Reconstruction of the Shape of Obstacles Located in Two-Dimensional Acoustic and Elastic Media from the Characteristics of Scattered Short Longitudinal Waves

The paper presents an algorithmAlgorithm for reconstructing the shape of non-convex solid obstaclesObstacle in two-dimensional acoustic and elastic media, as well as cavity defectsDefect in an elastic material in the ray approximation. We consider simply connected regions of obstaclesObstacle in continuous media with a non-smooth boundary contourBoundary contour of positive curvature, which has a finite number of corner points, the opening angle of which is greater than the right one. Circular irradiation of the object boundary by a longitudinal waveLongitudinal wave is carried out in the echo modeEcho mode. The reconstructionReconstruction algorithmAlgorithm includes two stages. At the first stage, a convex shell of the obstacleObstacle boundary is constructed from the known arrival time of the reflected short-wavelength pulse. At the second stage, the convex parts of the object boundary located inside the convex shell are reconstructed from the known real amplitude of the echo signal. It has been established that the accuracy of the object shape reconstructionReconstruction improves with an increase in the oscillation frequency.