Keywords: 3D seismic tomography, tetrahedral elements, ray trace algorithms, statistical identification, isoparametric mapping, irregular shapes, structural engineering, earthquakes, concrete structures, energy dissipation, geotomography, finite element analysis, FEA, hexahedral elements
Three–dimensional seismic tomography with tetrahedra element on isoparametric mapping
The author has developed a method of three–dimensional seismic tomography on concrete structures. This method is based on ray–trace and identification technique, and the distribution of slowness or energy dissipation is identified based on simultaneously iterative reconstruction technique (SIRT) or the other kind of statistical identification technique. This kind of technique was originally developed for investigation of underground that is called geotomography, however, this technique was difficult to apply to concrete structures because the structures generally have irregular shape. A hexahedral element was implemented by the author to overcome this difficulty based on the idea of isoparametric mapping of hexahedral element on finite element analysis, however, it is still difficult to apply the method to the structures that have highly irregular shape. In this respect, an implementation of tetrahedral element is proposed for the three–dimensional seismic tomography on concrete structures to solve the difficulty in this paper. This implementation is based on the idea of isoparametric mapping as well as the case of hexahedral element and it enables to apply the method to structures of complex shape that is insufficient to represent by hexahedral elements. The validity of the proposed method is checked by some numerical example.