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Laferrière & Gaonac’h 1999
Laferrière, A. and Gaonac’h, H. (1999). Multifractal properties of visible reflectance fields from basaltic volcanoes. Journal of Geophysical Research 104: doi: 10.1029/1998JB900023. issn: 0148-0227.

We investigate the multifractal characteristics of the visible reflected radiance field of active basaltic volcanoes acquired from satellite (SPOT) and aircraft sensors. using various statistical methods, we first have demonstrated the scaling behavior of volcanic reflectance fields from Mount Etna (Italy) and Mauna Loa (Hawaii). For example, using box counting, we show that areas darker than a given threshold are fractal sets but with dimension depending critically on the threshold. Hence on the one hand, the optimum threshold for defining lava flows from the images is simply the one that gives the same dimension as that for flows measured on geological maps (even if maps and images are at quite different resolutions). On the other hand, the areas of the lava flows will themselves be strong power law functions of the resolution. For more quantitative statistical analysis we studied how statistical moments change with scale over a range of scales from 3 m to more than 40 km. Once again we found that the observed scaling involved a nonlinear exponent function instead of unique fractal dimension; i.e., we find multiscaling rather than monoscaling. This multiscaling is then shown to be well described by a universal multifractal process whose three parameters we estimate. We find quantitative similar multiscaling for the three fields with an index of multifractality (α=1.8), which is near the theoretical maximum (α=2) and which implies that monofractal frameworks (α=0) are too simplistic. We compare and contrast these multifractal parameters with those of related geophysical fields, finding in particular that (unsurprisingly) the radiance field is statistically very close to the gradient of the topography. Finally, we argue that this scaling framework provides a promising avenue for understanding and modeling the heterogeneity, integrating remotely sensed data and other geological data into Geographical Information System (GIS) algorithms, and studying volcanological phenomena existing on Earth and other planets. ¿ 1999 American Geophysical Uni

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Abstract

Keywords
Mathematical Geophysics, Fractals and multifractals, Volcanology, Lava rheology and morphology, Volcanology, Eruption mechanisms, Mathematical Geophysics, Nonlinear dynamics
Journal
Journal of Geophysical Research
http://www.agu.org/journals/jb/
Publisher
American Geophysical Union
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