Lateral variations of the modal (a/b) values for the different regions of the world

Abstract

Several catalogues of global earthquakes reported for the time period from 1900 to 2000 have been compiled to examine lateral variations of the modal (a/b) values as derived from the Gutenberg–Richter empirical law. For this purpose, the world was divided into 27 different seismic regions in terms of tectonic environments. The parameters a and b were calculated using the least-squares method. The modal values computed for each region were used to produce a global map of the modal values using a grid space of 3°. The results show that a and b-values do not always supply much information about tectonic environments of the different regions. It is observed that the modal values estimated for different tectonic regions are consistent with seismicity of the world and represent global seismic sources better than a or b values. The highest modal values have been found in the oceanic subduction zones, and the lowest values in the oceanic ridges. Lowest b values are observed in trenches. These observations suggest that there is a correlation between apparent stresses and b values. Mapping of the modal values provides detailed images of the zones presenting low and high seismic activity and it may be used as a measure of seismic potential sources and relative hazard levels.

Introduction

Studying the seismic activity of the world has been done extensively, several researchers calculated different parameters of seismicity by using various methods. The empirical relationship between magnitude and frequency of earthquake occurrences is well known as the Gutenberg–Richter (G–R) relationships. Since Gutenberg and Richter (1944) estimated the parameters a and b, the evaluation of the parameters have been frequently used in statistical calculation of seismicity. The parameter a depends on the seismicity rate which varies greatly from region to region (Olsson, 1999). The parameter b is related to properties of focal material and represents tectonic characteristics of a region (Allen, Amand, Richter, and Nordquist, 1965, Hatzidimitriou, Papadimitrou, Mountrakis, and Papazachos, 1985, Wang, 1988). Details in the sense of these parameters may be found in Yılmaztürk et al. (1999). Gutenberg and Richter (1954) suggested that the b parameter changes between 0.45 and 1.5, while Miyamura (1962) found that b-values, ranging from 0.4 to 1.8 for different tectonic areas, are larger in the oceanic crust than in the Circum-Pacific and the Alpine orogenic zones. Tsapanos (1990) observed that b-values are between 0.75 and 0.85 for 11 different seismic regions of the world. Several empirical scaling functions based on the parameters of a and b have been proposed for different regions and different time intervals (Kaila, Rao, and Narain, 1974, Kaila, and Rao, 1975, Bath, 1981, Bender, 1983, Smith, 1986, Christova, 1992, Tsapanos, and Papazachos, 1998, Al-Amri, Punsalan, and Uy, 1998, Yılmaztürk, et al., 1999).

Recently, Yılmaztürk et al. (1999) and Bayrak et al. (2000) showed that distribution of the modal (a/b) values provide detailed images of the local areas presented by high and low seismic zones in and around Turkey. The main purpose of this study is to calculate the ratio of the parameters a and b from the G–R relations for the different regions of the world and to find relation between the tectonic structures and these values. For this purpose, the world has been divided into different 27 seismic regions and evaluated the parameters of a and b in the G–R relations for each region.