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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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Acknowledgements

We would like to acknowledge Michigan State University HPCC for providing the computational resources that contributed to the research results reported here. Qian is partially supported by the NSF (Grant Nos. 2012046, 2152011, and 2309534). Yang is partially supported by the NSF (Grant Nos. DMS-1715178, DMS-2006881, and DMS-2237534), NIH (Grant No. R03-EB033521), and startup fund from Michigan State University.

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Authors and Affiliations

  1. Petroleum Geo-Services, Houston, TX, 77079, USA

    Guanghui Huang

  2. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Jianliang Qian

  3. Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI, 48824, USA

    Jianliang Qian & Yang Yang

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  1. Guanghui Huang
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Correspondence to Jianliang Qian.

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Dedicated to Prof. Stan Osher on the occasion of his 80th birthday.

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Huang, G., Qian, J. & Yang, Y. Piecewise Acoustic Source Imaging with Unknown Speed of Sound Using a Level-Set Method. Commun. Appl. Math. Comput. 6, 1070–1095 (2024). https://doi.org/10.1007/s42967-023-00291-9

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