Nonlinear Dynamics, Magnitude-Period Formula and New Research on Earthquake

Abstract

Based on the geodynamics, an earthquake does not take place until the momentum-energy excess a faulting threshold due to the movement of the fluid layer under the rock layer and the transport and accumulation of the momentum. From the nonlinear equations of fluid mechanics, we can derive a simplified nonlinear solution of momentum, which correspond to the accumulation of the energy. Otherwise, a chaos equation could be obtained, in which chaos corresponds to the earthquake, which shows complexity on seismology, and impossibility of exact prediction of earthquakes. But, combining the Carlson-Langer model and the Gutenberg-Richter relation, the magnitude-period formula of the earthquake may be derived approximately, and some results can be calculated quantitatively. For example, we forecast a series of earthquakes, especially in 2019 in California. Combining the Lorenz model, we discuss the earthquake migration to and fro, and apply the qualitative analysis theory. Moreover, many external causes for earthquake are merely the initial conditions of this nonlinear system. Finally, we research some new ways, and propose the topology of earthquake.