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

Guanghui Huang; Jianliang Qian; Yang Yang

doi:10.1007/s42967-023-00291-9

Communications on Applied Mathematics and Computation ›› 2023, Vol. 6 ›› Issue (2) : 1070 -1095. DOI: 10.1007/s42967-023-00291-9

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

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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.

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Guanghui Huang, Jianliang Qian, Yang Yang. Piecewise Acoustic Source Imaging with Unknown Speed of Sound Using a Level-Set Method. Communications on Applied Mathematics and Computation, 2023, 6(2): 1070-1095 DOI:10.1007/s42967-023-00291-9