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

Dmitriy Klyuchinskiy, Nikita Novikov and Maxim Shishlenin
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Dmitriy Klyuchinskiy: Department of Mathematics and Mechanics, Novosibirsk State University, 630090 Novosibirsk, Russia
Nikita Novikov: Department of Mathematics and Mechanics, Novosibirsk State University, 630090 Novosibirsk, Russia
Maxim Shishlenin: Department of Mathematics and Mechanics, Novosibirsk State University, 630090 Novosibirsk, Russia

Mathematics, 2021, vol. 9, issue 2, 1-13

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.

Keywords: acoustics; tomography; first-order hyperbolic system; inverse problem; Godunov method; gradient descent method; density reconstruction; speed of sound reconstruction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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