Dyadic Elastic Scattering by Point Sources: Direct and Inverse Problems
This chapter is concerned with the scattering of elastic point sources by a bounded obstacle, as well as with a related near-field inverse problem for small scatterers. We consider the Dirichlet problem, where the displacement field is vanishing on the surface of the scatterer. A dyadic formulation for the aforementioned scattering problem is considered in order to gain the symmetry–compactness of the dyadic analysis [TAI94].
For acoustic and electromagnetic scattering, results on incident waves generated by a point source appear in [DK00], [AMS02]; see also references therein. In all these studies, scattering relations by point sources are established; related simple inversion algorithms for small scatterers can be found in [AMS01]. For elasticity, related problems such as the location and identification of a small three-dimensional elastic inclusion, using arrays of elastic source transmitters and receivers, are considered in [AK04], [ACI08].
KeywordsElastic Scattering Boundary Integral Equation Boundary Integral Equation Method Small Scatterer Navier Equation
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