Abstract
This paper presents a numerical method for reconstructing the spatial distribution of sound speed in inhomogeneous media based on the inverse analysis of acoustic wave propagation. The mathematical model relies on the second-order wave equation with variable coefficients. The inverse problem is formulated as an optimization task to minimize the residual functional between simulated and observed pressure data at the domain boundaries. To efficiently calculate the gradient of the functional, an adjoint (auxiliary) problem method is employed, derived via variational calculus. The numerical implementation is performed using an explicit finite-difference scheme. Computational experiments on a one-dimensional model of a heterogeneous medium (soil-metal-soil) demonstrate that the proposed algorithm allows for reliable reconstruction of the velocity profile, particularly in zones of sharp contrast. The study analyzes the sensitivity of the solution and the convergence rate, showing that 500 iterations provide an optimal balance between accuracy and computational cost.