Standard methods for monitoring and analysing thermal volcanic fields have difficulty taking into account the large dynamical range of temperatures and radiative fluxes which occur over enormous ranges of spatial scale. They typically are either qualitative or if quantitative, only in the identification of a small number of 'anomalies' mapped at coarse resolutions. We argue that remote sensing of such fields invariably involves averages over small 'hot spots', and that the results depend sensitively and systematically on the space-time resolutions of the sensors. In order to overcome these difficulties and to provide resolution and hence observer-independent characterizations, we use various statistical scaling analysis techniques. We demonstrate their advantages on images of various volcanic features in the thermal infrared spectral region (8-12 µm) acquired above the active part of Kilauea volcano in December 1995 using a helicopter-borne infrared (IR) camera. We first demonstrate the scaling of the thermal remotely sensed radiances using energy spectra and show they are of the power law form E( k) ∝ k−, where k is a spatial wavenumber in the image, and is a scale-invariant spectral exponent. Over the range of over 104 in scale (from 4 cm to 775 m) and for a variety of volcanic structures, we find ≈2.0±0.1. Moreover, the thermal fields show multiscaling behaviour characterized by universal multifractal parameters; we find the degree of multifractality α≈1.7±0.2, the codimension of the singularity contributing to the mean C1≈0.14±0.04 (characterizing the sparseness of the mean gradients) and finally the conservation parameter H≈0.65±0.05, which largely determines the roughness (scale by scale) of the radiance field. These three universal multifractal parameters characterize the resolution dependence of both low- and high-radiance regions over the entire range of spatial scales studied. We compare and contrast these parameters with those (found in other studies) of the topography and volcanic albedo.
We also propose a new way to enhance the thermal volcanic anomalies of daytime images through filtering. This is done by shifting the H values (power law filtering) to those of the observed night-time images and produces 'simulated' nocturnal images with essentially the same (scale by scale) statistics; it is a kind of scale-invariant contrast enhancement. Finally, we show how knowledge of the scaling statistics can be used to determine the statistical expectation of large-scale thermal fluxes conditioned on the corresponding large-scale temperatures.
The multifractal properties demonstrate the necessity of explicitly taking into account the (essentially subjective) sensor resolution when interpreting and modelling active volcanic thermal fields. It underlines the need to properly characterize the non-classical geostatistics of the radiance field before interpreting the latter in terms of temperatures and anomalies.
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Document Type: Research Article
Centre GEOTOP, Université du Québec à Montréal, C.P. 8888, succursale Centre-Ville, Montréal, Québec, H3C 3P8, Canada; e-mail: gaonac'[email protected]
Physics Department, McGill University, Montreal, QC, H3A 2T8, Canada
Laboratoire de modélisation en mécanique, Université Pierre et Marie Curie, Paris cedex 05, 75252 France
Publication date: 2003-06-01
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