An analytical point‐source‐based approach is presented to convert the Joyner–Boore () distance to various source‐to‐site distance metrics for a given tectonic region. The analytical‐based approach is combined with the effects of the region‐specific propagation path to define a new effective distance‐conversion equation for use in ground‐motion simulations and the existing stochastic‐based ground‐motion prediction equations (GMPEs), in which the effect of extended‐fault rupture on the ground motions is ignored. The proposed region‐specific distance‐conversion approach may also be used to capture the effect of extended‐fault sources on ground‐motion amplitudes in the probabilistic seismic hazard analysis (PSHA) studies in which earthquake occurrences are modeled as point‐source models. In this approach, virtual sites are defined on a bathtub‐shaped surface around an extended‐fault source on which all sites have identical distances. The source‐to‐site distances are analytically derived using the law of sines and cosines. The distance‐conversion process is then combined with region‐specific geometrical spreading and attenuation functions to improve and adjust the point‐source distance metrics into new effective epicentral distance or hypocentral distance metrics, and to mimic the effect of extended‐fault sources at close distances.
A general effective point‐source‐based distance‐conversion equation is developed in this study, which can be employed for any arbitrary input parameters and functions, such as the relations between the fault dimensions and magnitude, location of the fault with respect to virtual sites, probability distribution of focal depths, and geometrical spreading and anelastic attenuation functions corresponding to the region under study. As an application for the hazard analysis, a simple PSHA study is performed within a circular areal source zone using a published ‐based GMPE and the source‐to‐site distance‐conversion equations developed in this study to demonstrate the effect of using inconsistent source‐to‐site distance metrics on the seismic hazard curves at a given site.