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Direct and inverse problems in elastic multilayers with reflection data. (English) Zbl 1094.74030

Summary: The paper deals with the reflection-transmission process generated by a multilayer with homogeneous, isotropic elastic slabs. The direct problem, namely the determination of reflected and transmitted (and internal) waves in terms of the incident one, is investigated and the solution is proved to exist and be unique. The proof is based on the validity of a first integral. Next, the inverse problem is considered to determine the material parameters of the slabs through the measurement of the (frequency-dependent) reflection coefficient at the boundary of the multilayer. As a result, the material parameters are found in closed form, though for two slabs only.

MSC:

74J20 Wave scattering in solid mechanics
74J25 Inverse problems for waves in solid mechanics
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