Journal of Modern Education Review, ISSN 2155-7993, USA February 2017, Volume 7, No. 2, pp. 154–160 Doi: 10.15341/jmer(2155-7993)/02.07.2017/010 © Academic Star Publishing Company, 2017 http://www.academicstar.us
Frequency Analysis of Aftershock Using Possion Distribution: A Case
Study of Aftershock in Nabire, Papua in 2014 in Every 6-Hour Interval
Yansen Alberth Reba1, Felix Reba2 (1. Indonesia Endowment Fund for Education (LPDP) and Universitas, Negeri Yogyakarta, Indonesia; 2. FMIPA Department Mathematics, Cendrawasih University, Indonesia)
Abstract: There have been many researchers using Poisson Distribution to analyze the parameters of earthquake magnitudes data. The results of parameter estimation of the magnitudes are then illustrated in some curves to be analyzed. In this article, there will be a discussion in analyzing the data of earthquake frequency using Poisson Distribution by estimating the parameters using Maximum Likelihood Estimation (MLE) method. Then, the parameters are used to determine the magnitudes and the energy of the earthquake. The case study in this research used the data of aftershock frequency in Nabire District in Papua in 2004 for every 6-hour interval. After conducting the compliance test using Chi Square test, it obtained that the data followed the pattern of Poisson Distribution. It is clearly seen that the period of 03.00 a.m.–09.00 a.m. has the biggest frequency of earthquake compared with other hours in which the parameter λ = 42.97, mean = 42.97, magnitude (M) = 6.03 richter scale, energy (E) = 75.55. For the description: this earthquake was felt by the people driving a car, and the buildings with bad constructions would be collapsed as well as for their chimneys. Thus, this research is expected to be able to reduce the number of victims as well as to minimize the loss caused by the earthquake. Key words: possion distribution, MLE, Newton Raphson, Chi Square Test, magnitude, energy, Marcelli Intensity
1. Introduction
Earthquake is a shock or shaking on the earth’s surface caused by a sudden release of endogenous energy that creates seismic waves. Indonesia is one of the vulnerable countries to earthquakes. It is because Indonesia is located in a meeting point of three tectonic plates. This condition makes the regions of Indonesia as the active tectonic regions with high seismicity including Papua and West Papua regions. This condition results in many earthquakes occurred in those regions. For example, in 2004, a 7.2 richter scale earthquake hit Nabire, Papua. It resulted in paralysis/isolation in the city due to the disconnected electrical and phone lines even damage in the Nabire airport. It needs special attention both from the government and related institutions, so that there will be a probability of occurrence in the future. By understanding the characteristics and history of disasters in the past, including the last occurrence and the
Yansen Alberth Reba, S.Pd.K, Indonesia Endowment Fund for Education (LPDP) and Universitas Negeri Yogyakarta; research areas/interests: science. E-mail: [email protected]. Felix Reba, S.Si, M.Sc., FMIPA Department Mathematics, Cendrawasih University; research areas/interests: science. E-mail: [email protected].
154 Frequency Analysis of Aftershock Using Possion Distribution: A Case Study of Aftershock in Nabire, Papua in 2014 in Every 6-Hour Interval estimation of repeating period of occurence can minimize the loss. If the occurrences of big earthquakes in the past in a certain region are studied carefully, the data can be used to estimate or predict the similar occurrences in the future. Thus, it can also be used for mitigation of earthquake in the future.
2. Basic Theory
2.1 Poisson Distribution (Walpole, 1995) A -discrete random variable is said to have a Poisson distribution with a parameter 0 having a pdf-discrete in the form of: