Determination of Wave Speed from point sources
Abstract
We consider the wave equation with variable wave speed in Euclidean space, with point sources modeled by Dirac delta initial displacement data. There are three special subsets of the whole space: (1) the source set where the delta initial conditions are supported, (2) the unknown set where the wave speed is not known a priori, and (3) the receiver set where the waves are measured. The inverse problem is to reconstruct the wave speed uniquely in the unknown set from an unlabeled collection of waves generated by point sources and measured in the receiver set. We use propagation of singularities and sharp finite speed of propagation to reduce this data to geometric travel-time data, whose form depends on how the three sets lie in relation to each other. We give three scenarios where this procedure leads to unique determination of the wave speed.
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BibTeX
@misc{ilmavirta2026determination,
title = {{Determination of Wave Speed from point sources}},
author = {Joonas Ilmavirta and Teemu Saksala and Ashwin Tarikere and Gunther Uhlmann},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.06225},
eprint = {2609.06225},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06225},
}
RIS
TY - UNPB
TI - Determination of Wave Speed from point sources
AU - Joonas Ilmavirta
AU - Teemu Saksala
AU - Ashwin Tarikere
AU - Gunther Uhlmann
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2609.06225
UR - https://arxiv.org/abs/2609.06225
AB - We consider the wave equation with variable wave speed in Euclidean space, with point sources modeled by Dirac delta initial displacement data. There are three special subsets of the whole space: (1) the source set where the delta initial conditions are supported, (2) the unknown set where the wave speed is not known a priori, and (3) the receiver set where the waves are measured. The inverse problem is to reconstruct the wave speed uniquely in the unknown set from an unlabeled collection of waves generated by point sources and measured in the receiver set. We use propagation of singularities and sharp finite speed of propagation to reduce this data to geometric travel-time data, whose form depends on how the three sets lie in relation to each other. We give three scenarios where this procedure leads to unique determination of the wave speed.
ER -