Math Geosci (2009) 41: 609–610 DOI 10.1007/s11004-009-9237-1 EDITORIAL
Special Issue on Applications of Wavelets in the Geosciences Margaret A. Oliver
Published online: 9 July 2009 © International Association for Mathematical Geosciences 2009
This special issue of five papers aims to show the range of applications of wavelet analysis to data from the geosciences. Wavelet analysis is a rapidly developing and expanding branch of mathematics. Following the seminal work of Ingrid Daubechies in the late 1980s, the concepts of wavelet analysis have been adopted with enthusiasm. The number of publications has mushroomed as has interest in the subject. I mention this background because geostatistics, with which this Journal has had a long and significant history in publishing papers in this field, was adopted much less readily. Wavelet analysis and geostatistics have developed differently and the driving forces behind their development have been distinct. In spite of these differences, there is common ground between the wavelet and the variogram that Bosch et al. (2004) drew attention to in this Journal. This special issue aims to broaden interest in wavelet analysis among the geosciences community and to respond to a criticism often levelled at wavelet analysis. This is that wavelet analysis is fascinating, but what are the practical applications in the earth sciences? The papers in this issue show a variety of ways in which the methods of wavelet analysis can be applied. The paper by Bosch et al. develops on the earlier paper mentioned above that was based on a one-dimensional wavelet variogram that could filter trend. In this paper they develop a two-dimensional wavelet variogram that also filters trend, and they illustrate this with an example of soil surface roughness. Watkins et al. tackle the difficult problem of anisotropy in groundwater flow by wavelet analysis. They have developed a technique to characterize the principal directions of anisotropy in stationary and non-stationary permeability fields. Milne and Lark’s contribution shows how to derive a discrete Haar wavelet transform for irregularly sampled data. Most wavelet methods require data at regular intervals and this represents an important step M.A. Oliver () Department of Soil Science, The University of Reading, Whiteknights, Reading RG6 6DW, UK e-mail:
[email protected]
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Math Geosci (2009) 41: 609–610
forward. They apply their method to apparent soil electrical conductivity data measured across a landscape. Gloaguen and Dimitrakopoulos propose a two-dimensional conditional simulation based on wavelet decomposition to simulate geological patterns at different spatial scales. They describe how a wavelet transform of geological training images can be decomposed into wavelet coefficients to understand the scale dependencies of geological processes. The information from the training images can then be used in the simulation. The paper by Hruska et al. provides a link with publications in the early history of this Journal concerned with the segmentation of borehole or transect data and the identification of boundaries. These authors describe a wavelet-transform-based method for automated segmentation of resistivity image logs that takes into account the apparent dip in the data and addresses the problem of discriminating lithofacies boundaries from noise and intrafacies variations.
