Piecewise Acoustic Source Imaging with Unknown Speed of Sound Using a Level-Set Method

doi:10.1007/s42967-023-00291-9

Abstract

Abstract: We investigate the following inverse problem: starting from the acoustic wave equation, reconstruct a piecewise constant passive acoustic source from a single boundary temporal measurement without knowing the speed of sound. When the amplitudes of the source are known a priori, we prove a unique determination result of the shape and propose a level set algorithm to reconstruct the singularities. When the singularities of the source are known a priori, we show unique determination of the source amplitudes and propose a least-squares fitting algorithm to recover the source amplitudes. The analysis bridges the low-frequency source inversion problem and the inverse problem of gravimetry. The proposed algorithms are validated and quantitatively evaluated with numerical experiments in 2D and 3D.

Key words: Inverse gravimetry, Acoustic source imaging, Inversion of sound speed, Level-set method, Inverse problem

Guanghui Huang, Jianliang Qian, Yang Yang. Piecewise Acoustic Source Imaging with Unknown Speed of Sound Using a Level-Set Method[J]. Communications on Applied Mathematics and Computation, 2024, 6(2): 1070-1095.

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