The First Version of the Amax?(MW?, R) Relationship for Kamchatka

To estimate for the first time the typical relation between peak acceleration Amax, moment magnitude MW and hypocentral distance R for Kamchatka, 101 analog strong motion records for 1969–1993 were employed as the initial data set. Records of acceleration and velocity meters were obtained at 15 rock to medium-ground Kamchatkan sites from 33 earthquakes with MW 4.5–7.8, at R 30–250 km. Amax values were determined from ‘‘true’’ acceleration time histories calculated by spectral deconvolution of digitized records. The maximum value over the two horizontal components was used as the Amax value in the further analysis. With the scarce data available, there were no chances to determine reliably the whole Amax(MW, R) average surface; thus the shape of this trend surface was determined on a theoretical basis and only the level was fitted to the data. The theoretical model employed included: (1) source spectrum: according to the Brune’s spectral model; (2) point-source attenuation: as 1:R plus loss specified by Q(f) 250 f0.8; (3) finite-source correction for a disc-shaped incoherent source, its size depending on MW; (4) accelerogram duration: including source-dependent and distance-dependent terms; (5) Amax value: based on random process representation. Distance trends calculated with this model agree with the empirical ones of FUKUSHIMA and TANAKA (1990). To calculate the absolute level for these trends, observed Amax(MW, R) values were reduced to MW 8, R 100 km using the theoretical trends as reference. The median of the reduced values, Amax(8, 100), equal to 188 gal. was taken as the absolute reference level for the relation we sought. Note that in the process of data analysis we were forced to entirely reject relatively abundant data of two particular stations because of their prominent local amplification ( 5.5) or deamplification ( 0.45).