First, based on the many levels and their cycles in geoscience, we research the hypercycle of geoscience. This is the hypercycle as a tool of self-organization applied to geoscience. It may form from a level to other higher levels. These levels influence each other and the co-evolution. Second, we discuss some possible mathematical methods, which include graph, vector, matrix, some equations, similar theories, etc. This method can be developed and perfected. Third, we propose the nonlinear whole geoscience and its three basic laws. Fourth, we discuss thermodynamics of geoscience, and in which possible entropy decrease under some sates, such as evolution and cycles of Earth, etc. Sustainable development of society must study the mode from high entropy to low entropy. Various cycles in geoscience cannot all be entropy increases, and cannot all be originated from the external interactions.

First, we propose the nonlinear whole seismology and its three basic laws. Next, based on the nonlinear equations of fluid dynamics in Earth’s crust, we obtain a chaos equation, in which chaos corresponds to the earthquake, and shows complexity on seismology. But, combining the Carlson-Langer model and the Gutenberg-Richter relation, a simplified nonlinear solution and corresponding magnitude-period formula of earthquakes may be derived approximately. Further, we research the topological seismology. From these theories some predictions can be calculated quantitatively and are already tested. Combining the Lorenz nonlinear model, we may discuss the earthquake migration to and fro. Finally, if various modern scientific instruments, different scientific theories and some paranormal ways for earthquake are combined each other, the accuracy of multilevel prediction will be increased.