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This study explores the methods of wave tomography in application to the problem of reconstructing the wave velocity inside flat objects. Numerical simulations were carried out for model problems that represent 2D inverse problems of nondestructive tomographic imaging of welded joints in metal samples. Numerical simulations were performed on the “Lomonosov–2” supercomputer at Lomonosov Moscow State University. Two tomographic diagnostic methods employing transducer arrays are proposed for imaging flat objects that are accessible only from a single side. In this case, the waves reflected from the flat bottom of the inspected object can be taken into account. The thickness of the flat object is assumed to be known. The use of reflections from the bottom is fundamental, since it significantly increases the number of sounding angles. The results of solving inverse problems on two model experimental setups are compared. Using the developed tomographic methods, a 2D sound speed image of a simulated test object was reconstructed with acoustic and geometric parameters corresponding to a real experiment. Most of the computational complexity in inverse problems of wave tomography is associated with simulating the wave propagation process. In this study we estimate the acceleration of wave propagation computations achieved on a multi-core Intel-compatible SIMD processor using AVX instructions.