Broadband Nonparametric Ground-Motion Evaluation of Horizontal Shear-Wave Fourier Spectra

The nonparametric method was employed to obtain detailed broadband attenuation characteristics of horizontal Fourier spectra based on the large spectral data set for small earthquakes in Korea. Before applying to the real data set, the nonparametric method was numerically tested by using artificial data set and the bias estimated. The inverted path terms show three linear regions roughly divided by 65km and 117km from the source. Also, the use of parametrically inverted Q functions was validated over the frequency band between 3-30Hz and distance range beyond 200km while complex behavior within 100km from the source was revealed which can not be properly fitted by combination of Q functional model and geometrical spreading models. Also, the near-source path terms show attenuation steeper than R-1.3 for broad range of frequencies. Finally, mixed wave phases were found in the inverted path terms for low frequencies at distances beyond 200km. Introduction Until recently, in Korea, several studies on the attenuation of shear-wave has been conducted mostly by parametric methods. In the parametric methods, the attenuation characteristic is modeled by physically based functional forms and the parameters for the models were obtained by fitting the functional to the observed data. For example, in the stochastic ground-motion model ([1]), one of the parametric methods, combination of Q model (Q0 f η ) and geometrical spreading function given by a piecewise continuous series of straight lines is assumed for the path effect. Previously, 348f0.54 and bilinear geometrical spreading model (R-1, R-0.5) with 50km crossover distance have been inverted as the parameters of the path function of the stochastic groundmotion model ([2]). Generally speaking, parametric method is preferred where there are small number of available recorded data for the analysis and has the advantage of providing physical insights, but the model itself should be justified before applying to a local region even though the model is validated elsewhere. Contrarily, nonparameteric method is capable of separating the path effect from the source and site effects based only on the observed data without assuming any functional forms and show the undistorted nature of path effect. Furthermore, it can also provide additional information that cannot be identified by the parametric method and can be used as a reference to validate the results of the parametric methods. However, it needs relatively large amount of good quality data for the analysis in the regional distances. In this paper, nonparametric evaluation of ground motion attenuation is conducted over the southern Korean Peninsula using a large amount of earthquake database accumulated after the modern earthquake observation stations operated mainly since 1999 ([3]). Also since we already performed parametric study of ground motion, systematic comparison between the results of two methods will be discussed. Analysis method The logarithm of the observed Fourier spectra (Y = log(Amp(f))) at a frequency f is the linear summation of the log of excitation term (E(f)), propagation term (D(R,f)), and site term (Site(f)) and the ground motion regression model can be written for a distance R as Y = Log (Amp(f)) = E(f) + Site(f) + D(R,f) (1) The nonparametric method is to separate the path term by removing the excitation and site terms from the observed Fourier spectra according to the simple formula (1). In equation (1), D (R,f) can be parameterized as a piecewise linear function with numerous nodes for a central frequency (fc), and a linear interpolation is taken between adjacent nodes.