AN APPLICATION OF BAYESIAN (ABIC) SMOOTHING METHODS TO ESTIMATING SPACE AND TIME VARIATIONS IN THE MAGNITUDE DISTRIBUTIONS OF EARTHQUAKES

MASAJIRO IMOTO

National Research Institute for Earth Science and Disaster Prevention, 3-1 Tennodai, Tsukuba-shi, Ibaraki 305, Japan

(Received April 26, 1989; revised January 8, 1990)

Abstract. On the basis of Akaike’s Bayesian information criterion (ABIC), a new method of estimating temporal and spacial variations in the magnitudefrequency relation (b value) is developed. The space-time volume studied is divided into a number of segments having equal volume, for which b values are estimated. The smoothness of the estimated b value is guaranteed by the introduction of a prior distribution. The parameters of the prior distribution are chosen in such a way as to minimize the ABIC. This method is employed to study the temporal and spatial variations of b values for microearthquake activity in the Kanto, Tokai and Tottori areas, where seven earthquakes having magnitudes of M6.0 and larger have recently taken place. States of temporal variations of b values are classified into three groups; increase, decrease and nochange. The space-time volume of decrease accounts for approximately 10% of the total volume. For a period before the occurrence of earthquakes, the decrease appears more frequently than might be expected. It is concluded that the decrease in the b value is a promising candidate to act as a precursory phenomena.

Key words and phrases: ABIC, b value, earthquake prediction, magnitudefrequency, microearthquakes, space time.