Measures of strong ground motion derived from a stochastic source model

Abstract

Taking the seismic spectrum of a ‘statistical’ source model¹ as the point of departure, we arrive at simple expressions for strong motion measures of engineering significance. Introducing inelastic attenuation through a frequency dependent Q-factor, the following relation is obtained for root-mean-square acceleration $\text{a}$: $\text{a}\text{̄}\text{≅}\text{M}{}_{\mathrm{o}}\text{aπρβ}{}^3\text{exp}\text{(−qR)}\text{R}\text{k}{}^{\mathrm{-1}}{}_{\mathrm{T}}\text{T}{}_{\mathrm{r}}\text{1}\text{2}\text{k}{}^3{}_{\mathrm{T}}\text{[D}{}_{\mathrm{a}}\text{(θ)]}\text{1}\text{2}$ where M₀ is seismic moment, β is shear-wave velocity, R is distance, k_T⁻¹ is the correlation time of the model, q is an attenuation parameter, T_r is the rupture duration, and D_a(Δ) is a directivity factor. The basic parameter k_T⁻¹ is estimated by regressing the Arias intensities of representative accelerograms from Italy and Yugoslavia through the analytical expression derived herein. The regression analysis shows that (a) k_T⁻¹ scales as M₀^0.26; (b) the ratio k_T⁻¹/T_r is virtually independent of M₀ so that $\text{a}\text{α M}{}_0{}^{0.23}$, and (c) the fit is improved when directivity is accounted for.

We also find that estimated values of k_T⁻¹ are grossly consistent with dimensions of source inhomogeneities inferred from other models.

Predicted and observed values of $\text{a}$ agree within a factor of 1.5 about 85% of the time for a total sample of 49 data which also includes a group of San Fernando earthquake recordings and an important accelerogram from the 1978 Miyagi-oki event.