Rapid three‐dimensional hypocentral determination using a master station method

Abstract

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.

Rapid estimation of rupture extent for large earthquakes: Application to the 2004, M9 Sumatra‐Andaman mega‐thrust

“…To build the pdf NLL uses a likelihood function based on the equal differential-time formulation (EDT) of Font et al [2004], a generalization of the master-station method [Zhou, 1994] and the ''method of hyperbolas'' cited by Milne [1886]. NLL with EDT is highly robust in the presence of outliers in the data [Lomax, 2005].…”

The Gutenberg Algorithm: Evolutionary Bayesian Magnitude Estimates for Earthquake Early Warning with a Filter Bank

“…Furthermore, at this stage, enough P-phase arrival times are available to make rough estimations of the epicenter using an equal differential time norm location scheme (Zhou, 1994;Satriano et al, 2008). If we include the additional Figure 6.…”

“…However, if other independent constraints on either of the two parameters are available, they can be combined with the estimates in much the same way that we combine estimates from multiple stations (equation 5). There are numerous candidate constraints that could be used in this sense: parameter estimates from other EEW algorithms that run in parallel, distance estimates from a real-time location algorithm (e.g., based on the concept of not-yet-arrived data; Zhou, 1994;Cua and Heaton, 2007;Satriano et al, 2008), S-P onset times t S−P , the waveform-based distance estimation method of Odaka et al (2003), or distance priors from seismicity observations (e.g., Kagan and Knopoff, 1981;Meier et al, 2014) and from proximity to mapped faults. Because distance and magnitude uncertainties are inherently coupled, any constraint that reduces the distance uncertainty will also reduce magnitude uncertainties.…”

Reliability of the automatic procedures for locating earthquakes in southwestern Alps and northern Apennines (Italy)

“…The first function is the standard approach of the least squares, L2 norm (LS-L2). The second function is based on the equal differential time (EDT) formulation of Font et al (2004) which is a generalization of the master station method (Zhou 1994). These approaches are extensions of the "method of hyperbolas" cited by Milne (1986).…”