To estimate for the first time the typical relation between peak acceleration A max , moment magnitude M W 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 M W =4.5 -7.8, at R =30-250 km. A max 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 A max value in the further analysis. With the scarce data available, there were no chances to determine reliably the whole A max (M W , 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 f 0.8 ; (3) finite-source correction for a disc-shaped incoherent source, its size depending on M W ; (4) accelerogram duration: including source-dependent and distance-dependent terms; (5) A max 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 A max (M W , R) values were reduced to M W =8, R =100 km using the theoretical trends as reference. The median of the reduced values, A max (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).
We recover the gross space–time characteristics of high-frequency (HF) radiator of the great Sumatra-Andaman islands earthquake of 2004 December 26 (M w = 9.1–9.3) using the time histories of the power of radiated HF P waves. To determine these time histories we process teleseismic P waves at 36 BB stations, using, in sequence: (1) bandpass filtering (four bands: 0.4–1.2, 1.2–2, 2–3 and 3–4 Hz); (2) squaring wave amplitudes, making ‘power signals’ for each band and (3) stripping the propagation-related distortion (P coda, etc.) from the power signal and thus recovering source time function for HF power. In step (3) we employ an inverse filter constructed from an empirical Green’s function, which is estimated as the power signal from an aftershock. For each ray we thus obtain signals with relatively well-defined end and no coda. From these signals we extract: total duration (joint estimate for all four bands) and temporal centroid of signal power for each band. Through linear inversion, the set of duration values for a set of rays delivers estimates of the rupture stopping point and stopping time. Similarly, the set of temporal centroids can be inverted to obtain the position of the space– time centroid of HF energy radiator. The quality of inversion for centroid is acceptable for lower-frequency bands but deteriorates for higher-frequency bands where only a fraction of stations provide useful data. For the source length and duration the following joint estimates were obtained: 1241 ± 224 km, 550 ± 10 s. The estimated stopping point position corresponds to the northern extremity of the aftershock zone. Spatial HF radiation centroids are located at distances 350–700 km from the epicentre, in a systematic way: the higher is the frequency, the farther is the centroid from the epicentre. Average rupture propagation velocity is estimated as 2.25 km s–1
Abstract-To determine the average relationship among the Fourier spectrum of horizontal acceleration FSA(f ), moment magnitude M W and hypocentral distance R for Kamchatka earthquakes, we analyzed 44 analog strong-motion records recorded here in 1969 -1993. The records of acceleration and velocity meters were obtained at 11 rock to medium-ground sites from 36 earthquakes with M W = 4.5-7.8, at distances R =30-250 km and depths 0 -80 km. Amplitude spectra FSA(f ) were calculated from digitized, baseline corrected records of 81 horizontal components, and then divided by instrumental transfer function. After smoothing the values were picked at a set of fixed frequencies. With the scarce amount of data at hand it was impossible to determine reliably the entire FSA(M W , R f ) average trend surface. Hence we first performed distance equalization with distance corrections calculated on a theoretical basis, and thus reduced the observed data to the reference distance of R 0 =100 km. The model of distance attenuation applied included point source decay terms (1/R plus attenuation specified by Q(f )= 250 f 0.8 ) and finite source correction (using the formula for a disc-shaped incoherent source, its size depending on M W ); its general applicability was later checked by analysis of residuals. After reduction we determined the FSA(M W , R 0 f ) vs. M W trends. To do this we employed a multiple regression procedure with ground type and station dummy variables. The M W dependence was assumed to consist of two linear branches intersecting at M W =6.5. The result of multiple regression represents the first systematic description of spectral properties of destructive ground motion for Kamchatka earthquakes. The empirical FSA vs. M W trend flattens as frequency increases. This flattening persists even between 3 and 16 Hz, suggesting the decrease of source-related f max with increasing magnitude.
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