Modeling of ground motion data to assess the seismic features for monitoring the seismic activity

Earthquakes are the disastrous seismic activity on earth that imposes substantial risks to human lives as well as infrastructure and environment. While earthquakes cannot be precisely predicted in terms of specific timing and location, the basic seismic features can be analyzed by using probabilistic models that help to develop building codes and risk-reduction strategies. Earthquake is a multivariate phenomenon comprising both positively and negatively correlated variables; hence its characteristics can be better explained by developing a joint distribution. In this paper a new bivariate exponential power (BEP) distribution is developed for modeling the positively correlated variables and the bivariate affine linear exponential (BALE) distribution is used for modeling the negatively correlated variables. Some important statistical properties of the BEP distribution are derived to determine the behavior of the model. The model parameters are estimated by employing the method of maximum likelihood estimation. A simulation study is also conducted to check stability of the model parameters using their average values, standard errors, biases, and confidence intervals. The BEP and BALE distributions are employed to examine the ground motion dataset of Italy that ultimately lead to earthquake preparedness, mitigation, and response efforts. In addition, the performance of the under study models is compared with some extant bivariate models on the basis of Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Finally, the joint probabilities of the proposed model are computed that provide insights into the dynamics of the ground motion across different ranges to monitor the seismic activity.