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We investigate the mathematical modeling of the 2D acoustic waves propagation, based on the conservation laws. The hyperbolic first-order system of partial differential equations is considered and solved by the method of S. K. Godunov. The inverse problem of reconstructing the density and the speed of sound of the medium is considered. We apply the gradient method to reconstruct the parameters of the medium. The gradient of the functional is obtained. Numerical results are presented. [ABSTRACT FROM AUTHOR]

• Gradient-based approach is a common scheme for solving the inverse problems. • It is crucial to efficiently compute the gradient of the functional. • The proposed algorithm for the gradient calculation is 10 percent faster. • Low memory requirements are important for large grids. Numerical solution of inverse problem for 2D acoustic system of conservation laws by gradient type method requires storage of O (N 3) elements which is crucial on large grids with O (N) points in single dimension. In this article we present an approach to save twice memory on the stage of adjoint problem and gradient calculation and compare it with usual approach in memory and CPU time cost. Numerical comparison for CPU time and memory of one step of iteration process which consists of direct problem solution, adjoint problem solution and calculation of the gradient are presented. [ABSTRACT FROM AUTHOR]