Solution path of Newton's method for determining epicenter earthquake hazard in Italy 24 august 2016

This paper is devoted to investigate the behavior of Newton's method for approximating the epicenter of earthquake. Here, the earthquake in center of Italy 24 August 2016 is considered. The seismic data of Pg waves only is used as preparation data. Here, three scenarios which are depend on the minimum, average and maximum velocity of seismic Pg waves for the numerical simulations are elaborated. The results show the trajectories have different directions for each scenarios with initial guess of epicenter is given to be a coordinate of Rome, Italy. For instance, the behavior by using maximum velocity, the solution is observed moves away toward other countries at beginning before it immediately moves back to the epicenter in Norcia. The numbers of final iteration of Newton's method using minimum, average and maximum velocity are obtained 12, 10, and 13 respectively by tolerance number 0.01. Moreover, the final numerical errors for minimum, average and maximum velocity are 0.159848, 0.099954 and 0.45736 respectively.