It has been shown in recent theoretical or numerical studies that nucleation, propagation and termination of earthquake rupture growth are affected by non-planar geometry of fault system, such as bending, branching and stepping. However, most of these studies have assumed a pre-existing fault system and the formation process of the fault system has not been considered. While the formation of fault system is studied in some of recent studies, they have two important limitations: (1) quasi-static deformation is assumed when interacting faults are considered, (2) an isolated fault is assumed when dynamic deformation is treated. We overcome these limitations and investigate a dynamic formation process of a non-planar fault system. We first develop a numerical method, which can treat dynamic interactions between non-planar fault segments, and then simulate a dynamic growth of two interacting faults. We show that resulting fault geometry significantly depends on initial arrangement of the faults and rupture velocity. The two faults coalesce or repel each other according to the initial fault distribution; the two faults are assumed to be of the same size and parallel at an initial state. We find the following important simulation results. The coalescence occurs when two non-coplanar faults are non-overlapped, or partly overlapped, and a strike slip offset, d2, is much smaller than an initial length of the faults. On the contrary, the two faults tend to repel each other when d2 is larger than the initial length of the faults. Our simulation suggests that large earthquakes tend to occur with evolutions of a fault system when the strike slip offset of the fault system is much smaller than the lengths of the segments.
A new probability process model for earthquake forecast is presented based on Bayesian treatment. The prior probability at the beginning of this process is estimated from long-term data from earthquake history and active fault activities in a target area. The posterior probability is deduced from Bayes' theorem in terms of the prior probability and two conditional probabilities: “alarm rate” and “null alarm rate”. The former is defined to be the probability that a precursory anomaly is detected on condition that an earthquake is accompanied, and the latter to be that on condition that no earthquake is accompanied. These probabilities are estimated mainly by statistical tests of previously accumulated observation data. The test consists of trials of detecting anomaly during each assigned detecting period and of registering earthquake events during the corresponding hypothetical forecasting period. Regarding the estimated posterior probability as the prior probability for the next step of the Bayesian process, we will obtain a new posterior probability when data from another anomaly event is input into the process. Successive application of this procedure continues to renew the posterior probability until a dicision is made to issue an earthquake warning. The final posterior probability pN for N independent anomaly observations with alarm rate qi and null alarm rate si for i=1, 2, …N is given by PN=x1x2…xN/x1x2…xN+a1-p0x1x2…xN, where p0 is the first prior probability, a1=(1-p0)/p0, xi=qi/si and the approximation (-) is valid if pN<<1. The well known terms, “secular probability” and “success rate” are interpreted in the above framework to be a prior probability and the induced posterior probability, respectively. The ratio of alarm rate to null alarm rate, i. e., xi in the above formula, for each precursory anomaly observation is a key factor for reliability on earthquake prediction. The probability gain, i. e., the ratio of the posterior probability to the prior probability, is approximated to be the product of the above ratios.
We developed digital maps of the geomorphological land classifications and the site amplification factors in Japan, and applied them to strong motion estimations immediately after earthquakes. For making the maps, we first digitized the geomorphological land classification maps of Japan (1:200, 000 or 1:100, 000 scale) and constructed 500m mesh data. Then, we made up the maps of site amplification factors using the empirical relation by Midorikawa and Matsuoka (1995). We evaluated their accuracies by comparing the estimated strong ground motions with the records of K-Net for recent earthquakes in the Kanto area. We estimated the strong motions using the site amplification factors and the two methods: the attenuation relation (Si and Midorikawa, 1999), and an interpolation method using the records. We found that the second method gave more reliable results than the first method, because the first method strongly depended on accuracies of the source and path effects. However, since we may not be able to obtain quickly strong motion records near highly damaged areas, it would be efficient to evaluate the strong motions using the first method immediately after an earthquake, then to replace them by the second method after getting the records. Finally, we compared the site amplification factors using the following two methods. The first is based on the average of shear wave velocities from the free surface to the 30m depths using boring data. The second is the above-mentioned method based on the land classifications. The comparisons showed that the first method was more accurate and reliable. Therefore, it is necessary to replace the digital maps of the site amplifications by those using the first method, when we obtain boring data.
The method of the inversion analysis to evaluate the distribution of seismic energy radiated from an earthquake fault plane based on seismic intensity distribution data has been developed. The fault plane is divided into small sub-faults. The optimized seismic energy distribution of each sub-fault is calculated using the least square method to minimize the error between evaluated and observed seismic intensities. The energy distribution of a seismic fault is related to seismic intensity using the attenuation formula with equivalent hypocentral distance. The parameters of the attenuation formula are obtained from a regression analysis with measured seismic intensity data of recent moderate earthquakes. The forward analyses using an assumed model are performed to verify the accuracy of the inversion analysis and to evaluate the effect of factors such as the standard deviation of seismic intensity, constraint condition of inversion analysis and configuration of observation stations. Finally, the method is applied to the Showa Tonankai earthquake in 1944 and the Showa Nankai earthquake in 1946 and the result is compared with the tsunami and strong motion waveform inversion results to confirm the efficiency and applicability of the method.
To understand the characteristics of seismic ground motions during the 1995 Hyogo-ken Nanbu earthquake in Higashinada area Kobe city, the effects of the underground structure at the edge of the sedimentary basin on seismic ground motion were investigated using observed moderate and weak earthquake motions. A later phase can be clearly identified after S-wave onset in southern part of this area, which was generated by 2D multiple reflection wave due to the effects of the underground structure. The result of simulations suggest that the distribution of synthetic maximum amplitude ratio referred to rock site depends on input motions. Due to the basin edge effects, the distribution of the maximum amplitude ratio shows a peak at the edge of the sedimentary basin using the sine wave with period of 1s and duration of 0.5s as an input wave. Besides, the ground motion of the 1995 Hyogo-ken Nanbu earthquake observed at Kobe Univ. was used as an input motion, which shows two peaks. One peak was located near the edge of the sedimentary basin and it was generated by the basin edge effects. The other one was generated by the interference between diffracted wave and 2D multiple reflection wave and it was located at the south border area with intensity VII determined by Japan Meteorological Agency. Our results indicate that the effects of 2D multiple reflection wave generated at the edge of sedimentary basin is important for the big earthquake motions.
We estimated S-wave attenuation (QS-1) in a wide frequency range between 4Hz and 60Hz using the twofold spectral ratio [Matsuzawa et al. (1989)] in the western Nagano region, Japan, where the 1984 Naganoken-Seibu earthquake (M6.8) occurred and the seismicity is still active. In the region, there are 49 seismic stations in a range of around 10km in diameter and station separation is several kilometers. In this analysis, 156 shallow (depth <10km) events (0.9≤MW≤2.6) are used. We can effectively reduce the errors of the estimation by using a number of ray paths. We also determined the focal mechanisms of these events and corrected the waveform amplitudes using them. The direct S-wave portions of the seismograms are relatively small in a high frequency range (above 60Hz) at surface stations compared to the lower frequency waves, and contaminated by P-coda waves. Thus, to estimate QS-1 value, we used only the waves whose S/N ratios are greater than 2, where the noise levels are calculated for the time windows just before S-wave arrivals. Obtained QS-1 values show strong frequency dependence below 10Hz, but weak above 10Hz. These values are slightly larger than the ones estimated by Yoshimoto et al. (1998) from the coda-normalization method. This difference is probably owing to the fracture area of the 1984 Naganoken-Seibu earthquake that has strong attenuation.