The dependence of topographically forced flows in a quasigeostrophic 2-layer model on the form of dissipation is investigated. In particular, the following 2 cases are examined. (1) The dissipation is proportional to the potential vorticity, and (2) the dissipation is proportional to the Laplacian of the streamfunction, i.e., Ekman dampings on the upper and lower boundaries. In the case (1), the bifurcation diagram is qualitatively the same as Pedlosky (1981)'s in which the dissipation is a sum of Ekman dampings on the upper and lower boundaries and an interfacial friction between the upper and lower layers. That is, there exist 2 steady solution bifurcation points, between which 2 stable solutions and 1 unstable one coexist for the same parameter values of the basic zonal flow. On the other hand, in the case (2), a wave-wave interaction occurs. As a result, although the steady solution diagram is not altered qualitatively, Hopf bifurcation points may emerge on the stable steady solution curve, and the steady solutions between them may lose their stability. So far as the considerations in this note are concerned, the stability of steady solutions is dependent on the form of dissipation although the steady solution diagram itself is not altered qualitatively.
Earthquake occurrence is not uniform in either space or time. It seems that earthquakes have relations with each other. In cases where the difference is small in both spatial location and occurrence time between two given earthquakes, they are defined to have ’relation’. We try to calculate the degree of relationship using the Fuzzy theory. Identification of pre-shocks and aftershocks is given automatically from the relationships. We will be able to obtain important information about previous earthquake activities by using the relationships.
We investigate static stress fields caused by rectangular reverse faults in an elastic half-space. Numerical computations are mainly made on fracture stresses which are defined as the summation of shear stress and a certain amount of normal stress and contribute to generating fracture. We present some examples of seismic activities which seem to have occurred in accordance with the simulation, i.e., cases where earthquakes occurred in regions where the fracture stresses are theoretically expected to increase. The fracture stresses generally increase in regions adjacent to the side ends of the fault. There are a lot of cases where earthquakes were generated in adjacent regions in connection with the occurrence of big thrust type earthquakes which are typical along the Kurile trench and the Nankai trough. These are, for example, the 1944 Tonankai earthquake followed by the 1946 Nankaido earthquake which occurred at the Nankai trough, and the 1958 and 1963 Etorofu earthquakes, the 1969 Hokkaido-toho-oki earthquake and the 1973 Nemuro-hanto-oki earthquake which occurred successively along the Kurile arc. The fracture stresses increase greatly in regions extending from the fault edges to the slip directions, and in dilatational regions extending normal to the fault surface. The case where the fracture extended in its slip direction may be the 1978 Miyagi-oki earthquake which is explained to be multiple shocks caused by successive fractures on descending low-angle planes. The cases where the conjugate activities were excited may be the 1982 Urakawa-oki earthquake and the 1991 Iriomotejima swarm earthquakes. However, there remain some questions as regards these cases. There are cases where normal faults were generated near the trench after the occurrence of reverse faults. These are the 1933 Sanriku earthquake which occurred after the 1896 Sanriku and 1897 Miyagi-oki earthquake, and the series of the 1938 Shioya-oki earthquakes. Numerical computation reveals that it is possible that normal faults are induced by the occurrence of reverse faults in their dilatational regions. This is mainly caused by the reduction of the frictional stress on the fault surfaces.