A Bayesian approach to the detection of temporal changes in P wave velocity

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Abstract
On the basis of Akaike's Bayesian information criterion (ABIC), a new method is proposed for detecting a temporal change in a seismic velocity in a source region. The method of joint hypocenter determination was modified in order to determine a seismic velocity in a source layer as a function of time together with hypocenters and station corrections. Arrival times of initial waves of shallow earthquakes in a small area are analyzed in this method. The smoothness of the estimated temporal variation in the velocity is guaranteed by the introduction of a prior distribution of the parameter. The hyperparameter of the prior distribution of the velocity, the reading error of arrival times, and the initial velocity in the source layer are chosen to minimize ABIC. This procedure was applied to the 1983 eastern Yamanashi M = 6.0 earthquake in central Japan. We analyzed P arrival times of 374 earthquakes observed at 12 stations in the network of the National Research Center for Disaster Prevention by dividing the whole period (from October 1981 to May 1987) into 12 six‐month subperiods. Calculating ABICs for different combinations of the three parameters above, we searched for the minimum value of ABIC and found two minima. The first one corresponds to a model of a constant velocity in time, and the other corresponds to a model of a variable velocity with 5% velocity change at maximum. However, since ABIC in the former is 10 smaller than that in the latter, the former constant velocity model is statistically more suitable than the latter. Furthermore, generating artificial data with the same reading errors as the actual data, we used computer simulation to examine the lower limit of the velocity change detectable for this data set. In conclusion, the velocity in the source region is 6.24±0.18 km/s, and the velocity change exceeding 6–7% at maximum did not exist during the 6 years before and after the M = 6.0 earthquake.