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.

中文翻译：

---

通过有限数目的观测值恢复一阶声学方程的二维双曲系统中的声音系数的密度和速度

我们考虑一阶双曲系统的系数逆问题，该问题描述了二维声波在异质介质中的传播。我们通过使用有限数量的数据测量来恢复介质的密度和声音的速度。我们使用二阶MUSCL-Hancock方案来解决直接和伴随问题，并将优化方案应用于系数反问题。通过使用基于梯度的方法，可以最大程度地减少获得的功能。为了获得更好的精度和稳定性，我们考虑了方法的不同变化，并提出了数值实验的结果。