Inversion of higher dimensional Radon transforms of seismic-type

TL;DR

This paper investigates higher-dimensional Radon transforms related to seismic imaging, providing inversion formulas for functions integrated over symmetric hypersurfaces, extending classical Radon transforms.

Contribution

It introduces a new class of Radon transforms involving symmetric hypersurfaces and derives their inversion formulas under specific conditions.

Findings

Derived inversion formulas for the transforms.

Extended classical Radon transforms to higher dimensions.

Applicable to seismic imaging scenarios.

Abstract

We study integral transforms mapping a function on the Euclidean space to the family of its integration on some hypersurfaces, that is, a function of hypersurfaces. The hypersurfaces are given by the graphs of functions with fixed axes of the independent variables, and are imposed some symmetry with respect to the axes. These transforms are higher dimensional version of generalization of the parabolic Radon transform and the hyperbolic Radon transform arising from seismology. We prove the inversion formulas for these transforms under some vanishing and symmetry conditions of functions.