Preface

Theoretical studies on earthquakes as well as practical applications are really important in order to define the assessment of seismic hazard and risk in a particular area. This is probably the most important contribution of seismology to society. Recent earthquakes have shown the inadequacy of a massive portion of the buildings erected in and around the epicentral areas, therefore research on earthquakes became more and more important. Up to date the scientific community agrees that the earthquake prediction is not possible. In fact, scientists cannot predict the exact location, magnitude and time of an earthquake striking a particular area. Scientists still do not know many of the details of the physical processes involved in earthquakes and they remain unpredictable. However, several scientists are working on earthquake precursors and forecasting studies and this represent a big challenge.

Chapters in this book will be devoted to various aspects of earthquake research and analysis, from theoretical advances to practical applications. The first two chapters are dedicated to statistical studies. About ten chapters in section II focus on studies about earthquake precursors and forecasting. Some chapters propose new methods for early detection, as well as the earthquake observation through the use of social sensors. The last section presents nice contributions that aim to link earthquakes and disaster triggered in the area struck by a large. The last chapter presents a study on simulating collective behavior during natural disasters.

I would like to express my special thanks to Mr. Igor Babic, Ms Ivana Lorkovic, and Ms Ivana Zec. Last but not least, I would like to thank the whole staff of InTech - Open Access Publisher, especially Mr Igor Babic, for their professional assistance and technical support during all the process steps that have led to the realization of this book.

> **Sebastiano D'Amico**  Research Officer III Physics Department University of Malta Malta

**Part 1** 

**Statistical Seismology** 

**Part 1** 

**Statistical Seismology** 

**1. Introduction**

Earthquakes are great complex phenomenon characterized by several empirical statistical laws (1). One of the most important statistical law is the Gutenberg - Richter law (2), where

Tomohiro Hasumi1, Chien-chih Chen2, Takuma Akimoto3 and Yoji Aizawa4

**The Weibull – Log-Weibull Transition of** 

**Interoccurrence Time of Earthquakes** 

*2Department of Earth Sciences and Graduate Institute of Geophysics,* 

*3Department of Mechanical Engineering, Keio University, Yokohama* 

*4Department of Applied Physics, Advanced School of Science and Engineering,* 

*1Division of Environment, Natural Resources and Energy, Mizuho Information and Research Institute, Inc., Tokyo* 

*National Central University, Jhongli, Taoyuan* 

*Waseda University, Tokyo* 

*1,3,4Japan 2Taiwan* 

where *a* and *b* are constants. *b* is so-called *b*-value and is similar to unity. Another important statistical law is a power law decay of the occurrence of aftershocks, called Omori law (3). The time intervals between successive earthquakes can be classified into two types: interoccurrence times and recurrence times (4). Interoccurrence times are the interval times between earthquakes on all faults in a region, and recurrence times are the time intervals between earthquakes in a single fault or fault segment. For seismology, recurrence times mean the interval times of characteristic earthquakes that occur quasi-periodically in a single fault. Recently, a unified scaling law of interoccurrence times was found using the Southern California earthquake catalogue (5) and worldwide earthquake catalogues (6). In Corral's

paper (6), the probability distribution of interoccurrence time, *P*(*τ*), can be written as

where *R* is the seismicity rate. He has found that *f*(*Rτ*) follows the generalized gamma distribution. In equation (3), *C* is a normalized constant and is *C* = 0.50 ± 0.05. *γ*, *δ*, and *B* are parameters estimated to be *γ* = 0.67 ± 0.05, *δ* = 0.98 ± 0.05, and *B* = 1.58 ± 0.15. It should

*<sup>f</sup>*(*Rτ*) = *<sup>C</sup>* <sup>1</sup>

log *n*(> *m*) = *a* − *bm*, (1)

**1**

*P*(*τ*) = *R f*(*Rτ*), (2)

(*Rτ*)1−*<sup>γ</sup>* exp(−(*Rτ*)*δ*/*B*), (3)

the cumulative number of *n*(> *m*) of magnitude *m* satisfy the following relation:
