Wavelets in the Geosciences

This book contains state-of-the-art continuous wavelet analysis of one and more dimensional (geophysical) signals. Special attention is given to the reconaissance of specific properties of a signal. It also contains an extension of standard wavelet approximation to the application of so-called second generation wavelets for efficient representation of signals at various scales even on the sphere and more complex geometries. Furthermore, the book discusses the application of harmonic (spherical) wavelets in potential field analysis with emphasis on the gravity field of the Earth. Many examples are given for practical application of these tools; to support the text exercises and demonstrations are available on the Web.

to continuous wavelet analysis.- Building your own wavelets at home.- II: Second generation wavelets.- Factoring wavelet transforms into lifting steps.- Spherical wavelets: Efficiently representing functions on a sphere.- Least-squares geopotential approximation by windowed fourier transform and wavelet transform.