## Abstract

We consider the coefficient inverse problem for the first-order hyperbolic system, which describes the propagation of the 2D acoustic waves in a heterogeneous medium. We recover both the denstity of the medium and the speed of sound by using a finite number of data measurements. We use the second-order MUSCL-Hancock scheme to solve the direct and adjoint problems, and apply optimization scheme to the coefficient inverse problem. The obtained functional is minimized by using the gradient-based approach. We consider different variations of the method in order to obtain the better accuracy and stability of the appoach and present the results of numerical experiments.

Original language | English |
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Article number | 199 |

Pages (from-to) | 1-13 |

Number of pages | 13 |

Journal | Mathematics |

Volume | 9 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2 Jan 2021 |

## Keywords

- Acoustics
- Density reconstruction
- First-order hyperbolic system
- Godunov method
- Gradient descent method
- Inverse problem
- Speed of sound reconstruction
- Tomography

## OECD FOS+WOS

- 1.01 MATHEMATICS