Abstract
Some techniques used in statistics, such as the variable change method, the penalty function method and the gradient projection method, are introduced to determine the location of a hypocenter with a definitely non-negative depth. Numerical simulations are carried out to compare the efficiency of them by using synthetic arrival time data for a four-station seismic array. They demonstrate that the penalty function method with a proper weight is the most efficient. However, if we take an improper weight, it may lead to a negative depth or an invalid solution. Since the variable change method and the gradient projection method do not have such arbitrariness, those can be implemented more easily into hypocenter determination processes operated routinely. The demonstration with real arrival time data shows that the variable change method as z=h2 has practical efficiency.
