I am concerned with the precise prediction of time- and history-dependent occurrence rates of an earthquake sequence, particularly, aftershock sequences, in order to test the hypothesis that abrupt stress-change due to a seismic or an aseismic slip triggers a seismicity-rate-change in the surrounding area. In principle, seismic activity should be enhanced in the zones where an increment of Coulomb failure stress (CFS) is positive, and also activity should be reduced (seismic quiescence) in the stress-shadow zones. However, stress changes in a region are very frequently affected by nearby events, which trigger further aftershock clusters. Unfortunately, such local stress transfers are too complex to be computed precisely, due to fractural features.
In order to extract regional stress-changes transferred from a far-field fault, we have to remove the effect of such complex, proximate triggering mechanics occurring within aftershock clusters. As a practical solution, we rely on the statistical empirical laws of aftershock activity. That is to say, the statistical model, such as the Omori-Utsu formula and its extension, the epidemic-type aftershock sequence (ETAS) model, is fitted to the sequence of events from the region, in order to precisely mimic the normal activity there. I am primarily concerned with seismicity-rate-changes (enhancement and reduction) relative to the predicted rate by the model, and explore the relation to the pattern of Coulomb's stress-changes, which occur due to a rupture or a silent slip.
I have shown a number of such examples from the recent seismic activities in Japan. These lead us to a summarized observation that even a small CFS increment of the order of millibars can trigger such seismicity-rate-change, which is also supported by the Dieterich's seismicity-rate-equation. Thus, I expect that the anomalous seismic activity relative to the ETAS rates is sensitive enough to detect and measure slight stress-changes.
For example, the figure shows the epicenters of earthquakes with magnitude 2 and over that occurred during the period from 1997 through October 2004, and pattern of CFS increments for the receiver faults (10km depth) of dominating angles in this region around the source of the 2004 Niigata-Ken Chuetsu earthquake. Regions of red and blue contours show positive and negative CFS increments, respectively. The ETAS model is applied to the sequence of events during 1997-2004 in each of four regions divided by the contours of neutral CFS increment. Each of the four panels shows the cumulative number and magnitude of the earthquakes from each of the four regions against the time. Thered curves show the theoretical or predicted cumulative curve. The actual cumulative number of events deviates upward in the region N and S, but downward in E and W, from the predicted cumulative curve after the change-point. These show that precursory slipmay have taken place on the Chuetsu mainshock fault plane.

Members
Yoshihiko Ogata (ISM)
Yasuaki Murata
Jiancang ZHUANG
Kazuyoshi Nanjo
Takaki Iwata
Masatsugu Wakamura
Ushio Tanaka