Recovering density and speed of sound coefficients in the 2d hyperbolic system of acoustic equations of the first order by a finite number of observations

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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 languageEnglish
Article number199
Pages (from-to)1-13
Number of pages13
JournalMathematics
Volume9
Issue number2
DOIs
Publication statusPublished - 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

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