An omnidirectional seismic image extension. (English) Zbl 1507.35344
Summary: This paper introduces an operator, which extends the Born operator for the linearized variable density acoustic wave equation. Inspired by angle dependent scattering, I will define it as acting on distributions depending on space and angle coordinates. I will show that it can be written as a weighted integral of space-shift extended operators associated to arbitrary directions after a suitable coordinate transform. I will also formulate conditions under which its normal operator is a pseudo-differential operator. These will be seen to be less restrictive than the ones imposed on horizontal space-shift extended operators in the sense that they allow diving wave paths.
MSC:
| 35R30 | Inverse problems for PDEs |
| 35L10 | Second-order hyperbolic equations |
| 35S30 | Fourier integral operators applied to PDEs |
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