6533b7dcfe1ef96bd1272cc0
RESEARCH PRODUCT
Unique continuation of the normal operator of the x-ray transform and applications in geophysics
Joonas IlmavirtaKeijo Mönkkönensubject
FOS: Physical sciencesx-ray transformSpace (mathematics)01 natural sciencesTheoretical Computer SciencePhysics - GeophysicsContinuationtomografiaClassical Analysis and ODEs (math.CA)FOS: MathematicsNormal operatorUniqueness0101 mathematicsAnisotropyMathematical PhysicsMathematicsX-ray transformgeophysicsApplied Mathematics010102 general mathematicsMathematical analysisgeofysiikkaShear wave splittingInverse problemFunctional Analysis (math.FA)Geophysics (physics.geo-ph)Computer Science ApplicationsMathematics - Functional Analysis010101 applied mathematicsMathematics - Classical Analysis and ODEsSignal Processingdescription
We show that the normal operator of the X-ray transform in $\mathbb{R}^d$, $d\geq 2$, has a unique continuation property in the class of compactly supported distributions. This immediately implies uniqueness for the X-ray tomography problem with partial data and generalizes some earlier results to higher dimensions. Our proof also gives a unique continuation property for certain Riesz potentials in the space of rapidly decreasing distributions. We present applications to local and global seismology. These include linearized travel time tomography with half-local data and global tomography based on shear wave splitting in a weakly anisotropic elastic medium.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-03-27 | Inverse Problems |