Investigation of Geometrical Spreading and Quality Factor Functions in the New Madrid Seismic Zone

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 eventsofmagnitudeMw 2.5to5.2,recordedbytheCenterforEarthquakeResearchand 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 areprocessedandusedtodefinethepatheffectterminfrequencyrangeof0.2to30Hz. 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)indicatesthatatdistanceslessthan70kmthespectralamplitudesdecay 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 � 614f 0:32 for frequencies greater than 1 Hz after the regression analysis. For the broader range offrequency used in this study (0.2 to 30 Hz), the Q function is described by a third-degree polynomial described as logQf �� 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 etal.(1997).Thepathtermobtainedinthisstudycanbeusedinthestochasticmethodto predict ground motions in the NMSZ and eastern North America (ENA).