上限をもつ地震の規模別度数分布について
1989 年 42 巻 1 号 p. 73-80
詳細
1989 年 42 巻 1 号 p. 73-80
Gutenberg-Richters' formula (GR), truncated GR formula (TGR) and modified GR formula (MGR) are known to represent the magnitude vs. frequency relation of earthquake occurrence. We discuss parameter estimations and goodness-of-fits of the three formulae by using actual data and maximum likelihood method.
In the case of using data of round magnitudes, an upperbound magnitude (parameter C) and maximum likelihood of TGR are not directly estimated by using the maximum likelihood method based on probability density function. However, this is indirectly estimated by using the maximum likelihood method based on probability distribution function induced from the density function. With the modified method and the information criterion AIC, goodness-of-fit of TGR can be discussed in comparison with other formulae.
A formula with 4 parameters is derived from an exponential function polynomial. The formula (4PGR) includes new parameter α as a convex index near the upperbound magnitude. The 4PGR corresponds to TGR and MGR in the cases of α→∞ and α→0, respectively, and either TGR or MGR can be regarded as a special case of 4PGR.
Goodness-of-fits of GR, TGR, MGR and 4PGR for earthquake data at 4 regions are compared by using AIC. The Result at each region indicates much better fit of the formulae with the upperbound magnitude than original GR. In these cases such as 200 earthquakes in sample size, the best fit does not seem to be 4PGR but to be TGR or MGR.
