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Consider the scattering of a time-harmonic acoustic plane wave by a boundedelastic obstacle which is immersed in a homogeneous acoustic medium. This paperconcerns an inverse acoustic-elastic interaction problem, which is to determinethe location and shape of the elastic obstacle by using either the phased orphaseless far-field data. By introducing the Helmholtz decomposition, the modelproblem is reduced to a coupled boundary value problem of the Helmholtzequations. The jump relations are studied for the second derivatives of thesingle-layer potential in order to establish the corresponding boundaryintegral equations. The well-posedness is discussed for the solution of thecoupled boundary integral equations. An efficient and high orderNystr\"{o}m-type discretization method is proposed for the integral system. Anumerical method of nonlinear integral equations is developed for the inverseproblem. For the case of phaseless data, we show that the modulus of thefar-field pattern is invariant under a translation of the obstacle. To breakthe translation invariance, an elastic reference ball technique is introduced.We prove that the inverse problem with phaseless far-field pattern has a uniquesolution under certain conditions. In addition, a numerical method of thereference ball technique based nonlinear integral equations is also proposedfor the phaseless inverse problem. Numerical experiments are provided todemonstrate the effectiveness and robustness of the proposed methods.

An inverse acoustic-elastic interaction problem with phased or phaseless far-field data