A Robust Maximum‐Likelihood Earthquake Location Method for Early Warning

This study proposes a robust method that estimates a reliable earthquake location from only a small number of P ‐wave arrival times. The method is based on the maximum‐likelihood estimation from differential P ‐wave arrivals. We formulate the problem using a probability density function (PDF) of the residual between observed and predicted differential P ‐wave travel times between two seismic stations and construct the likelihood function from the sum of the products of the independent PDFs. The hypocenter is determined by an iterative grid‐search algorithm that finds the point with the largest probability on successively finer grids. To reduce the effect from outliers possibly concealed within a small number of observations, the Student’s t ‐distribution is used for the PDF of the location likelihood. The jackknife resampling technique is also used to discriminate outliers from the observations. The robustness of the method is tested using the Monte Carlo experiments that locate 10,000 events from small numbers of P ‐wave arrivals observed within an epicentral distance of 100 km, including both arrival‐time error and velocity‐model error. The earthquakes are located within an epicentral distance of 8.5±10.8  km and 20.6±33.1  km for events inside the seismic network and outside the network, respectively, using only five P ‐wave arrivals, including a large arrival‐time error between ±1 and 5 s. This shows that this method can estimate the location of the event reliably with only a few P ‐wave arrivals, even when contaminated by an outlier. Therefore, it is believed that this location method could significantly improve the robustness of an earthquake early warning system.