Spectral element technique for efficient parameter identification of layered media. I. Forward calculation

This contribution deals with the use of spectral analysis as a means of analysing the dynamic behaviour of the axially symmetric multi-layered systems as a result of a transient force. The objective of this research work is to develop an accurate and computationally ecient forward tool suitable for solving inverse problems. The spectral element technique is utilized. Details of the mathematical derivation, implementation and veri®cation of newly developed axisymmetric and half-space spectral elements are presented. It is shown that the suitability of the spectral element method to such a problem encompasses in its ability to model a whole layer without the need for subdivisions. As a consequence, the size of the modelled structure becomes as large as the number of the layers involved. This reduces the computational requirements substantially and hence enables ecient utilization of the method in iterative algorithms for solving inverse problems