Source-to-Site Distance Computation for Virtual Fault Ruptures in PSHA

Abstract The modeling of seismicity not identifiable with specific faults has been a problematic issue for probabilistic seismic hazard analysis (PSHA) calculations. Modern ground-motion models have recognized that distances to a fault plane (either in 3D or surface projection of the plane) are a more accurate and seismologically consistent distance metric to a site than an epicenter or hypocenter. Where the orientation and depth distributions of such seismicity are not known, point-source corrections have been derived historically, through empirical observations or rupture simulations, to account for the finite rupture characteristics. However, as seismic source models have become more explicitly defined in terms of rupture orientations and faulting type (e.g., strike slip versus normal versus thrust), the need to model virtual fault ruptures (VFRs) explicitly and distribute them within an areal zone, or as part of a gridded seismicity treatment, have become common. The first part of this article reveals the problematical nature of developing point-source corrections in a source model where strikes, dips, and dip direction are specified. The second part presents the formulas needed for calculating distances Rrup (site to rupture surface) and RJB (site to surface projection of the rupture plane) to a site from a rectangular fault plane of any orientation within a seismogenic crustal thickness. Additional distance metrics required by other ground-motion prediction equations (such as current ones for subduction zones) can be derived from the virtual fault geometric parameters. Finally, hazard curves showing differences between those using possible point-source corrections and those using VFRs are presented.