Diagnostic Analysis of Space-Time Branching Processes for Earthquakes
It is natural to use a branching process to describe occurrence patterns of earthquakes, which are apparently clustered in both space and time. The clustering features of earthquakes are important for seismological studies.
Based on some empirical laws in seismicity studies, several point-process models have been proposed in literature, classifying seismicity into two components, background seismicity and clustering seismicity, where each earthquake event, no matter it is a background event or generated by another event, produces (triggers) its own offspring (aftershocks) according to some branching rules. There are further ideas on probability separation of background seismicity from the clustering seismicity assuming a constant background occurrence rate throughout the whole studied region and other authors proposed a stochastic declustering method and made the probability based declustering method practical.
In this paper, we show some useful graphical diagnostic methods for improving model formulation.
Key wordsBranching processes Patterns of earthquakes Point process models Stochastic declustering
Unable to display preview. Download preview PDF.
- A.J. Baddeley, R. Turner, J. Möller and M. Hazelton. Residual analysis for spatial point processes. Technical report, School of Mathematics & Statistics, University of Western Australia, 2004.Google Scholar
- P. Brémaud. Point Processess and Queues. Springer-Verlag, 1980.Google Scholar
- R. Console, M. Murru and A.M. Lombardi. Refining earthquake clustering models. Journal of Geophysical Research, 108(B10):doi:10.1029/2002JB002130, 2003.Google Scholar
- D.J. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes, 2nd edition. Springer, New York, 2003.Google Scholar
- Y.Y. Kagan. Likelihood analysis of earthquake catalogues. Journal of Geophysical Research, 106(B7):135–148, 1991.Google Scholar
- Y.Y. Kagan and L. Knopoff. Statistical study of the occurrence of shallow earthquakes. Geophysical Journal of the Royal Astronomical Society, 1978.Google Scholar
- F. Omori. On after-shocks of earthquakes. Journal of the College of Science, Imperial University of Tokyo, 7:111–200, 1898.Google Scholar
- S.L. Rathbun. Modeling marked spatio-temporal point patterns. Bulletin of the International Statistical Institute, 55(2):379–396, 1993.Google Scholar
- T. Utsu. Aftershock and earthquake statistics (i): Some parameters which characterize an aftershock sequence and their interrelations. Journal of the Faculty of Science, Hokkaido University, 3, Ser. VII (Geophysics):129–195, 1969.Google Scholar
- T. Utsu, Y. Ogata and R.S. Matsu’ura. The centenary of the omori formula for a decay law of aftershock activity. Journal of Physical Earth, 1995:1–33, 1995.Google Scholar
- Y. Yamanaka and K. Shimazaki. Scaling relationship between the number of aftershocks and the size of the main shock. Journal of Physical Earth, 1990:305–324, 1990.Google Scholar
- J. Zhuang, C.-P. Chang, Y. Ogata and Y.-I. Chen. A study on the background and clustering seismicity in the taiwan region by using a point process model. Journal of Geophysical Research, 110(B05S18):doi:10.1029/2004JB003157, 2005.Google Scholar
- J. Zhuang, Y. Ogata and D. Vere-Jones. Analyzing earthquake clustering features by using stochastic reconstruction. Journal of Geophysical Research, 109(No. B5):doi:10.1029/2003JB002879, 2004.Google Scholar