## Abstract

We investigate the mathematical model of the 2D acoustic waves propagation in a heterogeneous domain. The hyperbolic first order system of partial differential equations is considered and solved by the Godunov method of the first order of approximation. This is a direct problem with appropriate initial and boundary conditions. We solve the coefficient inverse problem (IP) of recovering density. IP is reduced to an optimization problem, which is solved by the gradient descent method. The quality of the IP solution highly depends on the quantity of IP data and positions of receivers. We introduce a new approach for computing a gradient in the descent method in order to use as much IP data as possible on each iteration of descent.

Original language | English |
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Article number | 73 |

Number of pages | 14 |

Journal | Computation |

Volume | 8 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Sep 2020 |

## Keywords

- Acoustics
- First-order hyperbolic system
- Godunov method
- Gradient descent method
- Inverse problem
- Tomography
- first-order hyperbolic system
- inverse problem
- HYPERBOLIC SYSTEMS
- RECONSTRUCTION
- ALGORITHM
- SPATIAL DISTRIBUTIONS
- NUMERICAL-SOLUTION
- REGULARITY
- tomography
- TRAVEL-TIME TOMOGRAPHY
- acoustics
- ABSORPTION
- gradient descent method
- SOUND-VELOCITY
- ULTRASOUND TOMOGRAPHY