Fractal density and local singularity analysis method for modeling extreme geological events

The systematic study of extreme geological events (e.g., plate collision and subduction, earthquakes, volcanoes, and mineralization) that occurred during the evolution of the earth is essential not only for understanding the "abrupt changes in the evolution of the earth", but also for an in-depth understanding of the co-evolution of material-life-environment of the livable earth. However, due to the temporal and spatial anomalies and complexity of extreme geological events, classical mathematical models cannot be effectively applied to quantitively describe such events. Comparative studies of many types of geological events indicate that such extreme geological events often depict "singular" characteristics (abnormal accumulation of matter or massive release of energy in a small space or time interval). On this basis, the author proposes a unified definition of extreme geological events, a new concept of "fractal density" and a "local singularity analysis” method for quantitative description and modeling of extreme geological events. Applications of these methods to several types of extreme geological events have demonstrated that the singularity theory and methods developed in the current research can be used as general approaches for the characterization, simulation, and prediction of geological events. The case studies to be introduced include anomalous heat flow over the mid-ocean ridges, and major flare up magmatism and marine sediment flux fluctuations over the past 3 Ga history of earth continental crust evolution.