NUMERICAL SOLUTION OF THE INVERSE COEFFICIENT ACOUSTIC PROBLEM USING LAPLACE TRANSFORM AND DIFFERENTIAL EVOLUTION METHOD

This paper addresses the solution of the inverse coefficient problem for the wave equation aimed at reconstructing the spatial distribution of the speed of sound in an inhomogeneous medium. The Laplace transform is applied to solve the direct problem, eliminating time dependence and reducing the problem to ordinary differential equations in the frequency domain, which significantly decreases computational costs. The inverse problem is formulated as an optimization task: minimizing the residual functional between calculated and measured acoustic pressure values using the stochastic global optimization method, Differential Evolution. Numerical experiments were conducted on a multilayer medium model (sand, soil, rock, water, air) using synthetic data with added random noise. An adaptive combined reconstruction method is proposed to reduce errors at medium boundaries. The results demonstrate high accuracy: the relative error of the sound speed profile reconstruction was approximately from 2.5 to 4.3%, confirming the approach's effectiveness for acoustic diagnostics and tomography applications.

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