| Since the concept of singularity and local singularity analysis method (LSA) were originally
proposed by the author for characterizing the nonlinear property of hydrothermal
mineralization processes, the local singularity analysis technique has been successfully
applied for identification of geochemical and geophysical anomalies related to various
types of mineral deposits. It has also been shown that the singularity is the generic
property of singular geo-processes which result in anomalous amounts of energy
release or material accumulation within a narrow spatial–temporal interval. In the
current paper we introduce several new developments about singularity analysis. First
is a new concept of “fractal density” which describes the singularity of complex
phenomena of fractal nature. While the ordinary density possesses a unit of ratio
of mass and volume (e.g. g/cm3, kg/m3) or ratio of energy over volume or time
(e.g. J/cm3, w/L3, w/s), the fractal density has a unit of ratio of mass over fractal
set or energy over fractal set (e.g. g/cmα, kg/mα, J/ mα, w/Lα, where α can be a
non-integer). For the matter with fractal density (a non-integer α), the ordinary
density of the phenomena (mass or energy) no longer exists and depicts singularity.
We demonstrate that most of extreme geo-processes occurred in the earth crust
originated from cascade earth dynamics (mental convection, plate tectonics, orogeny
and weathering etc) may cause fractal density of mass accumulation or energy
release. The examples to be used to demonstrate the concepts of fractal density and
singularity are earthquakes, floods, volcanos, hurricanes, heat flow over oceanic
ridge, hydrothermal mineralization in orogenic belt, and anomalies in regolith over
mine caused by ore and toxic elements vertical migration. Other developments of
singularity theory and methodologies including singular Kriging and singularity
weights of evidence model for information integration will also be introduced. |