Journal of Applied Mathematics
Volume 2003 (2003), Issue 12, Pages 605-645

Multiscale deformation analysis by Cauchy-Navier wavelets

M. K. Abeyratne, W. Freeden, and C. Mayer

Geomathematics Group, Department of Mathematics, University of Kaiserslautern, P.O. Box 3049, Kaiserslautern 67653, Germany

Received 6 June 2003; Revised 20 August 2003

Copyright © 2003 M. K. Abeyratne et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A geoscientifically relevant wavelet approach is established for the classical (inner) displacement problem corresponding to a regular surface (such as sphere, ellipsoid, and actual earth surface). Basic tools are the limit and jump relations of (linear) elastostatics. Scaling functions and wavelets are formulated within the framework of the vectorial Cauchy-Navier equation. Based on appropriate numerical integration rules, a pyramid scheme is developed providing fast wavelet transform (FWT). Finally, multiscale deformation analysis is investigated numerically for the case of a spherical boundary.