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[SSS04-P02] Physical equations for calculating fault-to-site distances used in NGA GMPEs based on earthquake source geometry
Keywords:NGA GMPEs, source-to-site distances, RJB
In this paper, we are interested in fault-to-site distances parameter. Scherbaum et al. (2004) (termed “SSC04”) ever developed empirical expressions for converting source-to-site distance measures using simulated source geometries. The conversion equations are in the form of polynomial functions of M, RJB, and style of faulting. Kaklamanos et al. (2011) (termed “KBB11”) derived physical equations relating the three distance measures (RJB, RRUP, and RX) found in the NGA 2008 models using various geometric principles. KBB11 used the Joyner-Boore distance (RJB) as the primary distance measure to compute other distances (RRUP, RX) by characterizing the earthquake source by the geometric parameters down-dip rupture width (W), depth-to-top of rupture (ZTOR), fault dip (), and source-to-site azimuth (alpha). When RX is also needed (as in the AS08 and CY08 models), KBB11 method is advantageous, because RX cannot be estimated using the SSC04 relationships (because RX had not yet been introduced as a distance measure in 2004). One other potential issue is that the SSC04 equations are technically only applicable for RJB<100 km, whereas KBB2011 equations are physically derived and are applicable for any distance range at which the flat-earth assumption is valid (typically, several hundred kilometers).
KBB11 used the Joyner-Boore distance (RJB) as the primary distance measure to compute other distances (RRUP, RX). But in one situation RJB is equal to zero, which means the site is located directly above the ruptured area; either RX or RRUP must be specified in order to calculate the third distance parameter using KBB11. In some other situations, when the fault trace and site location is known, we need to simulate the ground motion caused by different segment rupture of the whole entire fault. In these cases, the RX and RXY are easily measured by GIS tools but the RJB is dependent on the down-dip rupture width (W). In this paper we introduce a new distance measure RXY (the closest distance from top of rupture) which is used to estimate source-to-site azimuth alpha (sin(alpha)= RX/ RXY) and RY (RY= RXY·cos()). Based on KBB11 we derived distance equations using the RX and RXY to compute RJB, RRUP, RX, and RY0.