized backprojection operators)
which allow to reconstruct some singularities of the searched-for function
from seismic measurements. We calculate and analyze the top order symbols of
these imaging operators as pseudo-differential operators to understand how they
map, emphasize or de-emphasize singularities. We use this information to develop
local reconstruction operators that reconstruct relatively independently of depth
and offset. Numerical examples illustrate the theoretical findings.

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Volltext §
DOI: 10.5445/IR/1000083268
Veröffentlicht am 06.06.2018
Seitenaufrufe: 24
seit 06.06.2018
Downloads: 17
seit 06.06.2018
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
urn:nbn:de:swb:90-832689
KITopen-ID: 1000083268
Verlag KIT, Karlsruhe
Umfang 22 S.
Serie CRC 1173 ; 2018/9
Schlagworte generalized Radon transforms, Fourier integral operators, microlocal analysis, seismic imaging
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