Rapid three‐dimensional hypocentral determination using a master station method

A master station (MS) method is presented in this paper to rapidly determine hypocenters in three‐dimensional (3‐D) heterogeneous velocities. An equal differential time (EDT) surface is defined as the collection of all spatial points that satisfy the time difference between two arrivals, which can be two picks at two stations or two different phase picks at one station. The EDT surface is independent of the origin time and will contain the hypocenter. For an event with J arrivals, there are (J‐1) independent EDT surfaces. The MS method determines the hypocenter that satisfies two types of constraints: to be traversed by most EDT surfaces and to yield minimum travel time residual statistics. The statistics include both the residual variance and the amplitude of the origin time error. The combined use of the EDT surfaces and residual statistics allows for a unique determination of the hypocenter and origin time using different types of phase arrivals. In principle, only three arrivals are minimally required to constrain a unique solution if three different stations are used. For a 3‐D velocity model, the EDT surfaces and the residual statistics can be computed efficiently using a reference file created by Moser's (1991) ray tracing method. An illustration of the MS method is given for 27 small events that occurred in southern California, using a P wave velocity model modified from that of Magistrale et al. (1992). The average misfit between the bulletin hypocenters and the new solutions is 3.8 km. If a 3‐D velocity model is accurate, the MS method can be a viable means of hypocenter determination.