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EnglishWe 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.
| Titolo: | Scaling Laws in Geophysics: Application to Potential Fields of Methods Based on the Laws of Self-similarity and Homogeneity | |
| Autori: | ||
| Data di pubblicazione: | 2016 | |
| 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. | |
| Handle: | http://hdl.handle.net/11588/625682 | |
| ISBN: | 978-3-319-24673-4 978-3-319-24675-8 978-3-319-24673-4 978-3-319-24675-8 | |
| Appare nelle tipologie: | 2.1 Contributo in volume (Capitolo o Saggio) |
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