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arXiv · 2606.28527

Classification of singularities of planar slowness surfaces

Antonio Cocan·Maarten V. de Hoop·Joonas Ilmavirta·Pieti Kirkkopelto·Antti Kykkänen
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Abstract

Slowness surfaces are algebraic varieties arising from propagation of elastic waves. In dimensions $2$, we completely classify the types of singularities slowness surfaces can have. The two types of possible singularities are a transversal self-intersection and a tangential singularity produced by a concentric circle and ellipse that are tangent to each other. To interpret these results analytically, in the case that the slowness surface has transversal self-intersections, we show that the principal symbol of the elastic wave operator is locally smoothly diagonalizable.

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Antonio Cocan, Maarten V. de Hoop, Joonas Ilmavirta, Pieti Kirkkopelto, Antti Kykkänen. 2026-06-26. Classification of singularities of planar slowness surfaces. https://arxiv.org/abs/2606.28527

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