Preliminary Model for Scaling of Fourier Spectra of Strong Ground Motion Recorded on Kamchatka

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.