Fractal Metrology: A toolbox for qualitative and quantitative research in Earth Science

Abstract

If you can not measure it you can not manage it (Cox, 2002).If you can not measure it with known precision and exactness you can not make unbiased conclusions. A diversified quatifying Fractal Geometry´s toolbox (Mandelbrot, 2002) enables the Earth Science with precise measures of scale invariance, universality, non linearity, complexity, criticality etc. However, the absence of the reference techniques for measurement of complex system basic attributes, as well as the lack of standards and quality assurance for analysis of sometimes extensive data surveys, makes difficult (why not impossible!) any comparison between conclusions derived, either from empirical observations or theoretical analyses.We use the basic principles of Metrology concerned with measurement, uncertainty and bias analysis (International Vocabularity of Basic and general terms in Metrology, 2004) in order to design the basic concepts of Fractal Metrology, devoted to the standard measurement of basic attributes of rough nonlinear sets and processes.