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 analyzing 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 efficient forward tool suitable for solving inverse problems. The spectral element technique is utilized. Details of the mathematical derivation, implementation and verification of newly developed axi-symmetric 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 efficient utilization of the method in iterative algorithms for solving inverse problems.