Maximum-likelihood estimation of hypocenter with origin time eliminated using nonlinear inversion technique

Physics

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Scientific paper

A new algorithm is applied to inverting arrival time data for hypocenter location. The algorithm incorporates both observed and prior data from a Bayesian point of view. We define marginal probability density function (pdf) to eliminate the origin time from the location problem; the posterior pdf of hypocenter parameters is integrated over the whole range of the origin time. The best estimate of the hypocenter is defined as a set of spatial coordinates which maximizes the marginal pdf. Assuming Gaussian errors in both observed and prior data, we obtain a simple algorithm. Estimation errors of parameters are evaluated by an asymptotic covariance matrix, with which an asymptotic posterior pdf is computed.
The algorithm is applied to observed data and is tested. An example of analysis is given for aftershocks of the 1969 Gifuken-chubu earthquake (M = 6.6) reported by the Japan Meteorological Agency (JMA). The spatial distribution of the aftershocks is supposed to be Gaussian with standard deviation of 15 km. A center of the aftershock distribution, which gives the prior estimates of hypocenters, is also estimated from observed data.
Results of the nonlinear inversion of arrival time data are examined in terms of the asymptotic posterior pdf. We found that relocated hypocenters of the aftershocks are concentrated in a narrow region of 2-3 km in width, while the hypocenters previously reported by JMA have a wide distribution of 5-7 km.

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