Huang Guanghui, Qian Jianliang, Yang Yang
Petroleum Geo-Services, Houston, TX 77079.
Departments of Mathematics and Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI 48824, USA.
Commun Appl Math Comput. 2024 Jun;6(2):1070-1095. doi: 10.1007/s42967-023-00291-9. Epub 2023 Aug 29.
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.
从声波方程出发，在不知道声速的情况下，通过单个边界时间测量来重构分段常数无源声源。当声源的幅度先验已知时，我们证明了形状的唯一确定结果，并提出了一种水平集算法来重构奇点。当声源的奇点先验已知时，我们展示了声源幅度的唯一确定，并提出了一种最小二乘拟合算法来恢复声源幅度。该分析架起了低频源反演问题与重力测量反问题之间的桥梁。所提出的算法通过二维和三维数值实验进行了验证和定量评估。
