The Random Distribution of the Loading and Unloading Response Ratio Under the Assumptions of Poisson Models

This paper discussed the random distribution of the loading and unloading response ratio(LURR) of different definitions(Y_1～Y_5)using the assumptions that the earthquakes occurfollowing the Poisson process and their magnitudes obey the Gutenberg-Richter law.Theresults show that Y_1～Y_5 are quite stable or concentrated when the expected number of eventsin the calculation time window is relatively large(>40);but when this occurrence ratebecomes very small,Y_2～Y_5 become quite variable or unstable.That is to say,a high value ofthe LURR can be produced not only from seismicity before a large earthquake,but also from arandom sequence of earthquakes that obeys a Poisson process when the expected number ofevents in the window is too small.To check the influence of randomness in the catalogue tothe LURR,the random distribution of the LURR under Poisson models has been calculated bysimulation.90%,95% and 99% confidence ranges of Y_1 and Y_3 are given in this paper,which is helpful to quantify the random influe

The Random Distribution of the Loading and Unloading Response Ratio Under the Assumptions of Poisson Models

This paper discussed the random distribution of the loading and unloading response ratio (LURR) of different definitions( Y1-Y5) using the assumptions that the earthquakes occur following the Poisson process and their magnitudes obey the Gutenberg-Richter law. The results show that Y1-Y5 are quite stable or concentrated when the expected number of events in the calculation time window is relatively large ( > 40); but when this occurrence rate becomes very small, Y2- Y5 become quite variable or unstable.That is to say, a high value of the LURR can be produced not only from seismicity before a large earthquake, but also from a random sequence of earthquakes that obeys a Poisson process when the expected number of events in the window is too small. To check the influence of randomness in the catalogue to the LURR, the random distribution of the LURR under Poisson models has been calculated by simulation. 90%,95% and 99% confidence ranges of Y1 and Y3 are given in this paper, which is helpful to quantify the random influence and to determine LURR precursory anomalies.