Diversity of threshold phenomena in geophysical media

The sample analysis of threshold phenomena in the lithosphere, atmosphere, and magnetosphere is conducted. The phenomena due to the flow of electric current and pore fluid in the rocks are considered, the scenario of wind-driven generation of atmospheric electricity is suggested, and the model of the geomagnetic storm time Dst variation is analyzed. An important general conclusion consists in the fact that in the geophysical media there is a wide class of threshold phenomena that are affine with phase transitions of the second kind. These phenomena are also related to the critical transitions in self-oscillatory systems with soft self-excitation. The integral representation of bifurcation diagrams for threshold phenomena is suggested. This provides a simple way to take into account the influence of the fluctuations on the transition of a system through the threshold. Fluctuations remove singularity at the threshold point and, generally, lead to a certain shifting of the threshold. The question concerning the hard transition through the threshold and several aspects of modeling the blow-up instability which is presumed to occasionally develop in the geophysical media are discussed.