The accuracy and applicability of geometrical spreading and quality factor functions are investigated for the New Madrid seismic zone (NMSZ) using recorded small and moderate earthquakes. These functions represent the path effect in frequency domain.

The database used in this study consists of 500 broadband seismograms from 63 events of magnitude Mw 2.5 to 5.2, recorded by the Center for Earthquake Research and Information (CERI) at the University of Memphis. The hypocentral distances range from 10 to 400 km. All the broadband stations are located within the Mississippi embayment with different site conditions. The vertical components of the records are processed and used to define the path effect term in frequency range of 0.2 to 30 Hz. A hinged-trilinear geometrical spreading and frequency-dependent quality factor functions are used to describe the path term. The regression analysis using a genetic algorithm (GA) indicates that at distances less than 70 km the spectral amplitudes decay as R-1; between 70 and 140 km spectral amplitudes increase with distance and the geometric spreading is defined as R+0.25; beyond 140 km, the attenuation is described by R-0.5. The quality factor function is expressed as Q=614f0.32 for frequencies greater than 1 Hz after the regression analysis. For the broader range of frequency used in this study (0.2 to 30 Hz), the Q function is described by a third-degree polynomial described as logQ(f)=2.898-0.464logf+1.238(logf)2-0.540(logf)3. The results of this study are compared with those of Atkinson (2004) and Samiezade-Yazd et al. (1997). The path term obtained in this study can be used in the stochastic method to predict ground motions in the NMSZ and eastern North America (ENA).

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