Frequency-Magnitude Distribution of Earthquakes

Abstract

Frequency magnitude distribution of all types of earthquakes has received considerable attention in the last few decades. Their linear logarithmic relationship remains the most accepted. The a and b constants of this equation, their values and variations have been studied in detail. It is largely agreed that for the seismicity of the whole Earth, its hemispheres, quadrants and large epicentral regions are a=10.0 and b=1.0. The b-variations have long been investigated and reported to occur in different forms and values. Long-and short-term b-variations occur in a continuous cyclic manner and may exceed ± (0.6-0.7) of its absolute value. These are observed to occur not only yearly or monthly but also daily. The b-value always attains maxima and minima before and after the occurrence of all large earthquakes. Many days before the occurrence of large earthquakes, b-values start increasing at variable gradients that are affected by foreshocks. It attains a maximum value shortly before each large earthquake and a minimum on its occurrence. Many factors have been proposed to explain the b-variations including prevailing stress, crustal heterogeneity, focal depth, pore pressure, geothermal gradient, tectonic setting, and other factors. Considering the b-variations of the whole Earth, its hemispheres and quadrants and considering that most proposed factors are directly or indirectly related to the stress, it is concluded that this remains the major factor. It is found that for large earthquakes with Mw ≥ 7, an increase of about 0.20 in the b-value implies a stress increase that will result in an earthquake with a magnitude one unit higher.