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Identification of obstacles using only the scattered P-waves or the scattered S-waves

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  • In this work, we are concerned with the inverse scattering by obstacles for the linearized, homogeneous and isotropic elastic model. We study the uniqueness issue of detecting smooth obstacles from the knowledge of elastic far field patterns. We prove that the 'pressure' parts of the far field patterns over all directions of measurements corresponding to all 'pressure' (or all 'shear') incident plane waves are enough to guarantee uniqueness. We also establish that the shear parts of the far field patterns corresponding to all the 'shear' (or all 'pressure') incident waves are also enough. This shows that any of the two different types of waves is enough to detect obstacles at a fixed frequency. The proof is reconstructive and it can be used to set up an algorithm to detect the obstacle from the mentioned data.
    Mathematics Subject Classification: Primary: 35R30, 35J40, 74B05.

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