A finite element reconstruction algorithm for frequency domain acoustic data based on the Helmholtz equation is presented. A dual meshing scheme is described that overcomes the large wave number problem involved in model-based ultrasound tomography. An adjoint sensitivity method is adopted for efficient inverse computation. The algorithm is implemented with the second-order absorbing boundary conditions and with a multi-transmitting and multi-receiving strategy. Simultaneous reconstruction of both acoustic speed and attenuation for a realistic reinforced concrete medium is achieved for multiple frequency data. The algorithm is evaluated using simulated data under various practical scenarios including different noise levels, varied number of receivers, different contrast levels between the heterogeneity and background region, and different transmission receiving modes. Results obtained suggest that the algorithm is insensitive to noise and that qualitative images can be produced that readily highlight the location and size of acoustic heterogeneities with a rectangular background region of 1616mmx500mm. Furthermore, the reconstructions are quantitatively accurate in terms of the location, size and acoustic property values of the target and background over a range of contrast levels.
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