Statistical Properties of the Inter-occurrence Times in the Two-dimensional Stick-slip Model of Earthquakes

We study earthquake interval time statistics, paying special attention to inter-occurrence times in the two-dimensional (2D) stick-slip (block-slider) model. Inter-occurrence times are the time interval between successive earthquakes on all faults in a region. We select stiffness and friction parameters as tunable parameters because these physical quantities are considered as essential factors in describing fault dynamics. It is found that inter-occurrence time statistics depend on the parameters. Varying stiffness and friction parameters systematically, we optimize these parameters so as to reproduce the inter-occurrence time statistics in natural seismicity. For an optimal case, earthquakes produced by the model obey the Gutenberg-Richter law, which states that the magnitude-frequency distribution exhibits the power law with an exponent approximately unity.Comment: 8 pages, 5 figures, contribution to the conference proceeding of 21COE International Symposium, Tokyo, Japan Sept 13-14 200

The Weibull - log Weibull Transition of the Inter-occurrence time statistics in the two-dimensional Burridge-Knopoff Earthquake model

In analyzing synthetic earthquake catalogs created by a two-dimensional Burridge-Knopoff model, we have found that a probability distribution of the interoccurrence times, the time intervals between successive events, can be described clearly by the superposition of the Weibull distribution and the log-Weibull distribution. In addition, the interoccurrence time statistics depend on frictional properties and stiffness of a fault and exhibit the Weibull - log Weibull transition, which states that the distribution function changes from the log-Weibull regime to the Weibull regime when the threshold of magnitude is increased. We reinforce a new insight into this model; the model can be recognized as a mechanical model providing a framework of the Weibull - log Weibull transition.Comment: 11 pages, 7 figure

Seismic Statistics : Universality and Interim Report on the 3. 11 Earthquake (2011) in Fukushima-Miyagi Area

We mainly study three empirical laws in earthquake statistics; the Omori formula in the aftershock frequency, the Gutenberg-Richter formula for the magnitude, and the interoccurrence time distribution, and we show a possibility to refine and to unify them by carrying out with the data analysis for natural earthquakes in Japan, Taiwan, and South California. Especially in the analysis of the 3.11 EQ (2011) in Fukushima-Miyagi area, firstly it is emphasized that the Omori formula is generalized to express the magnitude-dependent form, and that the Omori coefficient reveals the same behavior as the Gutenberg-Richter(GR)law in the nonstationary regime after the big shock. Next, the multi-fractal diagram, that connects the GR law and the Weibull distribution for interoccurrence times, is studied to characterize the shock sequences before and after the main shock. A universal relation is well confirmed in the long stationary regime before the main shock, but in the nonstationary regime such as the foreshock region and the aftershock region, the multi-fractal diagram reveals big deviations from the stationary case. In spite of those deviations, it is shown that the empirical laws are approximately confirmed even in the nonstationary regime. Lastly,the moving ensembles are used to describe the temporal change of the multi-fractal diagram. We could not find out any signals to suggest the occurrence of the big shock in statistical parameters, but the multi-fractal diagram obeys the time-dependent universal relation in the nonstationary regime. These results imply that the universality is also existing even in the nonequilibrium moving ensemble. In relation to these remarkable points, we will discuss some theoretical conjectures to seismic statistics, which enable us to understand the origin of statistical laws of earthquakes beyond the traditional ergodic-theoretical interpretation

Seismic Statistics : Universality and Interim Report on the 3. 11 Earthquake (2011) in Fukushima-Miyagi Area

We mainly study three empirical laws in earthquake statistics; the Omori formula in the aftershock frequency, the Gutenberg-Richter formula for the magnitude, and the interoccurrence time distribution, and we show a possibility to refine and to unify them by carrying out with the data analysis for natural earthquakes in Japan, Taiwan, and South California. Especially in the analysis of the 3.11 EQ (2011) in Fukushima-Miyagi area, firstly it is emphasized that the Omori formula is generalized to express the magnitude-dependent form, and that the Omori coefficient reveals the same behavior as the Gutenberg-Richter(GR)law in the nonstationary regime after the big shock. Next, the multi-fractal diagram, that connects the GR law and the Weibull distribution for interoccurrence times, is studied to characterize the shock sequences before and after the main shock. A universal relation is well confirmed in the long stationary regime before the main shock, but in the nonstationary regime such as the foreshock region and the aftershock region, the multi-fractal diagram reveals big deviations from the stationary case. In spite of those deviations, it is shown that the empirical laws are approximately confirmed even in the nonstationary regime. Lastly,the moving ensembles are used to describe the temporal change of the multi-fractal diagram. We could not find out any signals to suggest the occurrence of the big shock in statistical parameters, but the multi-fractal diagram obeys the time-dependent universal relation in the nonstationary regime. These results imply that the universality is also existing even in the nonequilibrium moving ensemble. In relation to these remarkable points, we will discuss some theoretical conjectures to seismic statistics, which enable us to understand the origin of statistical laws of earthquakes beyond the traditional ergodic-theoretical interpretation

Causes of the Multidecadal-Scale Warming of the Intermediate Water in the Okhotsk Sea and Western Subarctic North Pacific

Causes of the multidecadal-scale warming of the intermediate water in the Okhotsk Sea and the western subarctic North Pacific during 1980–2008 are investigated using an ice–ocean coupled model with interannually　varying atmospheric forcing. A hindcast experiment qualitatively reproduces the warming and decadal　fluctuations of the intermediate water that are similar to those of observations: the warming is significant along the western part of the Okhotsk Sea and subarctic frontal region. The effects of the thermohaline- and　wind-driven ocean circulation on the warming are evaluated from perturbation experiments on thermohaline (turbulent heat and freshwater fluxes) and wind causes, respectively. The thermohaline causes are shown to contribute positively to warming in the Okhotsk Sea Intermediate Water (OSIW). The heat budget analysis for the OSIW indicates that the warming is related to a decrease in cold and dense shelf water (DSW) flux, which is caused by a decrease in sea ice and surface water freshening. In contrast, the wind cause has a cooling effect in the OSIW through an increase in DSW. In the subarctic frontal region, the warming is mainly caused by the wind stress change. The heat budget analysis indicates that the warming is related to an increase in the northward advection of the subtropical warm water. These results imply that both thermohaline- and winddriven ocean circulation changes are essential components of the warming in the intermediate water. The atmospheric conditions responsible for the warming are related to a weakened Aleutian low and Siberian high in early and late winter