Seismic Imaging with the Elliptic Radon Transform in 3D: Analytical and Numerical Aspects

Grathwohl, Christine

doi:10.5445/ir/1000105093

Cited by 2 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The result of the above proposition differs fundamentally from a similar result in the situation of a constant sound speed v(•) = b where singularities (y, η) of n with η 2 = 0 are not visible in Λn (whatever the choice of ψ and S is), see [10]. The increasing sound speed (3.1), however, allows to recover those singularities, in principle.…”

mentioning

confidence: 72%

Seismic imaging with generalized Radon transforms: stability of the Bolker condition

Kunstmann,

Quinto,

Rieder

2023

Pure and Applied Mathematics Quarterly

View full text Add to dashboard Cite

Generalized Radon transforms are Fourier integral operators which are used, for instance, as imaging models in geophysical exploration. They appear naturally when linearizing about a known background compression wave speed. In this work we first consider a linearly increasing background velocity in two spatial dimensions. We verify the Bolker condition for the zero-offset scanning geometry and provide meaningful arguments for it to hold even if the common offset is positive. Based on this result we suggest an imaging operator for which we calculate the top order symbol in the zero-offset case to study how it maps singularities. Second, to support the usage of background models obtained from linear regression we present a stability result for the Bolker condition under perturbations of the background velocity and of the offset.

show abstract

mentioning

confidence: 72%