Effects of Varying Incident Wave Inclination and Azimuthal Angles on Multi-Dimensional Ground Response Analyses at the Delaney Park Downhole Array Site

Abstract

Even when large-scale, site-specific three-dimensional (3D) subsurface models are used to represent spatial variability, multi-dimensional ground response analyses (GRAs) at downhole array sites continue to exhibit amplitude discrepancies between simulated theoretical transfer functions (TTFs) and recorded empirical transfer functions (ETFs), with ETFs at the Delaney Park Downhole Array (DPDA) showing notably lower amplitudes at the fundamental frequency (f0). This discrepancy suggests greater apparent attenuation from wave scattering and destructive interference than is currently captured in multi-dimensional GRAs. However, most prior studies assume vertically propagating shear-wave input, neglecting inclined and azimuthally varying wavefields. This study evaluates the effects of inclination and azimuth in 2D and 3D GRAs at DPDA to assess whether non-vertical wave incidence improves agreement with observed ETFs. Two approaches for modeling inclined waves, the Input Lag Method (ILM) and the Inclined Domain Method (IDM), are compared, with ILM found to be more effective and computationally efficient for large-scale models. A parametric study using ILM shows that inclination angles up to 15{\deg} produce only minor reductions in TTF amplitudes near f0, with limited improvement in ETF agreement. Larger inclination angles reduce amplitudes but introduce systematic shifts in f0 to higher frequencies that are not observed in the ETFs. Azimuthal variation in 3D GRAs has a relatively minor effect, primarily influencing trough amplitudes while leaving f0 and higher-mode peaks largely unchanged.