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Scaling Laws in Geophysics: Application to Potential Fields of Methods Based on the Laws of Self-similarity and Homogeneity
- Source :
- Fractal Solutions for Understanding Complex Systems in Earth Sciences ISBN: 9783319246734
- Publication Year :
- 2015
- Publisher :
- Springer International Publishing, 2015.
-
Abstract
- We analyse two classes of methods widely diffused in the geophysical community, especially for studying potential fields and their related source distri- butions. The first is that of the homogeneous fractals random models and the second is that of the homogeneous source distributions called “one-point” distributions. As a matter of fact both are depending on scaling laws, which are used worldwide in many scientific and economic disciplines. However, we point out that their appli- cation to potential fields is limited by the simplicity itself of the inherent assumptions on such source distributions. Multifractals are the models, which have been used in a much more general way to account for complex random source distributions of density or susceptibility. As regards the other class, a similar generalization is proposed here, as a multi-homogeneous model, having a variable homogeneity degree versus the position. While monofractals or homogeneous functions are scaling functions, that is they do not have a specific scale of interest, multi-fractal and multi-homogeneous models are necessarily described within a multiscale dataset and specific techniques are needed to manage the information contained on the whole multiscale dataset.
Details
- ISBN :
- 978-3-319-24673-4
- ISBNs :
- 9783319246734
- Database :
- OpenAIRE
- Journal :
- Fractal Solutions for Understanding Complex Systems in Earth Sciences ISBN: 9783319246734
- Accession number :
- edsair.doi.dedup.....a8967599bc7c86e14db0ecfb12490a4c