Recovering Obstacles from their Travelling Times

TL;DR

This paper extends a method for reconstructing convex obstacles from travel times, originally for planar cases, to obstacles on Riemannian surfaces with certain curvature conditions, assuming geodesics intersect at most two obstacles.

Contribution

It generalizes obstacle recovery from Euclidean planes to Riemannian surfaces under specific curvature and intersection constraints.

Findings

Extended obstacle recovery method to Riemannian surfaces.

Established conditions for geodesic intersections.

Provided theoretical framework for obstacle reconstruction.

Abstract

Noakes and Stoyanov (2021) introduced a method of recovering strictly convex planar obstacles from their set of travelling times. We provide an extension of this construction for obstacles on Riemannian surfaces under some general curvature conditions. It is required that no smooth geodesic intersect more than two obstacles.